Sterownik skyhook i sterownik logiki rozmytej dla zawieszenia półaktywnego samochodu Skyhook and fuzzy logic controller of a semi active vehicle suspension
15
0
0
Pełen tekst
(2) 98. Grzegorz laski, Micha Maciejewski. elements of a variable stiffness and damping elements of a variable damping ratio, a suspension is able to adapt to various driving conditions. As in case of a passive suspension the designer has to find an optimal parameter set for the spring and the damper to reach the trade-off between comfort and safety, in case of a suspension with variable stiffness and damping he can define an area of a compromise (not just single values for both stiffness and damping). Having the variable-parameter suspension the main problem lies in finding of a real-time control algorithm for these parameters. There are some known control strategies such as on-off skyhook, on-off groundhook, continuous skyhook, hybrid control strategy and many others. This article presents an application of fuzzy logic control theory to building of a controller for semi-active suspension. The presented suspension is a precise model of a real passenger vehicle (compact class front wheel drive car with estate body) rear suspension and real shock absorber with a continuously changeable damping coefficient.. 2. SUSPENSION MODEL A linear quarter car model (an example is presented in figure 1) is a model of a car suspension that is most often used for a preliminary design of a suspension and semi-active suspension controllers. This model is adequate only for investigation of the bounce motion of the chassis and the wheel without taking into account pitch and roll vibration. However, it was used due to its comparability with the physical one quarter car model used by the authors during laboratory tests of semi-active suspension control.. Fig. 1. Quarter car passive suspension model. However, in this paper a more complicated quarter car model was used to investigate a behavior of a suspension of a chosen type of a car with electronically controlled shock absorbers. The model has nonlinear characteristics of spring and shock absorber determined by experimental tests conducted on a real suspension and suspension elements. These test were performed by the authors with components of a passenger car and the. .
(3) Sky-hook and fuzzy logic controller of a semi active vehicle suspension. 99. methodology and the results were described in earlier papers [1,2] – the obtained characteristics are presented in figure 2.. Fig. 2. Characteristics of nonlinear quarter car suspension model: a) characteristics of spring, b) characteristics of passive shock absorber, c) characteristics of semi-active shock absorber. Figure 2c presents the characteristics of the semi-active shock absorber controlled with various level of electric current by the use of a by-pass valve as this type of a shock absorber is used in the modeled suspension. The shock absorber was of electrohydraulic damper type [3] similar to piezoelectric dampers [4]. However, in general other types of semiactive dampers can also be used – for example magnetorheological [3,5,6] or electrorheological [3] and even friction dampers [7].. .
(4) 100. Grzegorz laski, Micha Maciejewski. The model was implemented in Matlab/Simulink environment and was described by a pair of second-order differential equations of motion:. z1. 1 (Fk1 Fc1 ) g m1. z2. 1 (Fk2 Fc2 ) (Fk1 Fc1 ) g m2. (1). where: z1 – vertical acceleration of the sprung mass, z2 – vertical acceleration of the unsprung mass, Fk1, Fk2 – stiffness forces of the suspension spring and the tire: Fk1. k1 (z 2 z1 ),. Fk2. k 2 (h z 2 ). Fc1, Fc2 – damping forces of the shock absorber and the tire: Fc1. g. c1 (z 2 z 1 ),. Fc2. c 2 (h z 2 ). – acceleration due to Earth's gravity; equal to 9,81 m/s2. Suspension stiffness and suspension damping coefficients are not a constants like in a linear model. The suspension stiffness coefficient is a function of suspension deflection, and damping coefficient is a function of suspension velocity and control signal level (controller use 0 for minimum value and 1 for maximum value and this is calculated to the shock absorber valve current in amps). Suspension model was implemented in Simulink and was built using blocks – each block for each functional element of the suspension model: body mass, spring and damper, wheel, tire and controller and also subsystem for calculation of longitudinal dynamics and road excitations (Fig. 3). The longitudinal dynamics block models vehicle dynamics in direction x as a rigid body dynamics with known initial velocity and deceleration value. This model can be generally more complicated; for example, it can allow to define time varying deceleration. It can be also expanded with a model of drive train dynamics. But the goal to add the x direction dynamics to the vertical suspension dynamics was to obtain the linearly decreasing frequency of the road excitation in a way similar to driving on road with constant wave length but variable vehicle speed. This allowed to investigate the suspension dynamics over a range of frequencies.. The road height block uses the interpolation method for finding the present road height by analyzing driven distance (the result of X_dynamics block) and the predefined road heights as the road x length function. The blocks “quarter_car_body” and “wheel (unsprung mass)” are modeling equations of vertical motions (1) of the sprung and unsprung mass respectively. The spring and the shock absorber block uses interpolation functions and saved characteristics functions to. .
