Development and Validation of Electronic Stability Control System Algorithm Based on Tire Force Observation

applied sciences

Article Development and Validation of Electronic Stability Control System Algorithm Based on Tire Force Observation

Dang Lu 1,*, Yao Ma 1, Hengfeng Yin 1, Zhihui Deng 1 and Jiande Qi 2

1 State Key Laboratory of Automotive Simulation and Control, Jilin University, Changchun 130025, China; [email protected] (Y.M.); [email protected] (H.Y.); [email protected] (Z.D.) 2 SAIC-GM-Wuling Automobile, Liuzhou 545007, China; [email protected] * Correspondence: [email protected]

Received: 10 October 2020; Accepted: 29 November 2020; Published: 7 December 2020

Abstract: In view of the higher and higher assembly rate of the electronic stability control system (ESC in short), the control accuracy still needs to be improved. In order to make up for the insufficient accuracy of the tire model in the nonlinear area of the tire, in this paper, an algorithm for the electronic stability control system based on the control of tire force feedforward used in conjunction with tire force sensors is proposed. The algorithm takes into consideration the lateral stability of the tire under extreme conditions affected by the braking force. We use linear optimal control to determine the optimal yaw moment, and obtain the brake wheel cylinder pressure through an algorithm combining feedforward compensation based on measured tire force and feedback correction. The controller structure is divided into two layers, the upper layer is controlled by a linear quadratic regulator (LQR in short) and the lower layer is controlled by PID (Proportional-integral-derivative) and feedforward. After that, verification of the controller’s algorithms using software cosimulation and hardware-in-the-loop (HIL in short) testing in the double lane change (DLC in short) and sine with dwell (SWD in short) conditions. From the test results it can be concluded that the controller based on tire force observation has partially control advantages.

Keywords: observation of tire force; electronic stability control system; control algorithm

1. Introduction Electronic stability control (ESC) is an active safety system that controls the braking of the wheels to adjust the body’s posture under extreme conditions. In recent years, the technology of ESC has become more and more mature, and the assembly rate on real vehicles has also become higher. Many researchers have optimized the ESC control strategy through modern control theory and performed simulation veriﬁcation, and achieved obvious control eﬀects [1]. Daegun Hong et al. of Hanyang University used a braking and wheel slip monitor to propose a target slip rate allocation algorithm for the vehicle stability control system [2]. Sungyeon Ko et al. of Sungkyunwan University proposed a method for a vehicle stability control algorithm for an in-wheel independent drive vehicle using vehicle speed and yaw rate during turning [3]. Li Zhai et al. proposed a new control strategy to improve vehicle stability by using the method of motor drive and regenerative braking torque distribution [4]. Ming Yue et al. introduced a supervisory mechanism for yaw moment control and slip rate adjustment, and proposed a novel control strategy to improve the stability performance of four-wheel independent drive electric vehicles during critical cornering [5]. However, none of the above studies considered that the ESC control strategy is limited by the tire adhesion limit. If the applied braking torque is too large, the lateral stability of the vehicle will be reduced.

Appl. Sci. 2020, 10, 8741; doi:10.3390/app10238741 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, 8741 2 of 20

The tires are the only component that connects the vehicle to the road. The force of the tires determines the body’s movement posture. Only by making full use of the friction conditions between the tires and the ground can ESC control be more precise [6]. Many scholars have also considered the influence of tire force in the control of the chassis electronic control system. Yue Xiaowei et al. of Tsinghua University used the magic tire formula to develop a vehicle stability control system (VSC in short) based on PID control and differential braking control [7]. Linsheng Jin et al. used the GIM tire model to propose a fuzzy logic controller based on the automotive electronic stability controller system to improve the stability of the vehicle at high speed on low-attached roads [8]. Matteo Corno et al. used the Burkhartd tire model to solve the problem of active lateral dynamics control during braking of four-wheeled vehicles [9]. However, the accuracy of using the tire model to estimate the tire force is limited. Taking the influence of the tire force into consideration, obtaining accurate tire force will help improving the control accuracy of the vehicle chassis electronic control system. Based on the research results that have been put forward by researchers in the industry [1–9], an ESC control algorithm with the tire force sensor to measure the three-component force of the tire is proposed. Based on the consideration of the longitudinal and lateral adhesion limits of the tires, the optimal yaw moment is determined by linear optimal control, and the brake wheel cylinder pressure is obtained by the algorithm combining feedforward compensation and feedback correction. In this paper, Section2 introduces the composition and working principle of the tire three-component force sensor. Section3 introduces the control strategy of ESC based on tire force observation. A software cosimulation of the proposed control strategy was carried out in Section4, using CarSim and Simulink to compare the ESC control algorithm with PID control under double lane change (DLC) and sine with dwell (SWD) conditions. Section5 uses NI Veristand to perform a hardware-in-the-loop (HIL) comparison test between ESC algorithms using tire force observation and PID control. Section6 summarizes the full text.

2. Three-Component Force Sensor for Tires The tire three-component force sensor in spoke form is one of the most common [10]. As shown in Figure1, the tire force sensor is connected to the rim and rotates with the wheel, and is installed betweenAppl. Sci. 2020 the, 10 rim, x andFOR PEER the hub. REVIEW The advantage of the sensor is that the force transmission path of the3 of tire 21 force passes completely through the sensor, and it can detect the tire force accurately. A common spoke-typemechanical three-componentbehavior of tires, improvements force sensor consists are ma ofde thebased strain on the gauge, three-component elastomer, encoder, force sensor adapter, to slipdesign ring smart-tire and conductor six-component pole etc. force products.

Figure 1. Spoke-type three-component force sensor.

The force measurement principle of the spoke-type three-component force sensor is based on the resistance strain eﬀect, and the resistance value changes with the deformation of the metal conductor under the action of external force. The internal components of the sensor are all installed on the elastic body. The strain gauges for electronic component on the elastomer are attached to the four strain

Figure 2. Installation location of the spoke-type three-component force sensor.

3. Design of Control Strategy 3.1. System Structure Different from the traditional ESC control strategy, this paper designs a controller based on optimal linear control, and proposes an ESC control strategy based on tire force observation control, in order to be able to use with tire force sensor to improve the control accuracy of the electronic stability control system. First, in the nominal value calculation part, the influence of the maximum lateral force of the tire under extreme conditions by the longitudinal force is considered, and the expected value of the control index is determined according to the road surface information, the vehicle state information, and the measured tire force. After that, based on the nominal and actual values of the control indicators that determine the vehicle’s instability state, if the vehicle is determined to be unstable, the controller will be triggered to work. Next, after the vehicle is determined to be unstable, the upper controller determines the tires to be braked according to the control command. Vehicle state controller outputs target longitudinal force based on desired state. What’s more, the lower controller determines the braking pressure applied to the target wheel based on the target longitudinal force. At last, spoke-type three-component force sensor detects the force of the controlled tire in real time and serves as input to the controller, making the system a closed loop. The controller structure is shown in Figure 3. Appl. Sci. 2020, 10, x FOR PEER REVIEW 3 of 21

mechanical behavior of tires, improvements are made based on the three-component force sensor to Appl.design Sci. smart-tire2020, 10, 8741 six-component force products. 3 of 20 gauge beams between the inner and outer rings of the elastomer, and each beam has eight strain gauges. The wiring form is designed according to the principle of Wheatstone bridge, three sets of output bridges are designed according to different combinations of strain gauges, and then the voltage output in three directions is detected respectively. The output voltages of the three bridges are all weak voltages, and the force values in the three directions of the wheels must be obtained through voltage amplification and the settlement of the coefficient matrix. The sensor of the three-component force rotates with the wheel and the angle changes all the time. Therefore, the encoder needs to be adapted to calculate the angle. When installing the sensor on a wheel, it is also necessary to configure the adapter, slip ring, conductor pole and other accessories. The installation position of the tire three-component force sensor is shown in Figure2. The strain gauges and the three bridge channels are arranged inside the elastomer, which is shown in the red part in the Figure2. The elastomer, strain gauges, and the three bridge channels make up theFigure three-component 1. Spoke-type three-component force sensor of theforce tire. sensor.

Figure 2. Installation location of the spoke- spoke-typetype three-component force sensor.sensor. The tire three-component force sensor is the first generation of smart wheels, which can only 3. Design of Control Strategy detect the force in three directions. In order to have a more comprehensive detection of the mechanical behavior3.1. System of Structure tires, improvements are made based on the three-component force sensor to design smart-tireDifferent six-component from the traditional force products. ESC control strategy, this paper designs a controller based on optimal linear control, and proposes an ESC control strategy based on tire force observation control, 3. Design of Control Strategy in order to be able to use with tire force sensor to improve the control accuracy of the electronic 3.1.stability System control Structure system. First, in the nominal value calculation part, the influence of the maximum lateral force of the tire under extreme conditions by the longitudinal force is considered, and the Different from the traditional ESC control strategy, this paper designs a controller based on expected value of the control index is determined according to the road surface information, the optimal linear control, and proposes an ESC control strategy based on tire force observation control, vehicle state information, and the measured tire force. After that, based on the nominal and actual in order to be able to use with tire force sensor to improve the control accuracy of the electronic stability values of the control indicators that determine the vehicle’s instability state, if the vehicle is control system. First, in the nominal value calculation part, the influence of the maximum lateral determined to be unstable, the controller will be triggered to work. Next, after the vehicle is force of the tire under extreme conditions by the longitudinal force is considered, and the expected determined to be unstable, the upper controller determines the tires to be braked according to the value of the control index is determined according to the road surface information, the vehicle state control command. Vehicle state controller outputs target longitudinal force based on desired state. information, and the measured tire force. After that, based on the nominal and actual values of What’s more, the lower controller determines the braking pressure applied to the target wheel based the control indicators that determine the vehicle’s instability state, if the vehicle is determined to be on the target longitudinal force. At last, spoke-type three-component force sensor detects the force of unstable, the controller will be triggered to work. Next, after the vehicle is determined to be unstable, the controlled tire in real time and serves as input to the controller, making the system a closed loop. the upper controller determines the tires to be braked according to the control command. Vehicle state The controller structure is shown in Figure 3. controller outputs target longitudinal force based on desired state. What’s more, the lower controller determines the braking pressure applied to the target wheel based on the target longitudinal force. At last, spoke-type three-component force sensor detects the force of the controlled tire in real time and serves as input to the controller, making the system a closed loop. The controller structure is shown in Figure3. Appl. Sci. 2020, 10, 8741 4 of 20 Appl. Sci. 2020, 10, x FOR PEER REVIEW 4 of 21

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FigureFigure 3.3. Controller system structure.

