89-3457-cp LINEAR QUADRATIC GAUSSIAN DESIGN FOR ROBUST PERFORMANCE OF A HIGHLY MANEUVERABLE AIRCRAFT'

This paper describes a technique for selecting the weighting functions of the LQGLTR formal synthesis procedure to satisfy a robust performance objective. The procedure is applied to a robust performance design problem for the longitudinal dynamics of a highly maneuverable aircraft. 1 . Introduction A major objective of feedback system design is to achieve a nominal performance specification for a given design model of the plant, and to maintain this performance over a range of expected errors between the design model and the true plant. Although no single performance specification can encompass all the relevant engineering design objectives, a reasonable compromise can be achieved by representing the basic performance specification as a bound on the weighted power spectrum of the input disturbances and performance outputs. Similarly, the errors between the design model and the true plant can often be reasonably represented with a nonparametric (unstructured uncertainty) model. In such cases, the structured singular value [Doy82] can be used to provide an exact measure of the robust performance of any given feedback system design. Since the structured singular value can be used to analyze the ability of a given design to achieve robust performance, it is reasonable to also use the structured singular value directly as the objective of the feedback system design problem. One such approach has been developed in [Doy83, Doy851. The feedback system design problem is formulated as an optimization problem, with the objective of minimizing the supremum (over all frequencies) of the structured singular value. While this approach has been successfully appEed to several problems [Doy84, SkM861, it is still experimental with many difficulties remaining to be resolved. An alternative approach to achieving a small structured singular value over all frequencies was introduced in [LoF88]. In this approach, the structured singular value objective is not optimized directly. Instead, recent results in the analysis of structured singular values are used to specify characteristics of the closed loop system transfer functions that result in good robust performance [Fre88a]. These characteristics are then translated into the design parameters that are used by the formal Linear Quadratic Gaussian/Loop Transfer Funcf on Recovery (LQGLTR) procedure: the design weighting transfer functions on the performance, disturbance and input signals. LQGLTR is then used to synthesize a candidate design. The design is again evaluated, and modified as required until the structured singular value performance objective is achieved. The design problem that is considered explicitly in this paper is one of tracking an exogenous reference signal (command following) in the presence of an unstructured multiplicative modeling error at the plant input. This design problem is a typical robust performance problem, and has been studied in the context of several different applications [DoS81, FLC82, DWS82, SLH811. It illustrates the essential features of the general robust performance problem within a more specific framework, while also providing a reasonable model for many design problems. For this problem, the characteristics of closed This work was supported at the University of Michigan by the Air Force Office of Sponsored Research under conmct number F33615-88-C-3601. James S. Freudenberg Dept. of Electrical Engrg. and Computer Science University of Michigan Ann Arbor, MI loop systems which result in a small structured singular value have been identified and quantified. These characteristics will be mapped into desired open loop transfer function characteristics. The well known relationships between LQG/LTR design weighting functions and the subsequent compensated open loop transfer function (c.f. [DoS81, StA871) will be used to select design weights that achieve the required robust performance characteristics. This approach has been formally presented in [LoF88] for both the LQG and H, formal synthesis procedures. The approach will be illustrated in this paper by the design of a control system for the longitudinal dynamics of a highly maneuverable aircraft. The paper is organized as follows. Section 2 formulates the problem of robust command following with input uncertainty. Section 3 summarizes results from [Fre88a, LoF881 that define design criteria in the form of desired characteristics of the compensated loop transfer function. These design criteria are then used to develop a procedure for selecting the LQGLTR weights in Section 4. The example using these weight selections is presented in Section 5. 2 . Robust Command Following with Input Uncertainty