(5) Sky-hook and fuzzy logic controller of a semi active vehicle suspension. 101. find the present values of the spring or damper forces adequately to the present suspension deflection or its velocity regarding the control current level. The tire model is a linear one of the vertical tire stiffness.. Fig. 3. Structure of nonlinear semi-active quarter car suspension model with a fuzzy logic controller. .
(6) 102. Grzegorz laski, Micha Maciejewski. 3. SUSPENSION CONTROLLER Authors investigated two controllers for the presented nonlinear quarter car suspension model. A classical skyhook strategy controller and a fuzzy logic controller which is a generalization of the former one. The results obtained for both controllers were compared to the results for passive nonlinear suspension. The model of suspension is based on rear suspension of real passenger car of compact class with electrohydraulic semi-active shock absorbers with a proportional by-pass valve.. 3.1. SKYHOOK CONTROLLER The skyhook control strategy is one of classical, comfort-oriented semi-active control strategies. The principle of this strategy is to mimic a theoretical situation where the body mass is linked with the damper to the so-called “sky” in order to reduce the vertical oscillations of car body. The control algorithm emulates the damping forces of skyhook damper using semiactive damper in order to achieve body comfort specifications [3,7]. The most known and simplest skyhook control strategy is called an on-off skyhook. Using this strategy the damper is controlled by switching between two damping values – minimum and maximum. Determination of whether the damper is to be adjusted to highor low-damping state depends on the product of the suspension velocity (relative velocity of the body against the wheel) and the absolute velocity of the vehicle body. If the product is positive or zero, the damper is adjusted to its high state, otherwise, the damper is set to the low state. For the quarter-car model (Fig. 1), this strategy is summarized by: 1 12 t 0 maximum damping 1 12 0 minimum damping. (1). . When the damper is in a rebound phase, the force of the damper acts to pull down on the vehicle body mass; when the damper is in a compression phase, the force of the damper pushes up on the mass. Thus, when the absolute velocity of the body mass is negative and it is traveling downwards the maximum (high state) value of damping is desired to push up the mass. If the absolute velocity of the body mass is positive – the mass is traveling upwards, the maximum (high state) value of damping is desired to pull down the mass. The on-off skyhook semi-active policy emulates the ideal body displacement control configuration of a passive damper “hooked” between the body mass and the “sky”.. 3.2. FUZZY SKY-HOOK CONTROLLER Fuzzy logic is a form of a multi-valued logic as opposed to a classical two-valued logic. It was based on fuzzy set theory by Lotfi Zadeh [9,10] and proposed to deal with. .
(7) Sky-hook and fuzzy logic controller of a semi active vehicle suspension. 103. impreciseness. Fuzzy logic, although being still controversial for some mathematicians, has gained a great popularity and appreciation, and has been successfully applied in many scientific areas. One of these areas is control theory where fuzzy logic is often applied to dynamic process control in a form of a fuzzy controller. Fuzzy controllers are widely used in the automotive industry where automatic transmissions, ABS and cruise control systems are frequently based on this paradigm of control theory. The idea of fuzzy control is to operate on rules that are human-readable and represent a human’s heuristic knowledge about how to control a process. All rules are represented in a form of fuzzy logic implications. The fuzzy controller consists of four main components [11] presented in figure4. Its goal is to generate the input u(t) for the controlled process based on the process output y(t) and the reference signal r(t). In case of suspension vertical dynamics control problem, u(t) signal is the suspension damping control signal, while y(t) is a pair of the sprung and unsprung mass velocities. In case of the sky-hook strategy there is no need for the reference signal r(t). Fuzzy control has many properties that make it suitable for semi-active suspension control. First of all, a semi-active suspension is a complicated nonlinear system. It consists of many elements that has nonlinear dynamics, e.g. tires, shock absorbers, springs and some rubber elements. Of course all these nonlinearities may be linearized with a lesser or greater impact on the model precision.. Fig. 4. General fuzzy controller architecture [11]. Secondly, and even more importantly, there exists no single optimal control criteria for semi-active suspension policy. In general, it is assumed that vehicle suspension operation should be considered with two criteria: safety and comfort. These two criteria are generally conflicting with each other, but neither of them can be described with a single commonly accepted and optimality proven measure. As a result, scientists and engineers use different arbitrary chosen heuristic measures. As it was stated in the previous sections, a fuzzy controller can be easily provided with different heuristic rules that directly or indirectly aim in maximization or minimization of any selected measures. In the conducted research the fuzzy controller was implemented as an extended version of classical skyhook control policy in Matlab/Simulink environment and with the use of Fuzzy Logic Toolbox [13].. .