3.2.3.2. Calculation of Nominal Value

The linear two-degree-of-freedom model is used as the reference model for calculating the nominal The linear two-degree-of-freedomFigure 3.model Controller is usedsystem asstructure. the reference model for calculating the valuenominal [11 ,value12]. As [11,12]. shown As in shown Figure in4 .Fi Thegure di 4.ﬀ Theerential differential equation equation of its motion of its motion is shown is shown in Equation in Equation (1). 3.2. Calculation of Nominal Value (1).  1 .  C + Cr β + aC bCr C δ = m v + uω  f u f − − f The linear two-degree-of-freedom model1 2 is used2 as the reference .model for calculating the (1)  aC bCr β + a C + b Cr ω aC δ = Izω nominal value [11,12]. As shownf −in Figure 4. uThe differentialf equation− f of its motion is shown in Equation (1).

Figure 4. The linear two-degree-of-freedom model.

FigureFigure 4. 4.The The linearlinear two-degree-of-freedom model. model. 1 𝐶 +𝐶 𝛽 + 𝑎𝐶 −𝑏𝐶 −𝐶 𝛿=𝑚(𝑣 +𝑢𝜔) 𝑢 Including, C f is the cornering stiﬀness1 for the front axis; Cr is the cornering stiﬀness for the rear(1) 𝐶 +𝐶 𝛽 + 𝑎𝐶1 −𝑏𝐶 −𝐶 𝛿=𝑚(𝑣 +𝑢𝜔) axis; β is side slip angle; u is𝑎𝐶 longitudinal −𝑏𝐶 𝛽 speed;𝑢 + 𝑎 a𝐶is+𝑏 the distance𝐶𝜔 − from𝑎𝐶 𝛿=𝐼 the𝜔 center of mass to the front 𝑢 (1) axis; b is the distance from the center of mass1 to the rear axis; δ is the steering angle of front wheels; m is 𝑎𝐶 −𝑏𝐶𝛽 + 𝑎 𝐶 +𝑏 𝐶𝜔 − 𝑎𝐶𝛿=𝐼𝜔 the massIncluding, of the vehicle;𝐶 is theω corneringis the yaw stiffness rate; Iz 𝑢isfor the the moment front axis; of inertia𝐶 is the of cornering the vehicle stiffness around for the theZ-axis; rear . ωaxis;is the 𝛽 yawIncluding,is side acceleration. slip 𝐶 angle; is the cornering𝑢 is longitudinal stiffness forspeed; the front 𝑎 is axis; the 𝐶distance is the cornering from the stiffness center forof massthe rear to the frontaxis; axis; 𝛽 is𝑏 side is the slip distance angle; 𝑢from is longitudinal the center speed;of mass 𝑎 tois the distancerear axis; from 𝛿 is the the center steering of mass angle to ofthe front front axis; 𝑏 is the distance from the center of mass to the rear axis; 𝛿 is the steering angle of front Appl. Sci. 2020, 10, 8741 5 of 20

. . Assuming the vehicle is in a steady state, v and ω are both equal to zero, meaning ω = Gω δ, d · β = G δ. In simultaneous Equation (1), there are transfer functions characterizing the steady-state d β· yaw rate and the steady-state side slip angle as shown in Equations (2) and (3).

Appl. Sci. 2020, 10, x FOR PEER REVIEW u 5 of 21 Gω = (2) L(1 + ku2) wheels; 𝑚 is the mass of the vehicle; 𝜔 is the yaw rate; 𝐼 is the moment of inertia of the vehicle ! around the Z-axis; 𝜔 is the yaw acceleration. u2 b ma Gβ = 𝑣 𝜔 + 𝜔 =𝐺 ∙ (3) Assuming the vehicle is in a steady Lstate,(1 + ku and2) · u2 areC bothrL equal to zero, meaning 𝛿, 𝛽 =𝐺 ∙𝛿. In simultaneous Equation (1), there are transfer functions characterizing the steady- where G is the transfer function of the yaw rate; G is the transfer function of the side slip angle; L is stateω yaw rate and the steady-state side slip angle asβ shown in Equations (2) and (3). k the wheelbase; is the stability factor; ωd is the expected𝑢 value of the yaw rate; βd is the expected value 𝐺 = of the side slip angle. 𝐿(1 + 𝑘𝑢) (2) If the value of the state maximum lateral force is limited according to the pavement friction 𝑢 𝑏 𝑚𝑎 condition [13,14], the maximum lateral𝐺 = force can be∙( defined+ ) as Equation (4) and the centripetal(3) 𝐿(1+𝑘𝑢) 𝑢 𝐶 𝐿 acceleration can be defined as Equation (5). Without regard to the effect of longitudinal forces on where 𝐺 is the transfer function of the yaw rate; 𝐺 is the transfer function of the side slip angle; 𝐿 the tires, according to the Equations (4) and (5), the expected yaw rate ωd can be limited as Equation (6). is the wheelbase; 𝑘 is the stability factor; 𝜔 is the expected value of the yaw rate; 𝛽 is the expected Combining equations ω = Gω δ and β = G δ can obtain Equation (7), and the limits of the desired d · d β· sidevalue slip angle of the canside be slip obtained angle. and defined as Equation (8). If the value of the state maximum lateral force is limited according to the pavement friction condition [13,14], the maximum lateral force can be defined as Equation (4) and the centripetal m ay mµg (4) acceleration can be defined as Equation (5). Without≤ regard to the effect of longitudinal forces on the . tires, according to the Equations (4) and (5), the expected yaw rate 𝜔 can be limited as Equation (6). ay = v + uω (5) Combining equations 𝜔 =𝐺 ∙𝛿 and 𝛽 =𝐺 ∙𝛿 can obtain Equation (7), and the limits of the µg desired side slip angle can be obtained and definedω as Equation (8). (6) | d| ≤ u 𝑚𝑎≤𝑚𝜇𝑔 (4) Gβ = β𝑎d =𝑣 +𝑢𝜔ωd (5) (7) Gω 𝜇𝑔 ! |𝜔| ≤b ma (6) β µg +𝑢 (8) d 2 ≤ u k2L 𝐺 𝛽 = 𝜔 (7) where ay is the lateral acceleration of the vehicle; µ 𝐺is the coefficient of adhesion between tire and road surface; g is the acceleration due to gravity; v is the lateral𝑏 𝑚𝑎 speed of vehicle. |𝛽| ≤𝜇𝑔( + ) (8) The controller in this paper considers the effect𝑢 of longitudinal𝑘𝐿 force on the lateral force of the tire, and the longitudinal and tangential forces of the tire at the limit of adhesion form a friction circle with where 𝑎 is the lateral acceleration of the vehicle; 𝜇 is the coefficient of adhesion between tire and a radiusroad surface; less than 𝑔 µ is[ 15the], acceleration as shown indue Figure to gravity;5. With 𝑣 isthe the introduction lateral speed ofof tirevehicle. force feedback, the tire force vectorThe andcontroller its longitudinal in this paper and considers lateral the components effect of longitudinal are known, force limiting on the the lateral maximum force of value the of the statetire, and according the longitudinal to the friction and tangential circle. Expressed forces of the in tire Equation at the limit (9). of adhesion form a friction circle with a radius less than 𝜇 [15], as shown in Figure 5. With the! introduction of tire force feedback, the X2 q X4 q tire force vector and its longitudinal and2 lateral2 components are known, limiting the2 maximum2 value Fymax = (Fziµi) F cosδ + Fxi sinδ + (Fziµi) F (9) of the state according to thei=1 friction circle.− Expressedxi· in Equation· (9).i= 3 − xi

FigureFigure 5. 5. FrictionFriction circle diagram. diagram. Appl. Sci. 2020, 10, 8741 6 of 20

In the Equation (9), Fymax is the maximum lateral force of vehicle; Fzi is the vertical force of tire; Fx is the longitudinal force of tire; in addition, i = 1, 2, 3, 4, They represent left front, right front, left rear and right rear wheels respectively.

Replacing Equation (4) m ay mµg with m ay Fymax obtains a constraint on the value of ≤ ≤ the maximum lateral force for the desired state based on real-time tire force observations.

3.3. Judgment of Vehicle Stability Under the extreme conditions, using formula (10) and formula (11) to determine whether the vehicle is unstable. Under extreme conditions, use Equations (10) and (11) to determine whether the vehicle is unstable. Equation (10) is the judgment condition for yaw rate, Equation (11) is the judgment condition for the side slip angle. When the vehicle state satisﬁes either one of (10), (11), it is in vehicle instability [16].

∆ω Cω (10) | | ≤ NO . B β + β µB (11) 1 ≤ 2 Among them, ∆ω is the diﬀerence between yaw rate and nominal yaw rate; ωNO is the nominal yaw rate. C, B1, B2 are stability coeﬃcients. According to experiences C = 0.165, B1 = 0.4, B2 = 0.12.

