MECHANICS Vol. 24 No. 2 2005 MECHANICS Vol. 24 No. 2 2005 Krzysztof PLAZA* SEMIACTIVE CONTROL STRATEGIES FOR A FULLY SUSPENDED BICYCLE SUMMARY The purpose of this work is to present methods for designing semiactive vibration systems, which include mathe- matical models of vibrating structures. Thus aspects of model building, identification and verification are descri- bed in the paper as well as determination of the performance indices, choice of the damping technique, shock ab- sorber modeling and algorithm selection. The article presents a semiactive vibration system analysis of a fully su- spended bicycle. For all of the simulation experiments and serving as a reference for the identification experiment a phenomenological model of the bicycle was developed in the Simulink environment. The model was confronted with the real time experiments, which were conducted with the help of an electrical system. The necessity of the discussion of the various performance indices is underlined. Simple control strategy is tested on the bicycle. Keywords: semiactive systems, vibration damping, nonlinear systems, full suspension bicycle, identification STRATEGIE STEROWANIA PÓ£AKTYWNYM ZWIESZENIEM W ROWERZE Artyku³ przedstawia metody sterowania uk³adem pó³aktywnego t³umienia drgañ w pe³ni zawieszonym rowerze Scott G-Zero Fx-2. Zaprojektowano elektryczny uk³ad wspomagaj¹cy sterowanie t³umikiem MR bazuj¹cy na pomiarze przyspieszenia. W celu przetestowania uk³adów regulacji zaprojektowano model fenomenologiczny roweru wyposa- ¿onego w t³umiki MR. W artykule zaprezentowano rozwa¿ania dotycz¹ce metody identyfikacji modeli nieliniowych zaproponowanych przez autora. Przedstawiono równie¿ strategie sterowania zawieszeniem pó³aktywnym roweru. 1. INTRODUCTION the recent publications state that proper control can provide fully active behavior of the semiactive MR suspension sys- Although the idea of semiactive suspension has been know tems [3]. and studied in the last decade there are few commercial ap- The paper introduces an MR suspension system in a fully plications in offer. The reason for that is the control difficul- suspended Scott G-Zero Fx-2 bicycle (Fig. 1). ty and still maintenance and resistance problems. One of the The bicycle rear suspension has been replaced by a Lord first commercial applications of other than passive suspen- RD-1005-03 MR damper and a dedicated spring, which can sion in the automotive industry was an active pneumatic generate a force of 2 kN to 2.5 kN. Lord W-Box is used for suspension introduced by Lotus. It is obvious that such su- current flow setting in the MR damper windings. An electri- spension requires huge amounts of energy, and is thus eco- cal circuit has been designed (MTB MRS Mountain Bike nomically unjustifiable. In applications were energy amo- Magnetorheological Suspension System) to control the MR unt is crucial and bounded like the automotive industry damper current depending on the measurements of the acce- semi and quarter active suspension systems are being recen- lerations of primarily 2 and eventually 4 elements of the tly developed. One of the known commercial applications is bicycle. For control tests a simplified phenomenological the Delphi MagneRide used in Cadillac STS automobi- les. MagnetoRheological (MR) suspension is effective, ho- wever because of the used MR fluids, which are temperatu- re sensitive and loose their agility under stress, there is still work to be done in the field of their design and the design of the control suspension systems with MR fluids. Recently most of the work devoted to applications of the MR and ER suspension dampers concentrates on vibration damping in the automotive machines [4, 5, 7, 11] and beam structures such as buildings or bridges for seismic protec- tion [6, 13, 15]. Although some attempts have been made to construct an MR damper for bicycles [2, 11] few applica- tions if any have been developed to yield a complete control system. Although semiactive suspensions offers low energy ope- ration it is difficult to control because of its nonlinear natu- re since the parameters change serves as a control signal. Furthermore it can only offer vibration damping throughout Fig. 1. MR suspension system in a fully suspended bicycle the control of the energy dissipation. However some of * Institute of Automatic Control, Silesian University of Technology, Gliwice, Poland, [email protected] 135 Krzysztof PLAZA SEMIACTIVE CONTROL STRATEGIES FOR A FULLY SUSPENDED BICYCLE model of the bicycle with MR damper [1] has been assem- of the suspension system design such model can be simpli- bled in the Simulink environment. Since behavior of the fied greatly just as it has been done in [3, 4, 10]. For the first most of the plants cannot be approximated by linear