(8) 104. Grzegorz laski, Micha Maciejewski. The aim of the research was to create a fuzzy sky-hook controller that would be a generalization of the classical sky-hook controller. Similar rules can be found in works of other researchers, for example in [12]. Therefore, the rules presented in (1) were used to create fuzzy logic rules according to Mamdani fuzzy control model. As in the classical sky-hook strategy, the (implicit) goal was to maximize the comfort, which means minimization of the body mass oscillations. Similarly to the classical skyhook controller, the input for the fuzzy controller were the sprung mass absolute velocity and the suspension velocity (velocity difference between the sprung mass (body) and the unsprung mass (wheel)). Input signals were fuzzified according to the set of trapezoid membership functions presented in figure 5a with three linguistic variables: N – negative, Z – zero, and P – positive. On the other hand, the controller output was the damping level (between 0 for minimum value and 1 for maximum value) of the semi-active damper. Figure 5b presents the set of membership functions used for defuzzification of the output. The linguistic variables for the output were: S – small, M – medium, and L – large. a). N. Z. P. 1. 0.5. 0 - 1.5. -1. - 0.5. 0. 0.5. 1. 1.5. b). Fig. 5. Membership functions: a) input signals (both input velocities), b) output signal (damping level). .
(9) Sky-hook and fuzzy logic controller of a semi active vehicle suspension. 105. The rules for the fuzzy controller were derived from the skyhook policy with the extension for Z (zero) variables. Fig.6 shows the set of rules in tabular and IF-THEN forms. . v12. v1. N. Z. P. N. L. M. S. Z. M. S. M. P. S. M. L. IF IF IF IF IF IF IF IF IF. (v1 (v1 (v1 (v1 (v1 (v1 (v1 (v1 (v1. is is is is is is is is is. N) N) N) Z) Z) Z) P) P) P). AND AND AND AND AND AND AND AND AND. (v12 (v12 (v12 (v12 (v12 (v12 (v12 (v12 (v12. is is is is is is is is is. N) Z) P) N) Z) P) N) Z) P). THEN THEN THEN THEN THEN THEN THEN THEN THEN. (c (c (c (c (c (c (c (c (c. is is is is is is is is is. L) M) S) M) S) M) S) M) L). Fig. 6. Fuzzy logic rules. 4. SIMULATION RESULTS The simulation tests were compared with results of measurements performed on a real suspension system built as a laboratory quarter car suspension test stand excitated by a mechanical system used to technical shock absorber inspection (Fig. 7). As can be seen in figure 7, a change in a damping level from the minimum to the maximum (the valve control current was changed from 1.65 A – the lowest damping, to 0 A – the highest damping) is decreasing almost twice the vertical velocity of the relative sprung and unsprung masses. But in the real system this process is more smooth due to current rising time in response to the control signal change. It is also important to remember that measured accelerations and displacements had some disturbances so the estimates of relative suspension velocities are not exactly those velocities. The simulation tests were conducted for three suspension models: nonlinear model of passive suspension, semi-active suspension with skyhook controller (SH), and semi-active suspension with fuzzy logic skyhook based controller (FL SH). The first case of road excitation was sinusoidal (wave length – 2 meters) with changing frequency because of modeled longitudinal dynamics - the vehicle was braking with deceleration of 3 m/s2 from velocity 20 m/s until stopped. The absolute body displacement was lowered using both skyhook and fuzzy logic controllers – especially in the lower frequencies (Fig. 8). Skyhook gave slightly better results. They were not as good as in the investigated earlier by the authors linear models [7] due to the real limitations of the modeled semi active shock absorber. The minimum damping forces for the semi active shock absorber for a compression phase were almost the same as for the passive shock absorber. This fact has a good implication for safety measured as the tire deflection and the wheel displacement. This is a very important because of the limited suspension working space and the vertical tire load variations.. .