3.4. The Selection of Control Wheel Using the same side two-wheel control, adopting the positive and negative yaw rate deviation and the front wheel steering to determine whether to control the left wheel or the right wheel. Through comprehensive analysis, when the Equation (12) is satisﬁed, the left wheel is controlled to satisfy the Equation (13) when controlling the right wheel.

∆ω = ω ω < 0 (12) − NO ∆ω = ω ω > 0 (13) − NO To prevent the brake command from switching back and forth between the wheels on both sides, the following explains the logic when the left wheel is under braking control. When the left wheel is under brake control, ∆ω < 0, switching from left wheel braking control to right wheel braking control is subject to Equation (14) and Equation (15). The switching logic of the left and right sides wheel braking control is shown in Figure6. ∆ω > D (14)

∆ω/ ω > P (15) | NO| Among them, D and P are the threshold value set. D and P represent the absolute error and the relative error of the yaw rate respectively, the two together constitute the switching criterion for the control of left and right-side wheel. When the values of D and P are small, the control accuracy is high, and the overshoot of yaw rate is small, but the wheel control on both sides is switched frequently, and the yaw rate jitter is obvious. When the values of D and P are large, the control accuracy is low and the overshoot of yaw rate is large, but the wheel control on both sides is not switched frequently, and the yaw rate hardly shakes. In practical applications, the balance between control accuracy and jitter should be weighed and the switching threshold should be set reasonably. Appl. Sci. 2020, 10, 8741 7 of 20

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FigureFigure 6.6. TheThe switchingswitching logiclogic ofof thethe leftleft andand rightright sidessides wheelwheel brakingbraking control.control. As shown in Figure5 5,, the ordinate of the coordinate system is ω and the abscissa is ω . The red line is determined by the ordinate of the coordinate system is 𝜔 and the abscissa is 𝜔NO. The red line is determined by the ∆ ∆ω = = theformula formula ω=𝑃 , theP, theblue blue line lineis determined is determined by the by theformula formula |∆𝜔|∆=𝐷ω , andD, andthe theblue blue dotted dotted line || NO | | line distinguishes| | the area where the left and right wheels brake when there is no brake switching distinguishes the area where the left and right wheels brake when there is no brake switching logic. logic. Therefore, unilateral braking needs to be performed in areas where the red line and blue line are Therefore, unilateral braking needs to be performed in areas where the red line and blue line are unexpected, and the controller does not work in the inner area. Obviously, whether it is switching from unexpected, and the controller does not work in the inner area. Obviously, whether it is switching the left braking control to the right braking control or from the right braking control to the left braking from the left braking control to the right braking control or from the right braking control to the left control, it will pass through an area where the controller does not work. braking control, it will pass through an area where the controller does not work. 3.5. Upper Control Strategy 3.5. Upper Control Strategy The longitudinal force of the tire is directly changed by braking to control the stability of the vehicle. AccordingThe longitudinal to the left and force right of sidesthe tire control, is directly diﬀerent changed diﬀerential by braking equations to control are listed: the stability the resultant of the lateralvehicle. force According is shown to in the Equation left and (16), right and sides the total control, moment different of inertia differential in the vertical equations direction are listed: is shown the inresultant Equation lateral (17). force is shown in Equation (16), and the total moment of inertia in the vertical direction is shown in Equation (17). . X m v + um = Fy (16)

𝑚(𝑣 +𝑢𝑚) =𝐹 (16) . X Izω = Mz (17)

P 𝐼𝜔 =𝑀P (17) where, Fy is the resultant lateral force of vehicle; Mz is the total moment about the vertical direction. From the equation of equilibrium for yaw motion, as shown in Equation (18), left wheel control where, ∑ 𝐹 is the resultant lateral force of vehicle; ∑ 𝑀 is the total moment about the vertical candirection. be derived as shown in Equations (19) and (20). From the equation of equilibrium. h for yaw motion, as shown ini Equation (18), left wheel control Iz ω = F + F sinδ + F + F cosδ a can be derived as shown in Equations· (19)x f l andxh f r (20). y f l y f r · i + F F cosδ + F F sinδ d + (Fxrr F ) d (18) x f r − x f l y f l − y f r · − xrl · 𝐼 ∙𝜔 =𝐹 +𝐹𝑠𝑖𝑛𝛿+𝐹 +𝐹F F𝑐𝑜𝑠𝛿∙𝑎yrr d − yrl − · +𝐹 −𝐹 𝑐𝑜𝑠𝛿+𝐹 −𝐹 𝑠𝑖𝑛𝛿∙𝑑+(𝐹 −𝐹 ) ∙𝑑 P (18) −𝐹 −𝐹 ∙𝑑. Fy β = ω + (19) − mu ∑ 𝐹 𝛽 =−𝜔+ (19) . z Fxrld + Fx f l(cosδ d sinδ a) ω = 1 + 𝑚𝑢· − · (20) Iz Iz 𝑧 𝐹𝑑+𝐹(𝑐𝑜𝑠 𝛿 ∙ 𝑑 − 𝑠𝑖𝑛𝛿∙𝑎) Inside, Fx f l is the longitudinal𝜔 = force+ on the left front wheel; Fxrl is the longitudinal force(20) on 𝐼 𝐼 h i the left rear wheel; z1 is the measurable distractors moment; z1 = Fx f rsinδ + Fy f l + Fy f r cosδ a h i − · − Inside, 𝐹 is the longitudinal force on the left front wheel; 𝐹 is the longitudinal force on the Fx f rcosδ + Fy f l Fy f r sinδ d Fxrr d + Fyrl Fyrr b. left rear wheel; −𝑧 is the measurable− · distractors− ·moment; 𝑧 =−𝐹 𝑠𝑖𝑛 𝛿 +𝐹 +𝐹𝑐𝑜𝑠𝛿∙ Inside, Fxrl is the longitudinal force on the right front wheel; Fxrr is the longitudinal force on 𝑎−𝐹 𝑐𝑜𝑠 𝛿 +𝐹 −𝐹𝑠𝑖𝑛𝛿𝑑−𝐹 ∙𝑑+𝐹 −𝐹∙𝑏. the right rear wheel; Fy f l is the lateral force on the left front wheel; Fy f r is the lateral force on the right Inside, 𝐹 is the longitudinal force on the right front wheel; 𝐹 is the longitudinal force on front wheel; Fyrlis the lateral force on the left rear wheel; Fyrr is the lateral force on the right rear wheel; dtheis theright half rear of wheelbase.wheel; 𝐹 is the lateral force on the left front wheel; 𝐹 is the lateral force on the right front wheel; 𝐹 is the lateral force on the left rear wheel; 𝐹 is the lateral force on the right rear wheel; 𝑑 is the half of wheelbase. Right-hand wheel control is as shown in Equations (21) and (22): Appl. Sci. 2020, 10, 8741 8 of 20

Right-hand wheel control is as shown in Equations (21) and (22): P . Fy β = ω + (21) − mu

. z Fxrrd F (cosδ d + sinδ a) ω = 2 + − − xrl · · (22) Iz Iz h i Inside, is the measurable distractors moment, and z2 = Fx f lsinδ + Fy f l + Fy f r cosδ a + h i − · F F F sinδ d + F d + F Fyrr b. x f l − y f l − y f r · xrl· yrl − · To facilitate the design of the controller, the left- and right-side controls are written as a uniﬁed expression. The equation of state is shown in Equations (23) and (24) as follows.

. β = ω + s (23) − . ω = z + U (24) P Fy where s is the interference term of side slip angle, and s = mu ; z is the measurable interference of the yaw rate, and the expression is shown in Equation (25); U is the virtual control unit, shown in Equation (26). ( z 1 ; control o f le f t side z = Iz (25) z2 ; control o f right side Iz   Fxrld+Fx f l(cosδ d sinδ a)  · − · ; control o f le f t side U =  Iz (26)  Fxrrd Fx f r(cosδ d sinδ a)  − − · − · ; control o f right side  Iz The equation of state is formulated into the error form as shown in Equations (27) and (28).

. . . . . e = β β = β ( ω + s) = (ω ω) + ω + β s = e + s0 (27) 1 d − d − − − d − d d − − 2 . . . . e = ω ω = ω z U = U0 (28) 2 d − d − − . where e1 is the error of the side slip angle; e2 is the error of the yaw rate. Inside, s0 = ωd + βd s ; . − U = ω z U. 0 d − − Presented in matrix form as in formula (29). " . # " # " # e1 e1 1 . = A + BU0 + s0 (29) e2 e2 0 " # " # 0 1 0 Inside, A = − ; B = . 0 0 1 To determine the controllability of the system, Rank(B, AB) = 2, when the matrix satisﬁes the full rank. In this paper, the feedback gain matrix for closed-loop control is designed by the LQR control algorithm to deﬁne the performance index function as shown in Equation (30). Z 1 T T J = e Qe + U0 RU0 (30) 2 where Q is the error weight matrix; R is the input weighting factor; the Riccati equation can be obtained as shown in Equation (31). T 1 T PA A P + PBR− B P Q = 0 (31) − − − Appl. Sci. 2020, 10, 8741 9 of 20

Solving the algebraic Riccati equation, we can get the P, then the feedback gain matrix can be . . equal to K, K = R 1BTPx(t), and then U = ω z U = k e k e , thus U = k e + k e + ω z, h i − − 0 d − − − 1 1 − 2 2 1 1 2 2 d − K = k1 k2 . Therefore, the brake for the left wheel is as in Equation (32):

. Fxrld + Fx f l(cosδ d sinδ a) U = k1e1 + k2e2 + ωd z = · − · (32) − Iz

Then we get the Equation (33):

. F d + F (cosδ d sinδ a) = Iz k e + k e + ω z (33) xrl x f l · − · 1 1 2 2 d − 1 the brake for the right wheel is as in Equation (34):

. Fxrrd Fx f r(cosδ d + sinδ a) U = k1e1 + k2e2 + ωd z = − − · · (34) − Iz

After that, we can get the Equation (35):

. Fxrrd + F (cosδ d + sinδ a) = Iz k e + k e + ω + z (35) x f r · · − 1 1 2 2 d 2 Due to the small longitudinal acceleration, the front and rear axle-load transfer is small. The front F and rear longitudinal force is distributed according to the static axle load: X f = b . Fxr a The constraint of maximum longitudinal force is based on the current friction circle to constrain the maximum longitudinal force, which is deﬁned as Equation (36): q F (F µ)2 F2 (36) xi ≤ zi − yi In addition, due to the existence of driving force, the calculated target longitudinal force can be a negative value, if its absolute value is not greater than the current driving force of the tire.

