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1、附录一英文文献翻译Fuzzy control for active suspensionsFernando J. D Amato, Daniel E. ViassoloAbstract:School of Aeronautics and Astronautics, Purdue University, West Lafayette, USAA methodology for the design of active car suspension systems is presented. The goal is to minimize vertical car body acceleratio
2、n, for passenger comfort, and to avoid hitting suspension limits, for component lifetime preservation. A controller consisting of two control loops is proposed to attain this goal. The inner loop controls a nonlinear hydraulic actuator to achieve tracking of a desired actuation force. The outer loop
3、 implements a fuzzy logic controller which interpolates linear locally optimal controllers to provide the desired actuation force. Final controller parameters are computed via genetic algorithm-based optimization. A numerical example illustrates the design methodology.1. IntroductionThe basic idea i
4、n active control of suspensions is to use an active element to apply a desired force between the car body and the wheel axle. This desired force is computed by the cars control unit to achieve certain performance objectives under external disturbances. Although passive suspension systems can effecti
5、vely handle some control objectives, active suspension systems are currently replacing them. This happens mainly because active systems offer more design flexibility, and thus the range of achievable objectives increases.Active suspension systems reduce car body accelerations by allowing the suspens
6、ion to absorb wheel accelerations. This is achieved at the expense of using more suspension travel, and thus increasing the probability of hitting the suspension rattle-space limits. Hitting the rattle-space limits translates into both passenger discomfort and wear of vehicle components. These consi
7、derations motivate us to investigate the ride/rattle-space trade-off for active suspensions. This paper focuses on the problem:Design an active suspension system to avoid hitting the rattle-space limits for large suspension travels, and to minimize the car body acceleration for small suspension trav
8、els.We present an approach for solving the problem stated above. Our approach uses both an inner control loop and an outer control loop. The inner loop controls the hydraulic actuator to track a desired actuation force. The outer loop implements a fuzzy logic controller, with parameters computed by
9、a GA-based optimization. Our major contribution is a detailed design methodology to solve this particular class of problems. The approach combines different control design techniques to achieve performance dependent of the perturbation size. The methodology is applied to a quarter-car suspension sys
10、tem.2. Mathematical modelThe mathematical model for the suspension dynamics is briefly described as follows. Consider the quarter-car active suspension system shown in Fig. l.The wheel and the axle are connected to the car body through the spring damper actuator combination. The tire is modeled as a
11、 simple spring.The parameters of this model are: the body mass Mb, the wheel mass Mw, the dampingcoefficient Ca, the spring coefficient Ka, the tire spring coefficient Kt.The dynamics for the suspension system, excluding the actuator and when the suspension travel is below its physical limit, is des
12、cribed by the linear equation:XT一 A 一 1 r-r A mi */WhereZ x x is the suspension travel, Z Z , Z x , and Z Z . The inputsare1 b213 w43the road disturbance r and the actuator force F.Numerical values for the model parameters are given below:Mb =49 kg, Mw =59 kg, Ka =16,812 N/m, Ca 1000 =Ns/m, Kt =190,
13、000 N/m3. Control problemThe control objective is to maximize the passenger comfort, while preserving the lifetime of suspension components, under road disturbances. The comfort is determined by the level of vertical car body acceleration experienced by the passenger. The lifetime of components is p
14、reserved by avoiding hitting the rattle space limits. Hence, the controller objectives can be stated as: (a) increase, with respect to open-loop, the range of typical road disturbances for which the suspension travel limits are not reached, and (b) minimize the peaks of the body accelerations under
15、road disturbances.a(1 cos(8兀)/2if 0.5 t 0.75let the set of typical road disturbances be of the form:r (t)I 0otherwise4. Design methodologyTo solve the control problem stated in the previous section we propose the following two-step procedure:1. Design an inner loop controller for tracking actuator c
16、ommands, and2. Design an outer loop controller to satisfy performance requirements.The inner loop controller produces the actuator input u which makes the actuator force F track the force command Fcmd. This controller attempts to cancel the actuator nonlinearities. The outer loopcontroller produces
17、the force command Fcmd to achieve performance. This controller has performance requirements that depend on the size of the perturbations. Namely, we have one performance objective when the perturbations are relatively small, and another performance objective when the perturbations are large. For thi
18、s outer loop controller we propose a fuzzy architecture, to schedule the control action according to the perturbation size. A representation of this configuration is shown in Fig. 2Fig. 2. Schematic of interconnection.Fig. 1. Quailer-cai model5. Methodology specifics5.1 Inner loop controller-sgn Sat