(10) 106. Grzegorz laski, Micha Maciejewski. The skyhook strategy, the best for the body displacement optimization, gave the greatest wheel displacements. The fuzzy logic skyhook based strategy gave wheel displacements comparable with the passive suspension displacements at frequencies from 10 to 5 Hz, and only greater at smaller frequencies. damping level[0...1] 1. controlled damping level semiactive SH semiactive FL SH. 0.5. 0 1 suspension velocity [m/s]. 1.2. 1.4. 1.6. suspension velocity. 1.8. time [s]. passive semiactive SH semiactive FL SH. 0.04 0.02 0 -0.02 -0.04. . 1. 1.2. 1.4. 1.6. 1.8. time [s]. a). . b). . Fig.7. Results of skyhook controlled suspension dynamics: a) simulation results, b) laboratory test stand measurements. .
(11) Sky-hook and fuzzy logic controller of a semi active vehicle suspension. 107. The first simulation tests were conducted for a quite high amplitude of road excitation and a quite long wave length – 2 meters. The second presented results (Fig.9) are for a shorter wave length – 0.85 m and 5 times smaller amplitude (0.002 m) of road excitations. What is important in these results – SH FL controller having smooth switching behavior due to fuzzy limits of membership functions – is giving the area of damper work much smaller than its full range of possible damping force limits. The shock absorber is working mainly in the area of 30 to 50 % of maximum damping force. This type of controller behavior is very useful due to the potential to diminish effect of nonlinearities of dynamics of suspension controlled by the on-off skyhook method described in literature [14]. absolute wheel displacement wheel displacement [m]. -0.01 -0.02 -0.03 passive semiactive SH semiactive FL SH. -0.04 0. 1. 2. semiactive SH semiactive FL SH. 3. 4 time [s]. 5. 6. 7. 8. 5. 6. 7. 8. 6. 7. 8. controlled damping level. damping level[0...1]. 1 0.8 0.6 0.4 0.2 0 0. 1. 2. 3. 4 time [s]. absolute body displacement body displacement [m]. -0.1 passive semiactive SH semiactive FL SH. -0.11 -0.12 -0.13 -0.14 -0.15. 0. 1. 2. 3. 4 time [s]. 5. Fig. 8. Simulation results for sinusoidal road input (wave length 2 m, amplitude 0.01 m). .
(12) 108. Grzegorz laski, Micha Maciejewski. This effect of added nonlinearities due to on-off control strategy analyzed with use of the Fourier transform is showing that the discontinuities of damping force are the reason of the sprung mass acceleration discontinuities. The on-off control method as used in the classical SH algorithm introduces new frequency content to the suspension system output while reducing the amplitude of vibrations at excitation frequency. The results obtained with use of the proposed FL SH algorithm show a potential to reduce this effect while being almost equally effective while the suspension relative velocity and the sprung mass velocity are quite high as in the SH control algorithm. wheel displacement [m]. absolute wheel displacement -0.018 -0.02 -0.022 passive semiactive SH semiactive FL SH. -0.024 -0.026. 0. 1. 2. 3. 4 time [s]. 5. 6. 7. 8. damping level[0...1]. controlled damping level 1. semiactive SH semiactive FL SH. 0.5. 0. body displacement [m]. 0. -0.12. 1. 2. 3. 4 5 time [s] absolute body displacement. 6. 7. 8. 6. 7. 8. passive semiactive SH semiactive FL SH. -0.125 -0.13 -0.135. 0. 1. 2. 3. 4 time [s]. 5. Fig.9 Simulation results for sinusoidal road input (wave length 0.85 m, amplitude 0.002 m). .