3.6. Lower Control Strategy The ﬁnal input to the vehicle due to the controller for tire force observation is the brake cylinder pressure, it is therefore necessary to convert the longitudinal force of the target tire into the target braking pressure. The tire force controller adopts feedforward and feedback control strategies as shown in Equations (37) and (38). Fxb_re f + Ft r P f = (37) Cb P = Kp F F (38) b xb_re f − xb where P f is the feed-forward brake-pressure; Fxb_re f is the target brake pressure; Ft is the driving force; r is the tire rolling radius; Cb is the brake eﬃciency factor; Pb is the feedback brake pressure; Kp is the feedback gain; Fxb is the actual brake-pressure. Feedforward is the corresponding relationship between braking force and braking pressure under completely ideal conditions, which can improve the response speed of the system; feedback is used to reduce errors and improve control accuracy.

4. Software Cosimulation The controller in this paper was simulated and analyzed by software in a Simulink environment and the vehicle dynamics model was in CarSim, which uses a nonlinear tire model. The ISO3888-2 Double Lane Change avoidance condition and FMVSS 126 Sine with Dwell were studied and analyzed Appl. Sci. 2020, 10, 8741 10 of 20 in comparison with the conventional PID control algorithm in ESC, which the PID controller is not Appl. Sci. 2020, 10, x FOR PEER REVIEW 10 of 21 basedAppl. on Sci. tire 2020 force, 10, x FOR sensor. PEER REVIEW 10 of 21 In the Figures 7–9, the reference represents the nominal yaw rate calculate by the controller 4.1. Double Lane Change Condition proposedIn the in Figures this article; 7–9, thethe open reference loop represents thethe yawnominal rate withoutyaw rate the calculate controller, by butthe stillcontroller keeps theproposedIn driver the Double inmodel; this Lanearticle; the closed Change the open loop condition, looprepresents represents the the vehicles yaw the yawrate were withrate set without the up controller for the simulation controller, in this testing pa but per; still at and di keepsff theerent speedsPIDthe driver control on di ffmodel; erentrepresents adhesionthe closed the yaw coe loop ffirate cientsrepresents with of traditiona pavement. the yawl PID rate Two control, with pavements the for controller which with the adhesionin PID this controllerpa coeper;ffi andcients is notthe of PID control represents the yaw rate with traditional PID control, for which the PID controller is not 0.5based and 0.8 on were a tire selected force sensor. to represent the low and high attached pavement respectively, and the vehicle based on a tire force sensor. speed wasAccording selected to to the be simulation 80 km/h, 100results km /shownh and 120in Figures km/h, the7–9, three it can speed be concluded limits commonly that the control applied According to the simulation results shown in Figures 7–9, it can be concluded that the control to vehicles.effect of the ESC controller with tire force observation-based control is more pronounced on low- effect of the ESC controller with tire force observation-based control is more pronounced on low- adhesionIn the Figuressurfaces.7 –The9, thebetter reference the follow-through represents of the the nominal nominal yaw yaw raterate for calculate vehicles by controlled the controller with thisadhesion controller, surfaces. the The more better pronounced the follow-through this phenomenon of the nominal will beyaw with rate increasingfor vehicles speed. controlled On withhigh proposedthis controller, in thisarticle; the more the pronounced open loop represents this phenomenon the yaw ratewill withoutbe with theincreasing controller, speed. but On still high keeps theadhesion driver model; coefficient the closed pavements, loop represents the difference the yawbetw rateeen withthe two the control controller methods in this is pa not per; obvious, and the and PID thereadhesion is a smallcoefficient error pavements, in the simulation the difference results. between the two control methods is not obvious, and controlthererepresents is a small error the yaw in the rate simulation with traditional results. PID control, for which the PID controller is not based on a tire force sensor.

15 15 reference 10 referenceopen loop close loop 10 open loop closePID control loop 5 PID control 5 0 0 -5 -5 -10 -10 -15 -15 -20 -20 -25 012345678910 -25 012345678910Time [sec] Time [sec] (a) (b) (a) (b) Figure 7. Comparison of yaw rate at 80 km/h with a coefficient of adhesion of 0.5 and 0.8. (a,b) reflect FiguretheFigure nominal 7. Comparison7. Comparison yaw rate, of ofand yaw yaw yaw rate rate rate at at 80 80of km km/hthree/h with withcont rolaa coeco methodsefficientfficient atof adhesiona adhesion speed of of of80 0.5 0.5 km/h and and 0.8.on 0.8. a( apavement (,ba,)b reflect) reflect thewiththe nominal nominal a pavement yaw yaw rate, adhesionrate, and and yaw coefficientyaw rate rate of threeof of three 0.5 control and cont 0.8.rol methods methods at aat speed a speed of 80of km80 km/h/h on aon pavement a pavement with a pavementwith a pavement adhesion adhesion coefficient coefficient of 0.5 andof 0.5 0.8. and 0.8.

15 15 15 reference 15 reference open loop open loop 10 reference 10 reference openclose looploop openclose looploop 10 10 closePID control loop closePID control loop 5 PID control 5 PID control 5 5

0 0 0 0

-5 -5 -5 -5

-10 -10 -10 -10

-15 -15 -15 -15

-20 -20 012345678 012345678 -20 -20 012345678Time [sec] 012345678Time [sec] Time [sec] Time [sec] (a) (b) (a) (b) FigureFigure 8. Comparison8. Comparison of of yaw yaw rate rate at at 100 100 kmkm/h/h withwith a coecoefficientfficient of of adhesion adhesion of of 0.5 0.5 and and 0.8. 0.8. (a (,ba,)b reflect) reflect Figure 8. Comparison of yaw rate at 100 km/h with a coefficient of adhesion of 0.5 and 0.8. (a,b) reflect thethe nominal nominal yaw yaw rate, rate, and and yaw yaw rate rate of of three three controlcontrol methodsmethods at at a a speed speed of of 100 100 km/h km/h on on a apavement pavement the nominal yaw rate, and yaw rate of three control methods at a speed of 100 km/h on a pavement withwith a pavement a pavement adhesion adhesion coe coefficientfficient of of 0.5 0.5 and and 0.8. 0.8. with a pavement adhesion coefficient of 0.5 and 0.8. According to the simulation results shown in Figures7–9, it can be concluded that the control e ffect of the ESC controller with tire force observation-based control is more pronounced on low-adhesion Appl. Sci. 2020, 10, 8741 11 of 20 surfaces. The better the follow-through of the nominal yaw rate for vehicles controlled with this controller, the more pronounced this phenomenon will be with increasing speed. On high adhesion coeAppl.ffi Sci.cient 2020 pavements,, 10, x FOR PEER the REVIEW difference between the two control methods is not obvious, and there11 of is 21 a smallAppl. error Sci. 2020 in, the10, x simulationFOR PEER REVIEW results. 11 of 21

10 10 10 reference 10 reference openreference loop referenceopen loop closeopen loop openclose loop loop 5 PIDclose control loop 5 closePID loop control 5 PID control 5 PID control

0 0 0 0

-5 -5 -5 -5

-10 -10 -10 -10

-15 -15 -15-15 0123456701234567 01234560123456 TimeTime [sec] [sec] TimeTime [sec] [sec] (a(a) ) (b()b )

FigureFigureFigure 9. 9.Comparison Comparison of of yaw yaw rate rate atat 120120 km/hkm/h with a a coefficient coecoefficientfficient of ofof adhesion adhesionadhesion of ofof 0.5 0.50.5 and andand 0.8. 0.8.0.8. (a , (ba), breflect) reflectreflect thethethe nominalnominal nominal yawyaw yaw rate,rate, rate, andand and yawyaw yaw raterate rate ofofof threethreethree controlcontrol methods methods at atat a aa speed speedspeed of ofof 120 120120 km/h kmkm/h/ hon onon a pavement aa pavementpavement withwithwith aa pavement pavementa pavement adhesionadhesion adhesion coecoefficient coefficientfficient of ofof 0.5 0.5 andand 0.8.0.8.

