A Design Synthesis Method for Robust Controllers of Active Vehicle Suspensions

In this study, we investigate a robust H∞ controller for a quarter-car model of an active inerter-based suspension system under parameter uncertainties and road disturbance. Its main objective is to improve the inherent compromises between ride quality, handling performance, suspension stroke, and energy consumption. Inerters have been extensively used to suppress unwanted vibrations from various kinds of mechanical structures. The advantage of inerter is that the realized ratio of equivalent mass (inertance relative to the mass of the primary structure) is greater than its actual mass ratio, resulting in higher performance for the same effective mass. First, the dynamics and state space of the active inerter-based suspension system were achieved for the quarter-car model with parameter uncertainties. In order to attain the defined objectives, and ensure that the closed-loop system achieves the prescribed disturbance attenuation level, the Lyapunov stability function, and linear matrix inequality (LMI) techniques have been utilized to satisfy the robust H∞ criterion. Furthermore, to limit the gain of the controller, some LMIs have been added. In the case of feasibility, sufficient LMI conditions by solving a convex optimization problem afford the stabilizing gain of the robust state-feedback controller. According to numerical simulations, the active inerter-based suspension system in the presence of parameter uncertainties and external disturbance performs much better than both a passive suspension with inerter and active suspension without inerter.

This paper investigates the problem of robust sampled-data Hinfin control for active vehicle suspension systems. By using an input delay approach, the active vehicle suspension system with sampling measurements is transformed into a continuous-time system with a delay in the state. The transformed system contains possibly non-differentiable time-varying state delay. The controller design is cast into a convex optimization problem with LMI constraints. A quarter-car model with active suspension system is considered and the effectiveness of the proposed approach is illustrated by a realistic design example.

Linear matrix inequality (LMI) methods, novel techniques in solving optimisation problems, were introduced as a unified approach for vehicle's active suspension system controller design. LMI methods were used to provide improved and computationally efficient controller design techniques. The active suspension problem was formulated as a standard convex optimisation problem involving LMI constraints that can be solved efficiently using recently developed interior point optimisation methods. An LMI based controller for a vehicle system was developed. The controller design process involved setting up an optimisation problem with matrix inequality constraints. These LMI constraints were derived for a vehicle suspension system. The resulting LMI controller was then tested on a quarter-car model using computer simulations. The LMI controller results were compared with an optimal PID controller design solution. The LMI controller was further tested by incorporating a nonlinear term in the vehicle's suspension model; the LMI's controller degraded response was enhanced by using gain-scheduling techniques. The LMI controller with gain-scheduling gave good results in spite of the unmodelled dynamics in the suspension system, which was triggered by large deflections due to off-road driving.

Some robust control methods have been developed in the past in order to increase tracking performance in the presence of parametric uncertainties. In the presence of parametric uncertainty, unmodelled dynamics and other sources of uncertainties, robust control laws are used. Corless-Leitmann [1] approach is a popular approach used for designing robust controllers for robot manipulators. In early application of Corless-Leitmann [1] approach to robot manipulators [2, 3], it is difficult to compute uncertainty bound precisely. Because, uncertainty bound on parameters depends on the inertia parameters, the reference trajectory and manipulator state vector. Spong [4] proposed a new robust controller for robot manipulators using the Lyapunov theory that guaranties stability of uncertain systems. In this approach, Leithmann [5] or Corless-Leithman [1] approach is used for designing the robust controller. One of the advantage of Spong’s approach [4] is that uncertainty on parameter is needed to derive robust controller and uncertainty bound parameters depends only on the inertia parameters of the robots. Yaz [6] proposed a robust control law based on Spong’s study [4] and global exponential stability of uncertain system is guaranteed. However, disturbance and unmodelled dynamics are not considered in algorithm of [4, 6]. Danesh at al [7] develop Spong’s approach [4] in such a manner that control scheme is made robust not only to uncertain inertia parameters but also to robust unmodelled dynamics and disturbances. Koo and Kim [8] introduce adaptive scheme of uncertainty bound on parameters for robust control of robot manipulators. In [8], upper uncertainty bound is not known as would be in robust controller [4] and uncertainty bound is estimated with estimation law in order to control the uncertain system. A new robust control approach is proposed by Liu and Goldenerg [9] for robot manipulators based on a decomposition of model uncertainty. Parameterized uncertainty is distinguished from unparameterized uncertainty and a compensator is designed for parameterized and unparameterized uncertainty. A decomposition-based control design framework for mechanical systems with model uncertainties is proposed by Liu [10]. In order to increases tracking performance of uncertain systems, design of uncertainty bound estimation functions are considered. For this purpose, some uncertainty bound estimation functions are developed [11-15] based on a Lyapunov function, thus, stability of

