AC Ward Leonard Drive Systems Revisiting the Four-Quadrant

European Journal of Control ∎ (∎∎∎∎) ∎∎∎–∎∎∎

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European Journal of Control

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AC Ward Leonard drive systems: Revisiting the four-quadrant operation of AC machines$

Qing-Chang Zhong n

Dept. of Automatic Control and Systems Engineering, The University of Shefﬁeld, Shefﬁeld S1 3JD, UK article info abstract

Article history: In this paper, the problem of controlling the speed of AC machines in four quadrants is revisited from a Received 13 May 2013 completely new viewpoint, based on the idea of powering an AC machine with a synchronous generator Accepted 13 May 2013 that generates a variable-voltage–variable-frequency supply. This is a natural, mathematical, but not ﬁ Recommended by Alessandro Astol physical, extension of the conventional Ward Leonard drive systems for DC machines to AC machines. As a result, AC drives can be regarded as generator-motor systems, which facilitate the analysis of AC Keywords: drives and the introduction of other special functions because a system consisting of a generator and a Variable speed drives motor is easier to be handled than the conventional AC drive that consists of an inverter and a motor. Ward Leonard drive systems Control strategies, with and without a speed sensor, are proposed to implement this idea and the AC machines experimental results are presented to demonstrate the feasibility. Synchronverters & 2013 European Control Association. Published by Elsevier Ltd. All rights reserved. Inverters that mimic synchronous generators Speed-sensorless

1. Introduction flux. It is widely used in open-loop drives, where the requirement of performance, e.g. speed accuracy and response, is not Motors consume the majority of electricity, of which 50–70% is high and/or the controller needs to be simple [25]. This is also consumed by asynchronous electric motors and 3–10% by synchro- called scalar control because only the amplitude of the voltage nous electric motors.1 Variable speed drives (VSD), often equipped is controlled. It is possible to add feedback, e.g. speed, torque with inverters, are hence widely used nowadays to save energy, and/or flux, to improve the performance [2,24]. increase productivity and improve quality in many applications, such (2) Vector control: The idea is to control AC motors in a way similar as home appliances, robots, pumps, fans, automotive, railway, to controlling separately excited DC motors, after introducing industrial processes and, recently, renewable energy. AC motors are some transformations. The three phase currents are converted themaindrivingforceinindustrybecauseoftheirsmallsize, into d, q current components id and iq, which correspond to the reliability, low cost and low maintenance [4,5,12,18]. Due to the field and armature currents of DC motors, respectively. If id is advancement of power electronics, digital signal processing (DSP), oriented (aligned) in the direction of the rotor flux and iq is etc., the technology of VSD for AC motors is matured and AC drives perpendicular to it, then the control of id and iq is decoupled, as have replaced DC drives in many application areas. There are mainly inthecaseofDCmotors.Thefrequencyisnotdirectlycontrolled three approaches developed for AC drives [4,6,12]: as in the scalar control but indirectly controlled; the torque is controlled indirectly via controlling the current. The advantage of (1) V/f control: The idea is to generate a variable-voltage–variable- vector control is that it provides good performance that is similar frequency sinusoidal power supply from a constant DC power to DC drives. The drawbacks of vector control are: (i) the flux source. The control variables are voltage and frequency while estimation and field orientation are dependent on motor para- maintaining their ratio constant to provide (almost) constant meters, which change in reality (e.g. with temperature); (ii) the controller is very complicated and (iii) the inverter is often current controlled via hysteresis-band PWM, which makes the fi ☆Some preliminary results of this work were presented at the 5th IET Interna- system analysis dif cult [3,9,11,16,22]. A lot of patches have been tional Conference on Power Electronics, Machines and Drives (PEMD) held in April developed for vector control to improve the performance 2010 in Brighton, UK and at the 20th International Symposium on Power [1,7,10,14,15,17,19,20,27]. Electronics, Electrical Drives, Automation and Motion (SPEEDAM) held in June (3) Direct torque (and flux) control: The torque (and stator flux) are 2010 in Pisa, Italy. n directly controlled via selecting appropriate inverter voltage Tel.: +44 114 22 25630; fax: +44 114 22 25683. E-mail addresses: Q.Zhong@Sheffield.ac.uk, [email protected] space vectors through a look-up table but the frequency is 1 http://encyclopedia2.thefreedictionary.com/Power+System+Load. indirectly controlled [8,26,30,28]. It uses hysteresis-based control,