4.2.4.2.4.2. Sine Sine with with Dwell Dwell Condition Condition TheTheThe sinesine sine withwith with dwelldwell dwell (SWD) (SWD) (SWD) simulation simulation simulation test test follows followsws the thethe standard standard standard FMVSS FMVSS FMVSS 126 126 126 requirements requirements requirements toto setsetto upset theupup the simulation the simulation simulation conditions. conditions. conditions. According According According to the to simulationthe simulation of the of of the vehiclethe vehicle vehicle model model model used used used to obtainto toobtain obtain A =A 13=A 13 deg.= 13 deg. At a speed of 80 km/h on the road surface adhesion coefficient of 0.5 and 0.8 on the test, each Atdeg. a speedAt a speed of 80 kmof /80h onkm/h the roadon the surface road surface adhesion adhesion coefficient coefficient of 0.5 and of 0.8 0.5 on and the 0.8 test, on each the conditiontest, each condition was drawn to 1.5 A, 2 A, 2.5 A,...,6.5 A and 270 deg as the maximum values of the yaw rate wascondition drawn was to 1.5drawn A, 2 to A, 1.5 2.5 A, A, 2 A,... 2.5, 6.5 A,...,6.5 A and A 270 and deg 270 as deg the as maximum the maximum values values of the of yawthe yaw rate rate for for the sinusoidal steer angle. thefor sinusoidalthe sinusoidal steer steer angle. angle. Based on Figures 10 and 11, it can be concluded that the vehicle model without the controller BasedBased on FiguresFigures 1010 andand 1111,, itit cancan bebe concludedconcluded thatthat thethe vehiclevehicle modelmodel withoutwithout thethe controllercontroller alreadyalready produces produces severe severe skidding skidding under under the the simulatedsimulated conditions at at both both low low and and high high road road adhesion adhesion alreadycoefficients. produces In the severe case ofskidding low-road-adhesion under the simulated coefficient, conditions the situation at both of following low and the high nominal road adhesion value coefficients. In the case of low-road-adhesion coefficient, the situation of following the nominal value coefficients.and jitter of In the the ESC case controller of low-road-adhesion based on tire forcecoeffi observationcient, the situation is better of than following those of the the nominal traditional value and jitter of the ESC controller based on tire force observation is better than those of the traditional andPID jitter control. of the In ESC the case controller of a high based road on adhesion tire force coefficient, observation no significant is better thandifference those in of the the following traditional PID control. In the case of a high road adhesion coefficient, no significant difference in the following PIDof control.nominal In yaw the rate case between of a high ESC road controller adhesion based coefficient, on tire forceno significant observation difference and conventional in the following PID of nominal yaw rate between ESC controller based on tire force observation and conventional PID of control,nominal and yaw there rate are between small fluctuations ESC controller in the based yaw rate on fortire both force control observation methods. and conventional PID control,control, andand therethere areare smallsmall fluctuationsfluctuations inin thethe yawyaw raterate forfor bothboth controlcontrol methods.methods. Yaw rate [deg/s] Yaw Yaw rate [deg/s] Yaw Yaw rate [deg/s] Yaw Yaw rate [deg/s] Yaw

(a) (b) (a) Figure 10. Cont. (b) Appl. Sci. 2020, 10, x FOR PEER REVIEW 12 of 21

Appl.Appl. Sci. Sci.2020 2020, 10, ,10 8741, x FOR PEER REVIEW 12 12of 21 of 20 Yaw rate [deg/s] Yaw Yaw rate [deg/s] Yaw Yaw rate [deg/s] Yaw Yaw rate [deg/s] Yaw

(c) (d) (c) (d) Figure 10. Yaw rate with a friction coefficient of 0.5 in the sine with dwell condition. (a–d) show the FigurenominalFigure 10. yaw 10.Yaw Yaw rate, rate rate open-loop with with aa frictionfriction control coefficient coeyawﬃ rate,cient ofPID of 0.5 0.5co inntrol inthe the sineyaw sine with rate with dwelland dwell closed condition. condition.-loop (controla–d) (showa– yawd) showthe rate theplotsnominal nominal for the yaw yawsine rate, rate,with open-loop open-loopdwell (SWD) control control condition yaw yaw rate, rate,on PID a PIDpavementcontrol control yaw with yawrate anand rate adhesion closed and closed-loop-loop factor control of 0.5. control yaw rate yaw rateplots plots for for the the sine sine with with dwell dwell (SWD) (SWD) condition condition on a on pavement a pavement with withan adhesion an adhesion factor factor of 0.5. of 0.5. Yaw rate [deg/s] Yaw Yaw rate [deg/s] Yaw Yaw rate [deg/s] Yaw Yaw rate [deg/s] Yaw

(a()a ) (b(b) ) Yaw rate [deg/s] Yaw Yaw rate [deg/s] Yaw Yaw rate [deg/s] Yaw Yaw rate [deg/s] Yaw

(c) (d) (c) (d) Figure 11. Yaw rate with a friction coefficient of 0.8 in the sine with dwell condition. (a–d) show the FigureFigurenominal 11. YawyawYaw rate,rate rate open-loopwith with a a friction friction control coefficient coe yawﬃ cientrate, of PID of 0.8 0.8 co inntrol in the the yawsine sine ratewith with and dwell dwellclosed condition.-loop condition. control (a–d ( ayaw) –showd) rate show the thenominalplots nominal for yaw the yaw rate, sine rate, open-loopwith open-loop dwell controlcondition control yaw on yaw rate, a pavement rate, PID PIDcontrol with control yawan adhesion yaw rate rateand factor andclosed closed-loopof-loop 0.8. control control yaw yawrate rateplots plots for the for sine the sinewith with dwell dwell condition condition on a on pavement a pavement with with an adhesion an adhesion factor factor of 0.8. of 0.8. 5. Hardware-in-the-Loop Test 5.5. Hardware-in-the-Loop Test The HIL test of this controller was done in an NI Veristand real-time simulation system, the upperTheThe HILcomputerHIL testtest of ofused this this controllerthe controller CarSim was vehicle was done done model, in anin NI anand VeristandNI the Veristand control real-time strategy real-time simulation was simulation built system,in the system,Simulink the upper the computerupper computer used theused CarSim the CarSim vehicle vehicle model, model, and and the the control control strategy strategy was was built built in in thethe SimulinkSimulink environment. The HIL frame contained the ESC system, braking circuit, wheel cylinder pressure Appl. Sci. 2020, 10, x FOR PEER REVIEW 13 of 21

environment. The HIL frame contained the ESC system, braking circuit, wheel cylinder pressure Appl. Sci. 2020, 10, 8741 13 of 20 sensor,Appl. Sci. upper 2020, 10 computer,, x FOR PEER lower REVIEW computer, and the corresponding function boards, shown in13 ofFigure 21 12. An HIL comparison test was performed under the same conditions as in Section 4. environment. The HIL frame contained the ESC system, braking circuit, wheel cylinder pressure sensor, upper computer, lower computer, and the corresponding function boards, shown in Figure 12. sensor, upper computer, lower computer, and the corresponding function boards, shown in Figure An HIL comparison test was performed under the same conditions as in Section4. 12. An HIL comparison test was performed under the same conditions as in Section 4.

Figure 12. Hardware-in-the-loop test bench.

5.1. Double Lane Change ConditionFigureFigure 12. 12. Hardware-in-the-loopHardware-in-the-loop test test bench. bench.

5.1.5.1. DoubleIn Double this Lane part Lane Change ofChange the ConditionHIL Condition test, the settings of vehicle speed and coefficient of pavement adhesion were consistent with the software cosimulation, using the common high speeds of 80 km/h and 100 InIn this this part part of theof the HIL HIL test, test, the the settings settings of vehicleof vehicle speed speed and and coe coefficientfficient of pavementof pavement adhesion adhesion were km/h, and the pavement adhesion coefficient was set at 0.5 and 0.8. consistentwere consistent with the with software the software cosimulation, cosimulation, using using the common the common high high speeds speeds of 80 of km 80/ hkm/h and and 100 100 km /h, In the hardware-in-the-loop test under the double lane change condition, the vehicle model andkm/h, the pavementand the pavement adhesion adhesion coefficient coefficient was set was at 0.5 set and at 0.5 0.8. and 0.8. based on tire force observation in the low pavement adhesion coefficient condition followed the InIn the the hardware-in-the-loop hardware-in-the-loop test test under under the the double double lane lane change change condition, condition, the vehiclethe vehicle model model based nominal yaw rate better than the traditional PID control, and the vehicle model based on tire force onbased tire force on tire observation force observation in the low in pavementthe low pavement adhesion adhesion coefficient coefficient condition condition followed followed the nominal the observation at the peak of the yaw rate curve had a clear advantage over the traditional PID control. yawnominal rate better yaw thanrate better the traditional than the traditional PID control, PID and control, the vehicle and the model vehicle based model on tirebased force on observationtire force However, when the value of the yaw rate was close to the largest negative value, the yaw rate of the at theobservation peak of at the the yaw peak rate of curvethe yaw had rate a curve clear advantagehad a clear advantage over the traditional over the traditional PID control. PID control. However, vehicle models controlled by the two controllers had a certain fluctuation. Comparing the test time whenHowever, the value when of the the yaw value rate of wasthe yaw close rate to thewas largest close to negative the largest value, negative the yaw value, rate ofthe the yaw vehicle rate of models the onvehicle the abscissa models of controlled a and b in by Figures the two 13–20, controllers it can beha dseen a certain that the fluctuation. response Comparing time of the theactuator test time brake controlled by the two controllers had a certain fluctuation. Comparing the test time on the abscissa of a pressureon the abscissa value slightlyof a and laggedb in Figures behind 13–20, the it cantime be at seen which that thethe responseyaw rate time curve of the separated actuator brakegreatly. and b in Figures 13–20, it can be seen that the response time of the actuator brake pressure value slightly Therefore,pressure thevalue high-frequency slightly lagged braking behind signal the time caused at whichthe actual the responseyaw rate pressurecurve separated of the brake greatly. wheel lagged behind the time at which the yaw rate curve separated greatly. Therefore, the high-frequency cylinderTherefore, to be the insufficient. high-frequency Thus, braking it affected signal the caused actuator the actual control response of the pressurevehicle modelof the brakeand made wheel the braking signal caused the actual response pressure of the brake wheel cylinder to be insufficient. yawcylinder rate following to be insufficient. worse. Thus, it affected the actuator control of the vehicle model and made the Thus,yaw it rate affected following the actuator worse. control of the vehicle model and made the yaw rate following worse.