models phenomenological model only vertical bicycle parts move- a nonlinear identification is considered with the use of the ment is taken into account. With that assumption the model method described by K. Plaza in [9]. presented in Figure 2 has been constructed. Determining the control index in the automotive machi- nes is more complicated than it is in 1-D simulations. Beha- vior of the suspension should be adjusted depending on the road situation. That aspect is considered in the paper. C C 1 2 1 4 A few of the control algorithms, which are mentioned in z z the publications [3, 4, 10] are discussed for the bicycle su- spension control. m r,J r C 3 2 d z d 3 z 1 k 1 2 k 2 r 2. BICYCLE AND MTB MRS DESCRIPTION z m m 2 ? 3 b a The fully suspended Scott G-Zero Fx-2 has been upgraded r r ko d ko d o by substituting its oil damper with an MR damper in the rear o suspension (Fig. 1). A 3.4 Ah, 12 V Panasonic Battery has been attached to the bicycle to provide the power supply for Fig. 2. Bicycle phenomenological model the Lord W-Box and the MTB MRS electrical system. The acceleration/orientation sensors have been attached to The forces assigned by C1, C2, C3, represent vertical for- the front fork and under the saddle. Eventually 4 measure- ces generated by the bicycle rider respectively on the han- ments in 2 axis will be used, additionally on the handlebars dlebars, saddle and pedals. According to that mechanical and the rear wheel axis. model the equations describing the bicycles vertical move- ment on the road were derived: 2.1. MTB MRS system &&=− − − & − & − − − mzrr k11()() z z 2 d 11 z z 2 m rg C 1 MTB MRS is an electrical circuit of the elements and (1) features (Tab. 1). −−− −−&& − CCkzz23243()() dzz 243 Table 1. MTB MRS parts description mz&&=−+−− k()() z z dz & z& 22 1 1 2 1 1 2 (2) −− −−−& & Element name Features mg22 kobob()() z r d z 2 r Core module with Rabbit processor, mz&&=−+−− k()() z z d z&z & RCM3000 core module 3.3V Supply, 512kB Flash, Ethernet, 33 2 4 3 2 4 3 (3) I/O, Low Power, Timers… −− −−& −& m33g kzoaoa()() r dz 3 r ADS8345 16 bits, 8 channels, SPI… DAC7513N 8 bits, 1 channel, SPI... Jrϕ=&& cos() α −ϕ ⋅ Cr −sin() α −ϕ ⋅ C − rC113212 C Atmel DataFlash 8MB Flash memory −α−ϕ⋅+rFcos() (4) Power Circuit 12V input, 5V,3.3V output 1 CT11 LCD Display Low power +α−ϕ⋅+α−ϕ⋅rFrmgsin() sin() 3 CTmgmgr22 Keyboard 4 buttons for communication where: 12V supply, 0-5V control, 0-2 A Lord W-Box™ output =− − −&& − (5) FkzzdzzT 11()() 2 11 2 MEMSIC 1 2 orthogonal outputs, ± 2g range accelerometers Fkzzdzz=−()() − −&& − (6) T2 24 3 24 3 The above described circuit allows for MR suspension control and data acquisition. zz=− rsin( α− ) 11,01 1r (7) −−+α+ϕ 3. BICYCLE PHENOMENOLOGICAL MODEL (zzrrr,0 ) 1 sin( 1 r ) To completely model bicycles behavior on the road an =− α− zz44,03 rsin( 2r ) enormous amount of factors would have to be taken into (8) −−+α+ϕ account as it has been done in [8]. However for the purpose (zzrrr,0 ) 3 sin( 2 r ) 136 MECHANICS Vol. 24 No. 2 2005 All of the parameters, which are not shown for the sake The model described by the above equation was assembled of clarity in Figure 2 are the geometrical parameters of the in the Simulink environment. tested bicycle (r1, r3, rmg, αC1, αC2, αmg, α1r, α2r). Assuming that the rear shock absorber includes an RD-1005-03 MR damper the following equations given by 4. CONTROL STRATEGIES B.F. Spencer Jr., S.J. Dyke, M.K. Sain, J.D. Carlson in [1], can be included in the phenomenological model descrip- Last 50 years of achievement in the field of semiactive con- tion: trol algorithms are shortly described by D. Hrovat [4]. In the recent years due to the growth of the application possibili- ties semiactive control has been developed further. Benefits f =+c y& kxx() − (9) 1 MR o of such approach are strongly underlined however the con- trol difficulties due to inherited nonlinear dynamics still nn−1 zx& =−γ&& −y zz −β() x && −y zAx + () && −y (10) make it challenging to apply. Automotive machines force higher level algorithms use for satisfactory riding perfor- mance. In automotive suspension system analysis the car 1 y&&=α++−[] zcxkxy() (11) models where simplified throughout quarter or semi car + 00 cc10 models and neglect the bounds of possible displacement of suspension parts, which stand an additional nonlinearity. α=α+α (12) ()uuab That also forces the performance indexes to be verified. Se- veral control strategies for a fully suspended bicycle are =+ (13) mentioned in the following paragraphs. cu111() cab cu =+ (14) 4.1. First principle control cu000() cab cu Assuming that the performance index trying to be mini- uuv& =−η() − (15) mized is the mean value of the acceleration of the saddle, a simple first principle control algorithm can be designed.