Please cite this article as: Q.-C. Zhong, , AC Ward Leonard drive systems: Revisiting the four-quadrant operation of AC machines, European Journal of Control (2013), http://dx.doi.org/10.1016/j.ejcon.2013.05.013i 2 Q.-C. Zhong / European Journal of Control ∎ (∎∎∎∎) ∎∎∎–∎∎∎

which generates flux and torque ripples, and the switching frequency is not constant. It also needs motor parameters to fl estimate the torque (and stator ux) [13,23,29]. Again, the Load hysteresis-based control makes system analysis very difficult. Prime mover These three schemes have been further advanced for a long period Constant Variable with the development of related technologies in e.g. control theory speed speed and microelectronics. They are suitable for different applications because of their different characteristics [4,12,21]. The vector control and direct torque (and flux) control provide very good performance but the control algorithms involve several transfor- Controllable field Fixed field mations and are very complicated. What is worse is that look-up tables are used in the direct torque (and flux) control, which Fig. 1. Conventional (DC) Ward Leonard drive systems. makes the analytical analysis of the system very difficult. The high order of the resulting complete system from these approaches also 2. Ward Leonard drive systems means that the system stability is difficult to guarantee. V/f control is simple but the performance needs to be improved. Hence, a Induction motors, particularly those of the squirrel-cage type, simple high-performance AC drive that facilitates the analytical have been the principal workhorse for long time. However, until the analysis of the system is desirable. beginning of 1970s, they had been operated in the constant-voltage– From the viewpoint of control system design, the AC motor is constant-frequency (CVCF) uncontrolled mode, which is still very simply the load to an inverter. The main control objective of a common nowadays. VSDs were dominated by DC motors in the drive is to regulate the speed and the torque to obtain fast and Ward Leonard arrangement. Ward Leonard drive systems, also good response and the change of the motor parameters (including known as Ward Leonard Control, were widely used DC motor speed the load) should not impose a major problem to the system. Such control systems introduced by Harry Ward Leonard in 1891. A Ward an attempt is made in this paper, following the concept of Leonard drive system, as shown in Fig. 1, consists of a motor (prime operating inverters to mimic synchronous generators [33–35] mover) and a generator with shafts coupled together. The motor, and motivated by the conventional Ward Leonard drive systems which turns at a constant speed, may be AC or DC powered. The (WLDS). The physical interpretation of this is that the AC motor is generator is a DC generator, with field windings and armature powered by a synchronous generator (SG) driven by a variable- windings. The field windings are supplied with a variable DC source speed prime mover. The synchronous generator and the prime to produce a variable output voltage in the armature windings, which mover are then replaced by an inverter that behaves as a isusuallyusedtopowerasecondDCmotorthatdrivestheload. synchronous generator. The torque and speed of the AC motor A natural analogy is to replace the DC generator with a synchro- are then controlled via controlling the torque and frequency of the nous generator and the DC motor with an AC machine (an induction synchronous generator. The resulting control scheme is very motororasynchronousmotor);seeFig. 2(a). This configuration is simple as it does not involve vector transformations nor the called AC Ward Leonard drive systems [31,32]. It is worth noting that estimation of flux. No complicated concepts, e.g. vector control the physical implementation of anACWardLeonarddrivesystemis and field orientation, are needed and the scheme is very easy to of limited use, as described below. The prime mover in a DC WLDS understand. This also unifies the drive for synchronous motors maintains a constant speed and the flux of the generator is variable; (SM) and induction motors (IM). In the proposed scheme, the the prime mover in an AC WLDS needs to have a variable speed (so attention of how to design AC drives has shifted from motor- that the frequency of the output can be varied) and the flux of the oriented to inverter-oriented. This has led to an extremely simple generator is constant. The output of the generator (voltage) in a DC controller. It can also be treated as the proposed AC drive is WLDS is varied via controlling the field voltage and the output of the powered by a synchronous generator while the vector-controlled generator (voltage and frequency) in an AC WLDS is varied via AC drives are powered by a DC generator with some transforma- controlling the speed of the prime mover. If the speed of the prime tions. Another important advantage is that the complete system mover could be varied, it could have been used to drive the load can be described by the analytic mathematical models of the straight-away and hence there is no need to have a physical AC generator and the motor, which facilitate the analytical analysis of WLDS. Instead of having a physical synchronous generator that is the system. The comparison of the different types of VSDs is given driven by a variable-speed prime mover, an inverter that captures the in Table 1. main dynamics of the physical system (the synchronous generator, The rest of the paper is organised as follows. The concept of the the variable-speed prime-mover and its controller), as shown in DC Ward Leonard drive systems is reviewed and then extended to AC Fig. 2(b), can be used to power the motor, following the synchron- machines in Section 2. The mathematical model of synchronous verter concept of operating inverters to mimic synchronous generators is described in Section 3 and a control scheme is proposed generators [33–35]. Ideally, if the motor has the same pole number in Section 4 to implement the concept. Experimental results are asthegeneratorandtherewasnoloss,thetorqueofthegenerator shown in Section 6 and conclusions are made in Section 7. wouldbethesameasthetorqueofthemotor.Hence,thetorqueof the motor could be controlled via controlling the torque entering the synchronous generator.