15 12

15 reference 12 WCP FL hard in loop WCP FR 10 reference 10 WCP FL WCP RL hard in loop WCP FR 10 10 WCPWCP RL RR 5 8 WCP RR 5 8

0 6 0 6

-5 4 -5 4

-10 2 -10 2

-15 0 -15 0

-20 -2 -20012345678910 -2 012345678910 012345678910 012345678910 Time [sec] TimeTime [sec] [sec] Time [sec] ((aa)) (b()b )

Figure 13. Test results based on the tire force observation controller at u = 80 km/h and µ = 0.5. (a) is a comparison of the nominal and actual values of the yaw rate, and (b) is the wheel cylinder pressure value collected from the wheel cylinder pressure sensor. Appl. Sci. 2020, 10, x FOR PEER REVIEW 14 of 21 Appl. Sci. 2020, 10, x FOR PEER REVIEW 14 of 21 Figure 13. Test results based on the tire force observation controller at 𝑢 = 80 km/h and 𝜇 = 0.5. (a) is Figure 13. Test results based on the tire force observation controller at 𝑢 = 80 km/h and 𝜇 = 0.5. (a) is a comparison of the nominal and actual values of the yaw rate, and (b) is the wheel cylinder pressure a comparison of the nominal and actual values of the yaw rate, and (b) is the wheel cylinder pressure value collected from the wheel cylinder pressure sensor. Appl. Sci.value2020 collected, 10, 8741 from the wheel cylinder pressure sensor. 14 of 20

14 14 WCP FL 12 WCP FLFR 12 WCP FRRL WCP RLRR 10 WCP RR 10 8 8 6 6 4 4 2 2 0 0 -2 -2 246810121416 246810121416Time [sec] Time [sec] (a) (b) (a) (b) Figure 14. Test results based on the conventional PID-based controller at 𝑢 = 80 km/h and 𝜇 = 0.5. (a) is a FigureFigure 14. TestTest results results based based on onthe the conven conventionaltional PID-based PID-based controller controller at 𝑢 = at 80u km/h= 80 and km /h𝜇 and= 0.5.µ (a=) is0.5. a comparison of the nominal and actual values of the yaw rate, and (b) is the wheel cylinder pressure (comparisona) is a comparison of the nominal of the nominal and actu andal values actual of values the yaw of therate, yaw and rate, (b) is and the ( bwheel) is the cylinder wheel pressure cylinder value collected from the wheel cylinder pressure sensor. pressurevalue collected value collectedfrom the fromwhee thel cylinder wheel cylinderpressure pressuresensor. sensor.

15 20 15 reference 20 WCP FL referencehard in loop WCP FLFR 10 hard in loop WCP FRRL 15 10 WCP RLRR 15 WCP RR 5 5 10 0 10 0

-5 5 -5 5 -10 -10 0 -15 0 -15

-20 -5 012345678910 -20 012345678910 -5 012345678910Time [sec] 012345678910Time [sec] Time [sec] Time [sec] (a) (b) (a) (b) FigureFigure 15. TestTest results results based based on onthe the tire tireforce force observation observation controller controller at 𝑢 = at 100u =km/h100 and km /h𝜇 and= 0.5.µ (a=) 0.5.is a Figure 15. Test results based on the tire force observation controller at 𝑢 = 100 km/h and 𝜇 = 0.5. (a) is a Appl.(comparisona) Sci. is a2020 comparison, 10 ,of x FORthe nominalPEER of the REVIEW nominal and actu andal values actual of values the yaw of therate, yaw and rate, (b) is and the ( bwheel) is the cylinder wheel cylinderpressure15 of 21 comparison of the nominal and actual values of the yaw rate, and (b) is the wheel cylinder pressure pressurevalue collected value collected from the fromwhee thel cylinder wheel cylinderpressure pressure sensor. sensor. value collected from the wheel cylinder pressure sensor.

14 WCP FL 12 WCP FR WCP RL WCP RR 10

-2 2 4 6 8 10 12 14 Time [sec] (a) (b)

FigureFigure 16. 16.Test Test results results based based onon the conventional PID-based PID-based controller controller at 𝑢 at =u 100= 100 km/h km and/h and𝜇 = µ0.5.= (0.5.a) is( a) is aa comparisoncomparison ofof thethe nominal and actual actual values values of of the the yaw yaw rate, rate, and and (b (b) is) isthe the wheel wheel cylinder cylinder pressure pressure valuevalue collected collected from from the the wheel whee cylinderl cylinder pressure pressuresensor. sensor.

15 5 reference WCP FL 10 hard in loop WCP FR 4 WCP RL WCP RR 5 3

0 2 -5 1 -10

0 -15

-20 -1

-25 -2 012345678910 012345678910 Time [sec] Time [sec] (a) (b)

Figure 17. Test results based on the tire force observation controller at 𝑢 = 80 km/h and 𝜇 = 0.8. (a) is a comparison of the nominal and actual values of the yaw rate, and (b) is the wheel cylinder pressure value collected from the wheel cylinder pressure sensor.

15 30 reference WCP FL 10 hard in loop WCP FR 25 WCP RL WCP RR 5 20

0 15 -5

10 -10

5 -15

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-25 -5 23456789101112 23456789101112 Time [sec] Time [sec] (a) (b) Appl. Sci. 2020, 10, x FOR PEER REVIEW 15 of 21 Appl. Sci. 2020, 10, x FOR PEER REVIEW 15 of 21

14 WCP FL WCP FR 12 WCP FL WCP RL 12 WCP FR WCP RR 10 WCP RL WCP RR 10 8 8 6 6 4 4

2 2

0 0

-2 -2 2 4 6 8 10 12 14 2 4 6 8 10 12 14 TimeTime [sec] [sec] (a()a ) (b(b) )

FigureFigure 16. 16. Test Test results results based based on on the the conventional conventional PID-based controllercontroller at at 𝑢 𝑢 = =100 100 km/h km/h and and 𝜇 𝜇= 0.5.= 0.5. (a )( ais) is a comparisona comparison of of the the nominal nominal and and actual actual values values of the yaw rate,rate, and and ( b(b) )is is the the wheel wheel cylinder cylinder pressure pressure Appl. Sci.valuevalue2020 collected, 10collected, 8741 from from the the whee wheel lcylinder cylinder pressurepressure sensor. 15 of 20

15 15 55 reference WCP FL reference WCP FL 10 hard in loop WCP FR 10 hard in loop 4 WCP FR 4 WCP RL WCP RL WCP RR 5 WCP RR 5 3 3 0 0 2 2 -5 -5 1 -10 1 -10 0 -15 0 -15 -20 -1 -20 -1 -25 -2 012345678910 012345678910 -25 -2 012345678910Time [sec] 012345678910Time [sec] Time [sec] Time [sec] (a) (b) (a) (b) Figure 17. Test results based on the tire force observation controller at 𝑢 = 80 km/h and 𝜇 = 0.8. (a) is FigureFigurea comparison 17.17. Test results of the nominal basedbased onon and thethe actual tiretire forceforce values observationobservation of the yaw controller controllerrate, and ( at bat)u is𝑢= the =80 80 wheel km km/h/h andcylinder andµ =𝜇 0.8.pressure = 0.8. (a )(a is) is a comparisona comparisonvalue collected of of the the from nominal nominal the whee and andl actualcylinder actual values values pressure of of the sensor.the yaw yaw rate, rate, and and ((bb)) isis thethe wheelwheel cylindercylinder pressurepressure valuevalue collectedcollected fromfrom thethe wheelwheel cylindercylinder pressurepressure sensor.sensor.

15 30 reference WCP FL 15 10 hard in loop 30 WCP FR 25 WCP RL reference WCP FL WCP RR 10 5 hard in loop WCP FR 25 20 WCP RL WCP RR 5 0 1520 0 -5 1015 -5 -10

105 -15 -10

-20 05 -15

-25 -50 -20 23456789101112 23456789101112 Appl. Sci. 2020, 10, x FOR PEERTime REVIEW [sec] Time [sec] 16 of 21 -25 -5 23456789101112(a) 23456789101112(b) Figure 18. Test resultsTime based [sec] on the conventional PID-based controller at 𝑢Time = 80[sec] km/h and 𝜇 = 0.8. Figure(a) is a 18.comparisonTest results of(a basedthe) nominal on theconventional and actual values PID-based of the controller yaw rate, at andu = 80 (b(b km) )is / hthe and wheelµ = 0.8. cylinder (a) is apressure comparison value of collected the nominal from and the actualwheel valuescylinder of pressure the yaw rate,sensor. and (b) is the wheel cylinder pressure value collected from the wheel cylinder pressure sensor.

15 2 reference WCP FL hard in loop 10 1.5 WCP FR WCP RL WCP RR 1 5

0.5 0

0 -5 -0.5 -10 -1

-15 -1.5

-20 -2 012345678910 012345678910 Time [sec] Time [sec] (a) (b)

Figure 19.19. Test resultsresults basedbased on on the the tire tire force force observation observation controller controller at atu =𝑢100 = 100 km km/h/h and andµ = 0.8.𝜇 = 0.8. (a) is (a a) comparisonis a comparison of the of nominal the nominal and actual and ac valuestual values of the yawof the rate, yaw and rate, (b) isand the (b wheel) is the cylinder wheel pressurecylinder valuepressure collected value fromcollected the wheelfrom the cylinder wheel pressure cylinder sensor.pressure sensor.

15 16 reference WCP FL hard in loop 14 WCP FR 10 WCP RL 12 WCP RR 5 10

0 8

-5 6

4 -10 2

-15 0

-20 -2 23456789101112 024681012 Time [sec] Time [sec] (a) (b)

Figure 20. Test results based on the conventional PID-based controller at 𝑢 = 100 km/h and 𝜇 = 0.8. (a) is a comparison of the nominal and actual values of the yaw rate, and (b) is the wheel cylinder pressure value collected from the wheel cylinder pressure sensor.

