RELIABLE ROBUST CONTROLLER FOR HALF-CAR ACTIVE SUSPENSION SYSTEMS BASED ON HUMAN-BODY DYNAMICS

The paper investigates a non-fragile robust control strategy for a half-car active suspension system considering human-body dynamics. A 4-DoF uncertain vibration model of the driver’s body is combined with the car’s model in order to make the controller design procedure more accurate. The desired controller is obtained by solving a linear matrix inequality formulation. Then the performance of the active suspension system with the designed controller is compared to the passive one in both frequency and time domain simulations. Finally, the effect of the controller gain variations on the closed-loop system performance is investigated numerically

The Institution of Engineering and Technology

Abstract: In a debate paper, Keel and Bhattacharyya have suggested, by means of simple examples taken from the open literature, that optimal and robust controllers can be fragile in the sense that a minute perturbation in the controller parameters can make the closed-loop system unstable. However, is it true that the optimal and robust controllers presented by Keel and Bhattacharyya are actually fragile? It is demonstrated that the particular parametric stability margin used by Keel and Bhattacharyya can be very conservative and to overcome this problem, two non-conservative measures of controller fragility are proposed. In addition, it will be shown that the examples in Keel and Bhattacharyya's paper are very special and the resulting fragility cannot be linked to the H 1 optimisation but to non-appropriate H 1 optimisation criterions and to bad choice of weights. Introduction In . Different explanations for the fragility problem can be found in the literature. Mäkilä [4] examine Examples 3, 4 and 5 of [1] and present a procedure for assessing the fragility on the basis of the inherent robustness of the closed-loop system to perturbation in the physical parameters that make up implementation, using first-and second-order active RC filters in the implementation of continuous-time controllers and considering the effects of floating point erros in the implementation of digital controllers. More recently, Examples 1 and 2 of [1] have been revisited In spite of all the works listed in the previous paragraph, some questions still remain to be answered. Is it true that the optimal and robust controllers presented in [1] are actually so fragile? More importantly, is it true that the controllers obtained as solutions of the simple optimisation criteria presented in [1] are necessarily fragile? In this paper, these questions are answered and it is demonstrated that the particular stability margin used by Keel and Bhattacharyya can be very conservative and to overcome this problem, two non-conservative measures, based on necessary and sufficient conditions, are proposed here. In addition, it will be shown that the examples presented in [1] are very special and the resulting fragility cannot be associated with H 1 optimisation but to non-appropriate H 1 optimisation criterions and to bad choice of weights. This paper is organised as follows: in section 2, the relative parametric stability margin is reviewed, and an example that suggests the conservativeness of this measure is presented. In section 3, two nonconservative measures of controller fragility are proposed and a comparison between the relative parametric stability margin and the two nonconservative measures introduced in this paper is drawn. In section 4, the examples used in [1] to label H 1 controllers as fragile are re-examined. Finally, conclusions are drawn in section 5. 2 Relative parametric stability margin Definition Consider a closed-loop system with unit negative feedback, wher

Defragilization in optimal design and its application to fixed structure LQ controller design

In this work, we present a general methodology to address the recently debated fragility issue in optimization-based modern control systems design. Based on this methodology we have developed a defragilization procedure which is applied to fixed structure linear quadratic (LQ) control design. Issues regarding computational efficiency of the procedure and the relationship between controller fragility and controller parameterization are discussed via two examples taken from practical applications. The first example is based on a rotary cement kiln control application and the latter example on a wing flutter control application. The procedure could also be used in design problems with specifications which are related to controller nonfragility requirements, e.g., so as to allow some degree of controller online tuning.Validerad; 2001; 20061222 (ysko)</p