Table 1 Comparison of control types for AC VSDs. 3. Model of a synchronous generator

Control type Frequency control Torque control Flux control The model of synchronous generators is very well documented V/f control Direct None None in many textbooks and other literature. Here, some changes are Vector control Indirect Indirect Direct made to the model developed in [34], assuming that the ﬂux Direct torque control Indirect Direct Direct established in the stator by the ﬁeld windings is sinusoidal AC WLDS Direct Direct Open-loop and that the stator winding resistance and inductance are zero.

Please cite this article as: Q.-C. Zhong, , AC Ward Leonard drive systems: Revisiting the four-quadrant operation of AC machines, European Journal of Control (2013), http://dx.doi.org/10.1016/j.ejcon.2013.05.013i Q.-C. Zhong / European Journal of Control ∎ (∎∎∎∎) ∎∎∎–∎∎∎ 3

The saturation effect of the machine is introduced by limiting the The mechanical dynamics of the machine is governed by ﬁ voltage to the rated value, as shown in Fig. 3. When the eld € _ T Jθ ¼ Tm−Te−Dpθ; current If is constant, the generated voltage e ¼½ea eb ec is ~ where J is the moment of inertia of all parts rotating with the rotor, e ¼ λθ_ sin θ ð1Þ Dp is the damping factor, Tm is the mechanical torque applied to where θ is the electrical rotor position (hence θ_ is the electrical the synchronous generator by the prime mover and Te is the angular speed), λ is the amplitude of the mutual ﬂux linkage electromagnetic torque given by ~ between the stator winding and the rotor winding, and sin θ is ~ Te ¼ pλ〈i; sin θ〉: ð2Þ the vector ½ sin θ sin ðθ−ð2π=3ÞÞ sin ðθ−ð4π=3ÞÞT : In fact, λ is also T the ratio of the generated voltage (amplitude) to the speed Here, p is the number of pole pairs per phase, i ¼½ia ib ic is the λ ¼ (angular) and Mf If , where Mf is the maximum mutual state current vector and 〈; 〉 denotes the conventional inner inductance between the stator winding and the rotor winding. ~ product. It is worth noting that if i ¼ I0 sin φ then Variable ~ ~ 3 T ¼ pλI 〈 sin φ; sin θ〉 ¼ pλI cos ðθ−φÞ; speed e 0 2 0 Prime Load SG SM/IM which is a constant DC value. This is a very important property, mover from which a simple control strategy can be designed to regulate Variable the speed of the AC machine. speed Fixed field 4. Control scheme with a speed sensor Inverter

Variable 4.1. Control structure speed Prime Load As explained before, the idea of the AC Ward Leonard drive system VDC SG SM/IM mover is to power the AC motor with a synchronous generator, driven by a Variable variable-speed prime mover that is implemented via an inverter. speed Hence, the focus of the control system is to control the generator instead of the motor. The mechanical torque T applied to the Fixed field m generator can be easily generated by a speed controller (governor), θ_ Fig. 2. AC Ward Leonard drive systems. (a) Natural implementation. (b) Proposed e.g. a PI controller, that compares the actual speed f with the _ implementation. reference speed θr. If the motor is synchronous, then the actual speed can be directly taken from the generator without a speed sensor as the motor runs at the synchronous speed θ_. If the motor is inductive, then the actual speed (mechanical) can be measured from the motor and it should be converted to the electrical speed via multiplying it with the number of pole pairs p. Usually this involves a low-pass ﬁlter to reduce the measurement noise. Another aspect could be easily taken into account is the voltage drop on the stator winding of the motor, particularly, when the speed is low. It can be compensated via a feed-

forward path containing the stator winding resistance Rs from current i to the generated voltage e. Thus, the resulting complete controller consists of a synchronous generator model, a speed measurement unit, a speed controller and a current feed-forward controller, as shown in Fig. 4. In order to speed up the system response and to minimise the number of tuning parameters, it is advantageous Fig. 3. Mathematical model of a synchronous generator. to choose the inertia of the generator to be J¼0 (i.e., zero inertia).