In high road adhesion conditions, the actuators controlled by the two controllers hardly trigger work. As far as the yaw rate follows, the controller based on tire force observation has obvious advantages. The test conditions of high and low road adhesion coefficients at a speed of 120 km/h are almost the same as those at a speed of 100 km/h.

5.2. Sine with Dwell Condition The setting of vehicle speed and road adhesion coefficient in the sine with dwell condition in the loop test is consistent with the software co-simulation. The vehicle speed is set to 80 km/h, the road adhesion coefficient is 0.5 and 0.8, and the peak steering angle is 1.5 A, 2 A, 2.5 A,…,6.5 A and 270 deg respectively. Compared with the software co-simulation, as shown in Figures 21–26, firstly, the overshoot caused by the fluctuation of the yaw rate during the steering hysteresis phase of the test of the Appl. Sci. 2020, 10, x FOR PEER REVIEW 16 of 21

Figure 18. Test results based on the conventional PID-based controller at 𝑢 = 80 km/h and 𝜇 = 0.8. (a) is a comparison of the nominal and actual values of the yaw rate, and (b) is the wheel cylinder pressure value collected from the wheel cylinder pressure sensor.

15 2 reference WCP FL hard in loop 10 1.5 WCP FR WCP RL WCP RR 1 5

0.5 0

0 -5 -0.5 -10 -1

-15 -1.5

-20 -2 012345678910 012345678910 Time [sec] Time [sec] (a) (b)

Figure 19. Test results based on the tire force observation controller at 𝑢 = 100 km/h and 𝜇 = 0.8. (a) is a comparison of the nominal and actual values of the yaw rate, and (b) is the wheel cylinder Appl. Sci.pressure2020, 10 value, 8741 collected from the wheel cylinder pressure sensor. 16 of 20

15 16 reference WCP FL hard in loop 14 WCP FR 10 WCP RL 12 WCP RR 5 10

0 8

-5 6

4 -10 2

-15 0

-20 -2 23456789101112 024681012 Time [sec] Time [sec] (a) (b)

Figure 20. Test results based on the conventional PID-based PID-based controller controller at at 𝑢u = 100100 km/h km/h and and 𝜇µ == 0.8. ((aa)) isis aa comparisoncomparison ofof thethe nominalnominal andand actualactual valuesvalues of thethe yawyaw rate,rate, andand ((b)) isis thethe wheelwheel cylindercylinder pressurepressure valuevalue collectedcollected fromfrom thethe wheelwheel cylindercylinder pressurepressure sensor.sensor.

InIn highhigh roadroad adhesionadhesion conditions,conditions, thethe actuatorsactuators controlled by thethe twotwo controllerscontrollers hardlyhardly triggertrigger work.work. As As far far as as the yaw rate follows, the controllercontroller based on tire forceforce observationobservation hashas obviousobvious advantages. The test conditions of high and low road adhesion coecoefficientsﬃcients at a speed of 120 kmkm/h/h are almost thethe samesame asas thosethose atat aa speedspeed ofof 100100 kmkm/h./h.

5.2. Sine with Dwell Condition The setting of of vehicle vehicle speed speed and and road road adhesion adhesion coef coeficientfficient in inthe the sine sine with with dwell dwell condition condition in the in theloop loop test test is consistent is consistent with with the the software software co-simul co-simulation.ation. The The vehicle vehicle speed speed is is set set to to 80 80 km/h, km/h, the road adhesion coecoefficientfficient is 0.5 and 0.8, 0.8, and and the the peak peak steering steering angle angle is is 1.5 1.5 A, A, 2 2A, A, 2.5 2.5 A,…,6.5 A, ... , A 6.5 and A and270 270deg degrespectively. respectively. Compared with the software co-simulation, as shown in Figures 2121–26,–26, firstly,firstly, thethe overshootovershoot caused byby the the fluctuation fluctuation of theof the yaw yaw rate rate during during the steering the steering hysteresis hysteresis phaseof phase the test of ofthe the test controller of the designed in this paper is smaller than that of the vehicle model with PID controller under the low adhesion coefficient condition. Secondly, the fluctuation of the yaw rate for the controller based on tire force observation during the steering hysteresis phase is larger for the vehicle model with PID control. Thirdly, at high pavement adhesion coefficients, the yaw rate response of the vehicle model with both controllers is improved at lower pavement adhesion coefficients, and the nominal yaw rate response of the vehicle model with the PID controller is also improved at lower pavement adhesion coefficients, both controller-controlled vehicle models have improved yaw rate response to low pavement adhesion coefficients, and also improved the follow-through of nominal yaw rate for low pavement adhesion coefficients conditions. Among them, the improvement in the yaw rate response of the vehicle model based on tire force observations is more pronounced. Appl. Sci. 2020, 10, x FOR PEER REVIEW 17 of 21 Appl. Sci. 2020, 10, x FOR PEER REVIEW 17 of 21 controller designed in this paper is smaller than that of the vehicle model with PID controller under thecontroller low adhesion designed coefficient in this paper condition. is smaller Secondly, than that the of fluctuation the vehicle of model the yaw with rate PID for controller the controller under basedthe low on adhesion tire force coefficient observation condition. during theSecondly, steering the hysteresis fluctuation phase of theis larger yaw ratefor the for vehiclethe controller model withbased PID on tirecontrol. force Thirdly,observation at high during pavement the steering adhe sionhysteresis coefficients, phase isthe larger yaw forrate the response vehicle modelof the vehiclewith PID model control. with Thirdly, both controllers at high pavementis improved adhe at sionlower coefficients, pavement adhesionthe yaw ratecoefficients, response and of the nominalvehicle model yaw rate with response both controllers of the vehicle is improved model withat lower the PIDpavement controller adhesion is also coefficients, improved atand lower the pavementnominal yaw adhesion rate response coefficients, of the both vehicle controller-co model withntrolled the PIDvehicle controller models is have also improvedimproved yawat lower rate responsepavement to adhesion low pavement coefficients, adhesion both coefficients, controller-co andntrolled also improved vehicle models the follow-through have improved of yawnominal rate yawresponse rate forto low low pavement pavement adhesion adhesion coefficients, coefficients andconditions. also improved Among thethem, follow-through the improvement of nominal in the yaw rate responsefor low pavement of the vehicle adhesi modelon coefficients based on tire conditions. force observations Among them, is more the pronounced.improvement in the yaw Accordingrate response to ofthe the images vehicle of model brake based cylinder on tire pres forcesure observations shown in Figures is more 23 pronounced. and 26, it can be concludedAccording that thereto the is aimages certain of discrepancy brake cylinder between pres thesure yaw shown rate of in actual Figures value 23 andand nominal 26, it can value be afterconcluded the controller that there control is a certain as well discrepancy as a small range between of fluctuation, the yaw rate this of isactual caused value by a and delay nominal in the brakevalue hydraulicafter the controller circuit for control a certain as wellperiod as aof small time, range insuff oficient fluctuation, response this to ishigh caused frequency by a delay braking in the signals, brake andhydraulic inconsistent circuit responsefor a certain of the period front of and time, rear insuff wheelsicient to response braking pressure.to high frequency braking signals, Appl.and inconsistent Sci. 2020, 10, 8741 response of the front and rear wheels to braking pressure. 17 of 20 Yaw rate [MPa] Yaw Yaw rate [MPa] Yaw Yaw rate [MPa] Yaw Yaw rate [MPa] Yaw

(a) (b) (b) Figure 21. The yaw rate(a) graphs of the vehicle model based on tire force observation when 𝜇 = 0.5. Figure(a,b) are 21. graphs The yaw of nominal rate graphs yaw of ofrate the and vehicle actual model model yaw rabased basedte when on on tire tirethe force forceroad observationadhesion observation coefficient when when 𝜇µ is= 0.5,0.5.0.5. (usinga,,b) areare the graphsgraphs vehicle of model nominalnominal based yaw on ratetire force and actual observation. yaw ra rate te when the road adhesion coefficient coeﬃcient is 0.5, using the vehicle model based on tire forceforce observation.observation. Yaw rate [MPa] Yaw rate [MPa] Yaw Yaw rate [MPa] Yaw rate [MPa] Yaw

(a) (b)

Figure 22. TheThe yaw yaw rate rate(a) graphs graphs of of the the vehicle vehicle model model based based on on tire tire force force observation observation(b) when when 𝜇µ = 0.8.0.8. Appl. Sci.(Figurea,b 2020) are ,22. 10 graphsgraphs, Thex FOR yaw of PEER nominal rate REVIEW graphs yaw of rate the and vehicle actual model yaw ra ratebasedte when on tire the forceroad observationadhesion coefficient coe whenﬃcient 𝜇 is is= 0.8,0.8. 18 of 21 using(a,b) are the graphs vehicle of model nominal based yaw on rate tire forceand actual observationobservation yaw ra control.control.te when the road adhesion coefficient is 0.8, using the vehicle model based on tire force observation control. 35 25 WCP FL WCP FL 30 WCP FR WCP FR WCP RL 20 WCP RL WCP RR WCP RR 25

15 20

15 10

10 5 5

0 0

-5 -5 012345678910 012345678910 Time [sec] Time [sec] (a) (b)

Figure 23. BasedBased on on the the observation observation of oftire tire force, force, the the brake brake wheel wheel cylinder cylinder pre pressuressure value value under under the thetest testcondition condition of the of the maximum maximum steering steering angle. angle. (a, (ba),b are) are the the brake brake wheel wheel cylin cylinderder pressure pressure values of the vehicle model using tire force observation when the maximum steering angle of the test conditions is 270 deg and the roadroad adhesionadhesion coecoefﬃficientcient isis 0.50.5 andand 0.80.8 respectively.respectively. Yaw rate [MPa] Yaw Yaw rate [MPa] Yaw