(13) Sky-hook and fuzzy logic controller of a semi active vehicle suspension. 109. Other road excitations consisted of two step inputs (plus 0.04 m and minus 0.04 m), one after another in specified distance, in order to simulate a pot hole and a bump in a kind of so-called “sleeping policeman”. The response of the semi-active suspension on excitation in form of pot hole (depth: 0.04 m, length 0.1 m) was clearly more efficient than the response of the passive suspension what is shown in figure 10.. body displacement [m]. absolute wheel displacement. -0.02 -0.025 -0.03. passive semiactive SH semiactive FL SH. -0.035 -0.04 1. 1.2. a). 1.4 time [s]. 1.6. controlled damping level. 1.8. 2. semiactive SH semiactive FL SH. damping level[0...1]. 1 0.8 0.6 0.4 0.2 0 1. 1.2. 1.4 time [s]. 1.6. 1.8. 2. absolute body displacement body displacement [m]. -0.126 -0.128 -0.13 -0.132 -0.134. passive semiactive SH semiactive FL SH. -0.136 -0.138 1. b). 1.2. 1.4 time [s]. 1.6. 1.8. Fig.10 Simulation results for pot hole road input (depth 0.04, length 0.1 m) a) body and wheel displacements, b) damping level and body displacement. . 2.
(14) 110. Grzegorz laski, Micha Maciejewski. Body displacement of both suspensions – with skyhook and fuzzy logic controllers were several times smaller than passive. Fuzzy logic controller gave slightly bigger body displacement but also smaller wheel displacement. Comparing damping levels of the skyhook and the fuzzy logic controller, we can see that in fact fuzzy logic controller gave continuously changeable damping levels.. 5. CONCLUSIONS In this paper, the example of the skyhook and the fuzzy logic skyhook based control method applied to semi-active suspension was presented. Investigations made by authors showed that this method provides better compromise between the body and the wheel displacements and gives much more elastic construction of the control strategy than the classical on-off skyhook control strategy. The use of the fuzzy skyhook logic controller helps also to manage the problem of generation of additional frequencies in suspension system response when using only simple on-off control with skyhook algorithm. Another advantage of the fuzzy logic controller is the fact that it uses a fuzzy set of membership of input signals which are not so precise in the reality as during mathematical simulation. With some level of statistical error they can be in one or second set – the linear membership function tries to model it in some way. The presented examples outlined also the future research areas, i.e. the problem of optimization of the fuzzy logic rules and the membership functions. In the conducted research the fuzzy controller was tuned manually, but due to the large search space, finding the optimal configuration of the controller requires an automatic optimization procedure. It should be pointed out that not only the controller but also the shock absorber characteristics (and its constraints) strongly influences the quality of the results. The investigated shock absorbers had a great potential for improving safety and comfort with higher vehicle loads but were not enough effective in improvement of comfort for sinusoidal road excitation. This was caused by a quite high level of the lower constraint for of the damping forces.. References 1. Pikosz H., laski G.: Problem zmiennoci obcienia eksploatacyjnego pojazdu w doborze wartoci tumienia w zawieszeniu, ARCHIWUM MOTORYZACJI, 1/2010 , pp. 35-44. 2. Pikosz H., laski G.: Badania charakterystyk pracy amortyzatorów o regulowanym elektronicznie tumieniu – metodyka i narzdzia bada , Zeszyty Naukowe Instytutu Pojazdów Politechniki Warszawskiej nr 1(77)/2010, pp. 321-332. 3. Savaresi, S. M. i inni: Semi-Active Suspension Control Design for Vehicles, Oxford: ButterworthHeinemann Ltd (Elsevier), 2010, 4. Makowski M., Grzesikiewicz W., Knap L.: Ograniczenie drga pojazdu za pomoc sterowanych tumików piezoelektrycznych, Zeszyty Naukowe Instytutu Pojazdów, 3(79)/2010, pp. 75-82. .