θ_ θ_ θ_ Fig. 4. Control structure for AC WLDS with a speed sensor. r , f and are all electrical speed.

Please cite this article as: Q.-C. Zhong, , AC Ward Leonard drive systems: Revisiting the four-quadrant operation of AC machines, European Journal of Control (2013), http://dx.doi.org/10.1016/j.ejcon.2013.05.013i 4 Q.-C. Zhong / European Journal of Control ∎ (∎∎∎∎) ∎∎∎–∎∎∎

Fig. 5. Control structure for AC WLDS without a speed sensor.

This also reduces the system order by one, which helps improve system stability. It is worth noting that the λ of the generator is always kept constant. When the speed of the generator exceeds the rated speed, the generated voltage is bounded by the rated voltage so that the insulation of the motor is not damaged (the voltage boost due to the current feed-forward path should not exceed the margin allowed, which is normally the case). It should be pointed out that p, λ and Rs shouldbechosenthesameasthoseofthemotor. The output u of the controller, which is the sum of the generated voltage and the compensated voltage drop on the motor stator winding, can be passed though a three-phase inverter, after appropriate scaling according to the DC-link voltage, to power the AC motor. Fig. 6. An experimental AC drive. The switches in the inverter are operated so that the average values of the inverter output over a switching period should be equal to u, which can be achieved by many known pulse-width-modulation Table 2 (PWM) techniques. Because of the inherent low-pass ﬁltering effect Parameters of the motor. of the motor, it may not necessary to connect LC ﬁlters to improve the total harmonic distortion. Parameters Values Parameters Values

Rs 0:17 Ω Rated frequency 128 Hz 4.2. System analysis and selection of parameters p 2 Rated speed 3621 rpm Rated voltage (line-to-line) 30 VRMS Rated torque 0.528 Nm In order to simplify the analysis, assume that the speed feedback _ _ _ is taken from θ, i.e., θf ¼ð1=ðτs þ 1ÞÞθ.ThetorqueTe can be regarded _ as a disturbance to simplify the analysis. The transfer function from torque −Te (regarded as a disturbance) to the speed θ is θ_ θ_ the speed reference r to the speed ,assumingzeroload,isthen 4τsðτs þ 1Þ H ðsÞ¼ ; ð þ Þðτ þ Þ T 2 KPs KI s 1 D ð2τs þ 1Þ _ ð Þ¼ : p Hθ s 2 Dpτs þðDp þ KPÞs þ KI which means that any step change in the (load) torque does not cause θ_ θ_ ð = Þθ_ _ For a step change of r, the speed jumps by KP Dp r,whichis a static error in the speed θ. If there is a step change Te in the torque, normally regarded as aggressive, and then settles down. In order to the speed jumps by ð1=DpÞTe and then recovers. Hence, in order to ¼ avoid this, take KP 0. Hence reduce the impact of the load on the speed, Dp should not be too small. The speed response is directly related to the time constant of KIðτs þ 1Þ H _ ðsÞ¼ : θ 2 the low-pass filter used in the speed measurement unit. The Dpτs þ Dps þ KI smaller the time constant, the faster the system response. This is a second order system and the poles are pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi The above analysis is approximate because the loop involving −17 1−4τKI=Dp the motor that affects Te is not fully considered and the speed s ; ¼ : 1 2 2τ feedback is not exactly taken from the motor. However, it does offer some insightful understanding to the system and, in princi- If K is chosen as I ple, reflects the system dynamics as can be seen from the Dp experimental results to be shown in the next section. It is worth KI ¼ ; 4τ noting that, although the above design leads to a non-oscillatory then the two poles are s1;2 ¼ −1=2τ and response, the closed-loop system in real implementation could be oscillatory because of the reasons mentioned above. τs þ 1 Hθ_ ðsÞ¼ : The four-quadrant operation of AC machines comes automati- ð2τs þ 1Þ2 cally with the proposed AC WLDS. There is no need to add any This would leave enough margin for the controller to cope with extra effort or device; the change of the sign of the speed reference uncertainties and parameter variations. The transfer function from changes the direction of the motor rotation. A positive frequency

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Fig. 7. Reversal at high-speed without a load. (a) Speed. (b) Torque of the generator. (c) Current. (d) Voltage.