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In this paper a fuzzy Sugeno rule based controller is used to manage a semi-active suspension of 1/4 vehicle model. Our semi-active suspensions have the characteristic to change the damping constant in order to reduce vertical oscillation of the vehicle, to restrain the shell vehicle acceleration and consequently to be more comfortable for passengers. On the other hand, if no control is present, the suspension works in passive mode, i.e. without damping parameters changing. The inputs of our fuzzy controller, three in total, are the dynamic wheel load described by five membership functions, its derivative and the vertical acceleration both described by three membership functions. By comparing the performances of the suspension with and without control, the Sugeno based model controller results in a more comfortable and safe system.

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<div class="section abstract"><div class="htmlview paragraph">The performance of suspension system has a direct impact on the riding comfort and smoothness. For the traditional suspension can not effectively alleviate the impact of road surface and the poor anti-vibration performance, The dynamics model of vehicle suspension system is established, and the control model of vehicle four-degree-of-freedom active suspension is designed with fuzzy control strategy. On this basis, a comprehensive simulation model of the control model of vehicle active suspension coupled with road excitation is established. and the ride comfort of vehicles under different types of suspension are tested through Simulink. The simulation results show that compared with the passive suspension, the reduction of vehicle acceleration and dynamic deformation of the active suspension controlled by fuzzy PID can reach 33.76% and 22.45%. and the reduction of pitch Angle speed and dynamic load of the active suspension controlled by fuzzy PID can reach 16.18% and 10.72%. Under fuzzy PID control, the amplitude of each evaluation index of active suspension in the suspension system is substantially reduced than that of the passive suspension, and the root-mean-square value decreases by about 10% on average. It can be seen that the active suspension with fuzzy PID control can improve the performance of the suspension system on the basis of ensuring the stability and rapid response of the system, and can well reduce the random vibration caused by the impact of the vehicle on the random road surface during the driving process, improve the ride comfort, smoothness and ride safety of the vehicle, and achieve a good control effect on the vehicle suspension.</div></div>

Design of robust PI controller is proposed to control the dynamic behavior of vehicle active suspension system with hydraulic actuator followed by road disturbances. A graphical approach, using stability boundary locus in the (k p , k i ) -plane is used to compute the PI controller parameters. The stability boundary locus in the (k p , k i ) -plane is plotted by applying a gain-phase margin tester in the system to achieve the required gain margin and phase margin. In reality, all physical systems contain uncertainties. To take care of parameter uncertainties present in all physical systems, Kharitonov theorem is used.

A nonlinear robust controller design method is proposed for the lateral control of heavy vehicles for automated highway systems. In the controller design, the actuator dynamics is explicitly taken into account. A first order pre-filter is introduced to reduce chattering which is inherent in the nonlinear robust controller and to prevent the saturation in the front wheel steering angle and steering system slew rate. A constructive backstepping design technique is utilized in the design of a robust controller for the augmented system. Simulation results are shown.