(15) Sky-hook and fuzzy logic controller of a semi active vehicle suspension. 111. 5. Makowski M., Grzesikiewicz W., Knap L., Pokorski J.: Badanie moliwoci ograniczenia drga pojazdu przy uyciu sterowanych amortyzatorów magneto-reologicznych, Zeszyty Naukowe Instytutu Pojazdów, 3(62)/2006, pp. 33-53 6. Sapi ski B.: Real-time control for a magnetorheological shock absorber in a driver seat, Journal of Theoretical and Applied Mechanics, 43, 3, pp. 631-653, Warsaw 2005 7. Guglielmino E. i inni: Semi-active Suspension Control: Improved Vehicle Ride and Road Friendliness, Springer-Verlag, London, 2008 8. laski G., Walerja czyk W.: Moliwoci poprawy bezpiecze stwa czynnego przez zastosowanie zawieszenia póaktywnego, Czasopismo Techniczne – Mechanika, Zeszyt 7, 2004, 9. Zadeh L.A.: Fuzzy sets. Information and Control. 1965. 8: pp.338–353. 10. Zadeh L.A.: Fuzzy logic and its application to approximate reasoning. Information Processing 74, Proc. IFIP Congr. 1974 (3), pp. 591–594. 11. Passino K.M., Yurkovich S.: Fuzzy Control, Addison Wesley Longman, Menlo Park, CA, 1998. 12. Carter A. K.: Transient Motion Control of Passive and Semiactive Damping for Vehicle Suspensions Thesis submitted to the Faculty of the Virginia Polytechnic Institute and State University, 1998 13. www.mathworks.com/products/fuzzylogic 14. Eslaminasab N.: Semi-active Intelligent Suspension System – From Theory to Implementation, VDM Verlag Dr Müller, Saarbrücken 2009.. STEROWNIK SKYHOOK I STEROWNIK LOGIKI ROZMYTEJ DLA ZAWIESZENIA PÓAKTYWNEGO SAMOCHODU Streszczenie: W artykule przedstawiono przykad zastosowania sterowania dwustanowego (typu „on-off”) skyhook oraz wykorzystania sterownika logiki rozmytej bazujcego na idei skyhook do sterowania zawieszeniem póaktywnym samochodu. Badania wykonano z wykorzystaniem nieliniowego modelu zawieszenia wiartki samochodu z charakterystyk rzeczywistego amortyzatora póaktywnego z zaworem obejciowym. Pozostae parametry modelu byy wyznaczone dla samochodu wyposaonego w ten typ amortyzatorów i zredukowane do parametrów modelu zawieszenia wiartki samochodu. Wyniki symulacji dynamiki zawieszenia porównano z wynikami pomiarów dla rzeczywistego zawieszenia sterowanego tym samym sterownikiem skyhook jak wykorzystany w badanym modelu. Autorzy porównali jako pracy zawiesze pasywnego, sterowanego wedug zasady skyhook oraz sterowanego z uyciem sterownika rozmytego bazujcego na zasadzie skyhook. Badania wykonane przez autorów pokazay, e ta metoda daje potencja do poprawy dziaania zawieszenia oraz znacznie bardziej szerokie moliwoci ksztatowania strategii sterowania w porównaniu z klasyczn dwustanow strategi skyhook Sowa kluczowe: wiartkowy model zawieszenia, zawieszenie póaktywne, sterownik logiki rozmytej. Recenzent: Wodzimierz Choromaski. . .
(16)
Powiązane dokumenty
Strategisch belang locatie voor het rijk: een aantal rijksgebouwen staat op locaties die, al is het gebouw niet meer van belang voor de huisvesting van de Rijksoverheid, van
The results from the model structure selection procedure and parameter estimation are presented in this section together with a model validation by applying the iden- tified
In a construction made of Steel S235 (fig. 3b) the total mass exceeds the assumptions while stress is the lowest. in this case an intensive optimization should be implemented in
The scheme of a suspension of a vehicle on the basis of a four-link lever mechanism is investigated, which involves the use of a main elastic element that perceives
[r]
Zdaniem wnioskodawcy, oznacza to wyłom w zasadach wykonywania zawodów, których istota polega na świadczeniu pomocy prawnej, tj. Wyjątek
Diagnozowanie zawieszeń przeprowadza się w dwojaki sposób. Pierwszy polega na prowadzeniu badań na obiektach rzeczywistych z zaprogramowanymi usterkami. Drugi to
The paper presents selected results of work in the Air Force Institute of Technology in research of fire suppression system SSP- FK (as one of main protection systems on-board)