Fig. 8. Reversal at high-speed with a load. (a) Speed. (b) Torque of the generator. (c) Current. (d) Voltage. 6 Q.-C. Zhong / European Journal of Control ∎ (∎∎∎∎) ∎∎∎–∎∎∎

Fig. 9. Reversal at low-speed without a load. (a) Speed. (b) Torque of the generator. (c) Current. (d) Voltage.

(speed) reference leads to a positive speed and a negative The slip of an induction motor can be compensated to some extent as _ frequency (speed) reference leads to a negative speed. A change well. It is well known that the speed drop θs is in proportion to the of the frequency from negative to positive, or from positive to torque over a wide speed range, i.e. negative, leads to the reversal of the motor rotation. _ In summary, the speed response is determined by the time θs ¼ KT Te: constant τ of the speed measurement unit and the torque response – is determined by Dp. The parameters of the controller can be This can be obtained from the torque speed characteristics of the chosen as follows: motor. For synchronous motors, KT¼0. This load (torque) effect can be _ compensated via adding KTTe to the speed reference θr. The resulting

(1) Choose p, λ and Rs the same as, or close to, those of the motor speed-sensorless control scheme for AC machines is shown in Fig. 5.It and choose J¼0. consists of the model of a synchronous generator, a speed controller, a (2) Determine the time constant τ to meet the requirement of the load-effect compensator and a current feed-forward controller, which speed response (also the requirement of the measurement is a feed-forward path containing the stator winding resistance Rs

noise) and Dp to meet the requirement of the torque response. from current i to the generated voltage e.Thisschemeisapplicablefor ¼ (3) Choose KP ¼0 and KI ¼ Dp=4τ. both synchronous (with KT 0) and induction motors. For synchronous motors, it provides zero-static-error speed control; for induction motors, there is normally a small static error depending on the compensation accuracy of the load (torque) effect. The accuracy can

5. Control scheme without a speed sensor beimprovedviausingatwo-dimensionaltabletodetermineKT according to the torque–speed characteristics of the motor, taking into 5.1. Control structure account both the synchronous speed and the torque.

If the motor is synchronous, then there is no need to have a speed sensor because the speed of synchronous motor converges to the speed θ_ of the generator, which is internally available in the 5.2. System analysis and selection of parameters controller for feedback. Even for induction motors, θ_ is the synchronous speed and can be used to reﬂect the actual motor In order to simplify the exposition below, consider the case speed (the difference is the slip). In this case, Dp canbechosenas0. when the motor is synchronous, i.e., KT¼0. The transfer function

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Fig. 10. Reversal at low-speed with a load. (a) Speed. (b) Torque of the generator. (c) Current. (d) Voltage.

_ _ from the speed reference θr to the speed θ, assuming zero load, is In summary, the control parameters can be chosen as follows:

KPs þ KI _ ð Þ¼ λ Hθ s 2 (1) Choose p, and Rs the same as, or close to, those of the motor Js þ KP s þ KI and choose Dp¼0. and the transfer function from torque −Te (regarded as a distur- (2) Determine the time constant τ to meet the requirement of the bance) to the speed θ_ is speed response and J to meet the requirement of the torque s response. HT ðsÞ¼ : 2 (3) Choose KP ¼ J=τ and KI ¼ KP=4τ. Js þ KP s þ KI (4) Choose KT according to the torque–speed characteristics of the The system is of second order and the poles are motor (K ¼0 for synchronous motors). qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi T − 7 − = 2 1 1 4KIJ KP s1;2 ¼ : 6. Experimental results 2J=KP The proposed AC WLDS was verified on an experimental Increasing KI tends to make the system response oscillatory. Define system, as shown in Fig. 6. The system consists of an inverter, a τ ¼ J=KP, i.e., KP ¼ J=τ.IfKI is chosen as board consisting of current sensors, a dSPACE DS1104 R&D con- K J K ¼ P ¼ ; troller board equipped with ControlDesk software, and an induc- I 4τ 4τ2 tion motor. The motor parameters are given in Table 2. According ¼ − = τ then the two poles are s1;2 1 2 . Under this set of parameters to the parameters, it can be found that λ ¼ 0:0305 and KT¼86.82. τ þ The inverter has the capability to generate PWM voltages from a ð Þ¼ 4 s 1 ; Hθ_ s constant 42 V DC voltage source and the motor is equipped with a ð2τs þ 1Þ2 bi-directional encoder with 1000 lines for speed measurement. 4τ2s HT ðsÞ¼ : 6.1. Case 1: with a speed sensor for feedback Jð2τs þ 1Þ2