Innovative approaches for analysis, design and modeling of advanced flight vehicles are demanded in response to requirements toward substantial performance improvements. Although control theory is thoroughly developed, the calculus of variations and Pontryagin's principle are not well suited because these methods exhibit rather poor robustness and are hampered by the limited time available for computations. This paper explores the robust control technology for uncertain nonlinear systems and presents innovative design procedures to enhance the robustness for open-loop unstable systems with constraints. Utilizing the Hamilton-Jacobi theory, the developed procedures allow one to find a straightforward avenue to design the robust controllers. A new control methodology is less conservative than the known results and allows us to solve the nonlinear control problem for uncertain systems. The explored time-optimal and antiwindup techniques are studied for a highly-manoeuvrable missile. The longitudinal and rolling flight control, as well as the guidance problem, are treated and solved. To evaluate the robustness, analytical and simulation results are performed.

Active vehicle suspension systems play a vital role in isolating vibration between the pavement and chassis. In this paper, to further enhance the driving comfort level while maintaining correlative suspension operation safety, a novel membership functions (MFs)‐dependent‐based optimization control policy is first proposed for quarter nonlinear active vehicle suspension systems under a Takagi‐Sugeno (T‐S) fuzzy framework. In view of that, different subsystems may have diverse interference attenuation upper boundaries. We combine the information of MFs with a common performance index, such that for the fuzzy rules that have high proportions, a relatively small disturbance attenuation index can be obtained. Compared with the existing traditional method, the practical response of the interference attenuation index is efficaciously decreased, thus a superior driving comfort level and better suspension requirements manifestations can be obtained. Lastly, an illustrative example is presented to testify to the superiorities and advantages of the proposed novel robust optimization control algorithm.

Suspension system is used to fulfil the criteria of ride comfort and road handling. In this paper, a quarter car active & semi-active suspension systems are designed using Matlab/Script software. Comparison of active & semi-active suspension systems are done using robust control theory for the control targets suspension deflection, body acceleration and body travel. H infinity controller is selected to compare the two suspensions using time domain analysis. Finally the simulation result prove the effectiveness of the active suspension system by decreasing the body acceleration & sustaining the suspension deflection and body travel outputs.

Most control techniques require the use of a plant model during the design phase in order to tune the controller parameters.The mathematical models are an approximation of real systems and contain imperfections by several reasons: use of low-order descriptions, unmodelled dynamics, obtaining linear models for a specific operating point (working with poor performance outside of this working point), etc.Therefore, control techniques that work without taking into account these modelling errors, use a fixed-structure model and known parameters (nominal model ) supposing that the model exactly represents the real process, and the imperfections will be removed by means of feedback.However, there exist other control methods called robust control techniques which use these imperfections implicity during the design phase.In the robust control field such imperfections are called uncertainties, and instead of working only with one model (nominal model), a family of models is used forming the nominal model + uncertainties.The uncertainties can be classified in parametric or structured and non-parametric or non-structured.The first ones allow representing the uncertainties into the model coefficients (e.g. the value of a pole placed between maximum and minimum limits).The second ones represent uncertainties as unmodelled dynamics (e.g.differences in the orders of the model and the real system) (Morari and Zafiriou, 1989).The robust control technique which considers more exactly the uncertainties is the Quantitative Feedback Theory (QFT).It is a methodology to design robust controllers based on frequency domain, and was developed by Prof. Isaac Horowitz (Horowitz, 1982;Horowitz and Sidi, 1972;Horowitz, 1993).This technique allows designing robust controllers which fulfil some minimum quantitative specifications considering the presence of uncertainty in the plant model and the existence of perturbations.With this theory, Horowitz showed that the final aim of any control design must be to obtain an open-loop transfer function with the suitable bandwidth (cost of feedback) in order to sensitize the plant and reduce the perturbations.The Nichols plane is used to achieve a desired robust design over the specified region of plant uncertainty where the aim is to design a compensator C(s) and a prefilter F(s) (if it is necessary) (see Figure 1), so that performance and stability specifications are achieved for the family of plants.