(a) (b)

Figure 24. The yaw rate graphs of the vehicle model based on traditional PID control when 𝜇 = 0.5. (a,b) are the nominal yaw rate and actual yaw rate of the vehicle model using traditional PID control when the road adhesion coefficient is 0.5. Yaw rate [MPa] Yaw Yaw rate [MPa] Yaw

(a) (b) Appl. Sci. 2020, 10, x FOR PEER REVIEW 18 of 21 Appl. Sci. 2020, 10, x FOR PEER REVIEW 18 of 21

35 25 WCP FL WCP FL 35 30 WCP FR 25 WCP FR WCP RL WCP FL 20 WCPWCP RL FL 30 WCPWCP RR FR WCP RR 25 WCP FR WCP RL 20 WCP RL WCP RR WCP RR 25 15 20 15 20 15 10

15 10 10 5 10 5 5 5 0 0 0 0 -5 -5 012345678910 012345678910 Time [sec] -5 -5 Time [sec] 012345678910 012345678910 Time [sec] Time [sec] (a) (b) (a) (b) Figure 23. Based on the observation of tire force, the brake wheel cylinder pressure value under the testFigure condition 23. Based of the on maximumthe observation steering of tireangle. force, (a, bthe) are brake the brakewheel wheelcylinder cylin prederssure pressure value undervalues theof thetest vehicle condition model of theusing maximum tire force steering observation angle. when (a,b the) are maximum the brake steering wheel cylin angleder of thepressure test conditions values of isthe 270 vehicle deg and model the usingroad adhesion tire force coefobservationficient is when 0.5 and the 0.8 maximum respectively. steering angle of the test conditions Appl. Sci.is 2702020 deg, 10, and 8741 the road adhesion coefficient is 0.5 and 0.8 respectively. 18 of 20 Yaw rate [MPa] Yaw Yaw rate [MPa] Yaw Yaw rate [MPa] Yaw Yaw rate [MPa] Yaw

(a) (b) (a) (b) Figure 24. The yaw rate graphs of the vehicle model based on traditional PID control when 𝜇 = 0.5. (FigureFigurea,b) are 24.24. the TheThe nominal yawyaw rate yaw graphs rate and of actual the vehicle yaw rate model of the based vehicle on traditional model using PID traditional control when PID µcontrol𝜇 == 0.5. (when(aa,,bb)) are arethe the theroad nominalnominal adhesion yawyaw coefficient raterate andand actualactualis 0.5. yawyaw raterate ofof thethe vehiclevehicle modelmodel usingusing traditionaltraditional PIDPID controlcontrol whenwhen thethe roadroad adhesionadhesion coecoefficientﬃcient is is 0.5. 0.5. Yaw rate [MPa] Yaw Yaw rate [MPa] Yaw Yaw rate [MPa] Yaw Yaw rate [MPa] Yaw

Appl. Sci. 2020, 10, x FOR PEER REVIEW 19 of 21 (a) (b) Figure 25. The yaw rate graphs of the vehicle model based on traditional PID control when 𝜇 = 0.8. (a) (b) Figure(a,b) are 25. theThe nominal yaw rate yaw graphs rate and of theactual vehicle yaw rate model of the based vehicle on traditional model using PID traditional control when PID µcontrol= 0.8. (whena,b) are the the road nominal adhesion yaw coefficient rate and actualis 0.8. yaw rate of the vehicle model using traditional PID control when the road adhesion coeﬃcient is 0.8.

60 30 WCP FL WCP FL WCP FR WCP FR 50 25 WCP RL WCP RL WCP RR WCP RR 40 20

30 15

20 10

10 5

0 0

-10 -5 23456789101112 23456789101112 Time [sec] Time [sec] (a) (b)

Figure 26.26. BasedBased onon thethe traditional traditional PID PID control, control, the the brake brake wheel wheel cylinder cylinder pressure pressure value value under under the testthe conditiontest condition of the of maximum the maximum steering steering angle angle is shown. is shown. (a,b) are(a,b the) are brake the wheelbrake wheel cylinder cylinder pressure pressure values ofvalues the vehicleof the vehicle model model using traditionalusing traditional PID control PID control when when the maximum the maximum steering steering angle angle is 270 is deg270 anddeg theand roadthe road adhesion adhesion coeﬃ coefficientcient is 0.5 is and 0.5 0.8.and 0.8.

6. Discussion In the software cosimulation, different vehicle speeds and different road adhesion coefficients were tested. As the vehicle speed increases, the ESC control algorithm based on the tire force sensor shows better stability. The PID-controlled ESC control algorithm will have a significant overshoot and the nominal yaw rate value will not follow tightly as the vehicle speed increases. The difference between the different ESC control algorithms on the road with low adhesion coefficient is more obvious. Generally speaking, the ESC controller based on tire force control follows the situation of the nominal yaw rate better than the traditional PID controller (without the tire force sensor), the difference between the two is not obvious on the road with high adhesion coefficient. In the hardware-in-the-loop test, in addition to obtaining the same conclusions as in the software cosimulation, it can also be concluded from the wheel cylinder pressure diagram in the sine with dwell condition that the conventional PID controller sends signals to the actuator more frequently than the ESC controller based on the tire force sensor, which indicates that the ESC control algorithm based on the tire force sensor can effectively improve the efficiency of ESC control of the vehicle, improve the control accuracy, and reduce the number of false triggers. However, this conclusion still needs to be further tested and verified. Compared with the traditional PID-controlled controller, the ESC controller based on tire force observation in this paper shows some advantages in the case of a low road adhesion coefficient and improves the following situation of the nominal value of yaw rate. This proves that the use of the tire force collected by the tire force sensor as the input of the ESC controller can compensate for the inaccurate expression of the tire model under extreme operating conditions and nonlinear conditions, thus proving that the use of a controller based on tire force observation can be a new idea to improve the control accuracy of the chassis electronic control system. There are still some limitations to this paper. Firstly, under extreme conditions, there is a large difference in the follow-through of the actual value to the nominal value of the side slip angle, but the vehicle is still in a stable state that does not require ESC access control. Therefore, this article does not carry out the test results of the side slip angle analysis. Secondly, another question is mostly focused on the actuator response in the hardware-in-the-loop test. The actuator response accuracy and rate will have a large impact on the control effect of the ESC controller; therefore, future work Appl. Sci. 2020, 10, 8741 19 of 20

According to the images of brake cylinder pressure shown in Figures 23 and 26, it can be concluded that there is a certain discrepancy between the yaw rate of actual value and nominal value after the controller control as well as a small range of ﬂuctuation, this is caused by a delay in the brake hydraulic circuit for a certain period of time, insuﬃcient response to high frequency braking signals, and inconsistent response of the front and rear wheels to braking pressure.

6. Discussion In the software cosimulation, different vehicle speeds and different road adhesion coefficients were tested. As the vehicle speed increases, the ESC control algorithm based on the tire force sensor shows better stability. The PID-controlled ESC control algorithm will have a significant overshoot and the nominal yaw rate value will not follow tightly as the vehicle speed increases. The difference between the different ESC control algorithms on the road with low adhesion coefficient is more obvious. Generally speaking, the ESC controller based on tire force control follows the situation of the nominal yaw rate better than the traditional PID controller (without the tire force sensor), the difference between the two is not obvious on the road with high adhesion coefficient. In the hardware-in-the-loop test, in addition to obtaining the same conclusions as in the software cosimulation, it can also be concluded from the wheel cylinder pressure diagram in the sine with dwell condition that the conventional PID controller sends signals to the actuator more frequently than the ESC controller based on the tire force sensor, which indicates that the ESC control algorithm based on the tire force sensor can effectively improve the efficiency of ESC control of the vehicle, improve the control accuracy, and reduce the number of false triggers. However, this conclusion still needs to be further tested and verified. Compared with the traditional PID-controlled controller, the ESC controller based on tire force observation in this paper shows some advantages in the case of a low road adhesion coefficient and improves the following situation of the nominal value of yaw rate. This proves that the use of the tire force collected by the tire force sensor as the input of the ESC controller can compensate for the inaccurate expression of the tire model under extreme operating conditions and nonlinear conditions, thus proving that the use of a controller based on tire force observation can be a new idea to improve the control accuracy of the chassis electronic control system. There are still some limitations to this paper. Firstly, under extreme conditions, there is a large difference in the follow-through of the actual value to the nominal value of the side slip angle, but the vehicle is still in a stable state that does not require ESC access control. Therefore, this article does not carry out the test results of the side slip angle analysis. Secondly, another question is mostly focused on the actuator response in the hardware-in-the-loop test. The actuator response accuracy and rate will have a large impact on the control effect of the ESC controller; therefore, future work will focus on the controller algorithm to consider the inherent problems of the actuator and improve the speed of solenoid valve boosting in ESC.

Author Contributions: Conceptualization, D.L. and Y.M.; methodology, Y.M.; software, H.Y.; validation, D.L., Y.M. and H.Y.; formal analysis, Y.M.; investigation, Z.D.; resources, J.Q.; data curation, H.Y.; writing—original draft preparation, H.Y.; writing—review and editing, Y.M.; visualization, Z.D.; supervision, D.L.; project administration, D.L.; funding acquisition, J.Q. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the Government of Liuzhou and SAIC-GM-Wuling Automobile, grant number 2018AA20501. Conﬂicts of Interest: The authors declare no conﬂict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results. Appl. Sci. 2020, 10, 8741 20 of 20

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