The speed response can be tuned by changing τ and the torque The control parameters were chosen as τ ¼ 0:1 s and Dp ¼0.08, response can be tuned by changing J. which results in KI¼0.2. Many experiments were carried out to

Please cite this article as: Q.-C. Zhong, , AC Ward Leonard drive systems: Revisiting the four-quadrant operation of AC machines, European Journal of Control (2013), http://dx.doi.org/10.1016/j.ejcon.2013.05.013i 8 Q.-C. Zhong / European Journal of Control ∎ (∎∎∎∎) ∎∎∎–∎∎∎

Fig. 11. Reversal at an extremely low speed without a load. (a) Speed. (b) Torque of the generator. (c) Current. (d) Voltage.

Fig. 12. Reversal at high-speed without a load (without a speed sensor). (a) Speed. (b) Torque of the generator. (c) Current. (d) Voltage. Q.-C. Zhong / European Journal of Control ∎ (∎∎∎∎) ∎∎∎–∎∎∎ 9 test the performance of the system and some of the results are that the sequence of the three phase currents/voltages changed at shown here. around t¼0.8 s.

6.1.1. Reversal at high-speed without a load 6.1.4. Reversal at low-speed with a load The reference speed was changed from −3600 rpm to 3600 rpm The reference speed was changed from −300 rpm to 300 rpm at at around t¼0.6 s. The responses (speed, torque, current and around t¼2.2 s. The responses are shown in Fig. 10. The motor voltage) are shown in Fig. 7. The motor quickly reversed from quickly reversed from −300 rpm to 300 rpm in about 2 s. There −3600 rpm to 3600 rpm and settled down in about 1.2 s. There was a noticeable stop in the middle of the reversal process. The was a very short period of over-current around 70%; the voltage over current was about 50%. dropped when the reversal was started and then gradually built up after the reversal. The phase sequence of the currents was changed 6.1.5. Reversal at an extremely low speed without a load at around 0.85 s, which corresponds to the change of the rotating The reference speed was changed from −4.5 rpm to 4.5 rpm at ﬁ direction of the magnetic eld, to enable the reversal. around t¼5 s. The responses are shown in Fig. 11.Ittookabout15s to complete the reversal and settle down due to the extremely low 6.1.2. Reversal at high-speed with a load speed. There were some ripples in the measured speed, which was The reference speed was changed from −1800 rpm to 1800 rpm owing to the error in the measurement unit (the motor actually at around t¼1 s. The responses are shown in Fig. 8. The motor rotated smoothly). The motor speed dropped to 0 quickly but quickly reversed from −1800 rpm to 1800 rpm in about 1.5 s, remained standstill for about 12 s, duringwhichthetorqueincreased which is slightly longer than the case without a load. There was almost linearly, before the torque was accumulated high enough to about 11% overshoot in the speed and the over current increased start the motor. Once the current gradually increased to a level that is to about 150%. enough to generate the required torque, the motor started rotating.

6.1.3. Reversal at low-speed without a load 6.2. Case 2: without a speed sensor for feedback The reference speed was changed from −150 rpm to 150 rpm at around t¼0.6 s. The responses are shown in Fig. 9. It took about The control parameters were chosen as τ ¼ 0:1 s and J¼0.08,

1.5 s to complete the reversal and settle down. The over-current which results in KP¼0.8 and KI¼2. Many experiments were was only about 15% and the speed overshoot was about 6%. Note carried out and some of the results are shown here.

Fig. 13. Reversal at high-speed with a load (without a speed sensor). (a) Speed. (b) Torque of the generator. (c) Current. (d) Voltage.

Please cite this article as: Q.-C. Zhong, , AC Ward Leonard drive systems: Revisiting the four-quadrant operation of AC machines, European Journal of Control (2013), http://dx.doi.org/10.1016/j.ejcon.2013.05.013i 10 Q.-C. Zhong / European Journal of Control ∎ (∎∎∎∎) ∎∎∎–∎∎∎

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