19、JF)Given a command signal Fcmd for the actuator force F, is described bywhere u is defined by：Z =人 Z K 人(F sat (F)cc c c cFlv = aA2 Z + (PX ) sat (F) + 人(F+ Z ) + F + Zt cmd c cmd c2t Flwe choose:人1260,人=2000K = 105.2. Outer loop controllerThe proposed outer loop controller is a so called parallel d
20、istributed compensator (PDC) based on a Takagi-Sugeno (TS) representation of the input/ output description of the dynamics. This TS representation can be interpreted as an interpolation of a set of linear systems. The proposed PDC consists in an interpolation of optimal controllers designed for each
21、 of the rules of the TS model.5.2.1. Takagi-Sugeno fUzzy systemThe input/output dynamics from r, Fcmd is approximately linear and replac F by Fcmd,then:zl = Azl + B r + B FIn the following, the fuzzy Takagi-Sugeno (TS) description is used to accommodate the nonlinear performance requirements for the
22、 linear dynamics equation. For small disturbances, the performance is measured in terms of body acceleration, while for large disturbances the performance is measured in terms of suspension travel. The suitability of the TS description is justified as follows. FIRST, it allows the specification of d
23、ifferent performance outputs for different disturbance amplitudes. Second, it provides the structure to schedule a set of optimal controllers for the local performance objectives. A key observation is that the scheduling in terms of the perturbation size a can be reformulated in terms of the suspens
24、ion travel amplitude Izll.Our TS description is based on the linguistic variable suspension travel amplitude h, defined by the set:,U ,(ti, tm),(巴,日)where U 0, Z1 is the universe of discourse of h.The m rules of the TS description defining the linear dynamics have the form:Rule i: IF h is Ti, THEN Z
25、 AZl + Br + B F for i = 1,. . .,m. hl12 cmd5.2.1.1. Membership functionsThe individual membership functions considered are piecewise combinations of 7th order polynomials. Each membership function is parameterized in terms of the transition abscissas, as described next.日；is given by:The membership f
26、unction for the first term setT；,11 - P (h)cl, dl0ififif0 h c1 c h dd hPc1, d1(h) is a 7 th order polynomial. For the term sets hi=2, (m-1)日ih is given by: 0P(h)ai ,bi11 - P(h)ci, di0if 0 h ai if ai h bi if bi h ci if ci h di if di h ziand for the last term set Tm ,日mh is given by: 0 ifPam ,bm (1ifi
27、f0 h amam h bmbr h Z1We impose the following constraints for the transition abscissas：a c , b d , i = 2,3mThe set of membership functions for the TS model is parameterized by the abscissas a , b , c , d , which are collected in the membership function parameter vector:i i i iP = a .a b .bc .cd .d m
28、2 m 2 m 1 m-11 m-15.2.1.2. TS representationFinally, the TS representation that accommodates the nonlinear performance requirements is given by the linear dynamics equation and the following fuzzy blending of the performance output:e(t) = C (t) Zl (t) + D(t) F (t)With: C(t)空n (t)C, d()空n (t)d ,t) =
29、.=1.=1乙目 j (h(t)lj=1The performance output e is parameterized in terms of 人.and p . ,for i =1,2,. . .,m, which are collected in the performance parameter vector:P =人.人p .p p 1 m1 m5.2.2. Parallel distributed compensatorWe use a parallel distributed compensator (PDC). This PDC is obtained by designin
30、g a static state-feedback controller Ki for each rule i = 1,2,. . .,m. A key point is that for the blending we utilize the same fuzzy sets as for the TS model. To be more precise, the actuator force command becomes:m5) = K(g(f) =j=iSince the local performance output is parameterized in terms of Pp a
31、nd the membership functions are parameterized in terms of Pm, the PDC inherits the same parameterization of the TS representation in terms of both Pm and Pp.5.2.3. GA-based parameter selectionAs stated before, the PDC is parameterized by Pm and Pp. Based on our knowledge of the control system, it is
32、 not difficult to select parameter vectors pm and pp that achieve a fairly good performance. However, to achieve an even better performance this intuitive approach is not good enough. In this section, we propose to use a GA for selecting the final pm and pp.The GA used for choosing Pm and Pp include
33、s the standard processes for population initialization, reproduction, crossover, and mutation, and maximizes a fitness function that captures the performance objectives. This fitness function is given by:J(Pm.PP) =J1-J2-J3WithJ1十J2+J3Ji 二 -(5) 1必1-(5)WO尤(5)力= 2 (11)1。* -1)-(U)-值弓-(U).小驾Where is the
34、ratio between the closed and open loop maximum peak of the body acceleration response to 5 cm bumps (11 cm bumps), and Z1 is the maximum peak of the suspension travel z1 for the closed loop response to 11 cm bumps.The controller evaluation is performed via time-domain simulations.6. Results一 -couc a
35、pe0UMP-llcmE -GAB=，UnwiHiGIBUMJ5CE05-U05 o=0, 【旦号el= -dsa*-time sedz一 JotenTSe-50CK?0DL511.52llm* |sc0.511.522.6tme secFig. 6 C2fs and 5 cm bumpFig. 5 C2fs and 11 cm bumpUsing the proposed design methodology, we obtained three controllers: C2fs, C3fs and C4fs, which make use of 2, 3 and 4 fuzzy sets
36、, respectively. The parameters defining these controllers are given in Tables 1-6.Table 1 Controller C?知 parameter勺 pin fin cm) defining the rneinbership functionsalblcldla2b2c2d24.45397.56094.45397.5609Table 2 Contiollei C2fc D parameters pp defimiig the perforniance outputsA 1A 2p 1p 21034.746237.
37、3661Table 3 Controller C3fs parameters pm (m cm) defining the membership fimctionsalblcldla2b20.39832.31650.39832.3165c2d2a3b3c3d35.33976.81835.33976.8183Table 4 Contiollei C3fc D parameteis pp defimiig the perforniance outputsA 1A 2A3P 1P 2P 310.9236039.548795.738328.2616Table 5 Controller C4fs par
38、ameters pm (in cm) defining the meiiibersliip fimctioiisalblcldla2b2c2d21.48643.06461.48643.06465.05856.5626a3b3c3d33.4b4c4poq0UMP=5crn11,52urng | 跑05Q&5 o-0. -U1 一TRJ-dsns11.5Hrhfi seela.511522 5lime seeQ5O05 o-0 巨-QAlth.dsnsFig. 7 C3fs and 11 cm bump-?gJoLo-nnBe站11.622.53iime sedl?IBauoenswnBUMP-1
39、1 cmFig. 8 C3fs and 5 cm bumpBUMP=5crrt1.522.5t Ti?l5c051S.52Z53lime 蚣 |Fig. 10. C4fs and 11 cm biunpFig. 11. C4fs and 5 cm bumpAs a result of the previous analysis performed on the three controllers C2fs, C3fs and C4fs, it is concluded that the controllers C2fs and C4fs, performed approximately the
40、 same, and better than controller C3fs.3 Then, a good candidate for implementation is C2fs, since it has the least associated complexity. The achieved performance for this controller can be summarized by: With respect to open-loop, the passenger comfort was improved by 58% for small/medium road dist
41、urbances, while the maximum bump amplitude for which the suspension limits are not hit was increased by 18%.7. ConclusionsAn approach is presented for active suspension design which uses both inner and outer control loops. The inner loop controls the nonlinear hydraulic actuator in order to track th
42、e desired actuation force. The outer loop implements a fuzzy logic controller with parameters computed by GA-based optimization.The major contribution is a detailed design methodology to solve this particular class of problems. The approach combines different control design techniques to achieve per
43、formance dependent on the perturbation size. The method consists in producing a class of controllers parameterized in terms of a small number of parameters, which are selected with the aid of a GA algorithm to obtain desired performance levels. Incorporation of other design objectives can be done in
44、 a straightforward manner.The methodology proved effective when applied to a quarter-car model of a suspension system.Further work is needed to address the robustness of the resulting controllers, and to exte nd the methodology to full-car models.汽车主动悬架模糊控制研究费尔南多阿马托，丹尼尔瓦索罗美国普渡大学航天航空学院摘 要：本文介绍了一种通用的汽
45、车主动悬架控制系统设计方法，设计主动悬架控制系统的 日的是保证乘客的舒适度，尽量减小车身垂直振动加速度，并避免车身碰撞悬架限位块，从 而延长各零部件的使用寿命。控制系统包括两个控制回路，外环控制是一个线性插值局部最 优控制器，用模糊逻辑控制器来实现，内环控制的对象为非线性液压执行机构，用来跟踪控制 器要求输出的控制力，最后应用遗传算法优化了控制参数，并通过数值分析验证了该设计方 法的有效性。1、引言关于主动悬架控制，最基本的理念是用有源元件产生控制力作用在的汽车车身和车轴之 间，这种控制力可以根据外部的扰动情况，由汽车的控制系统控制作动器产生。传统的被动 悬架系统只能实现个别的控制日标，而主动悬架系统具有很多的设计灵活性,可以增加日标 的控制范围，所以，主动悬架系统正在逐渐取代被动悬架。主动悬架系统通过悬架吸收车轮的加速度来降低车身垂直振动加速度，这是以增加 悬架动行程为代价实现的，而且增加了车身与限位块碰撞的概率。车身与限位块碰撞会使得 乘客感到不舒适，并且会导致汽车零部件的磨损，这些因素促使我们对悬架的动行程进行控 制研究。本
