Nonlinear Discrete-time Design Methods for Missile Flight Control Systems

Abstract

Abstract : Design methods for discrete-time linear control systems have reached an advanced level of maturity. However, the direct design of nonlinear discrete-time control systems remains to be fully developed. Although textbooks are available on nonlinear control system design literature on discrete-time nonlinear control system design is rather sparse. From an applications point-of-view, discrete-time designs are important because most controllers are implemented using digital computers. Design techniques of interest in this paper are those that permit the synthesis of discrete-time controllers for continuous-time nonlinear dynamic systems. The present work is motivated by the need to implement nonlinear control system designs synthesized using computer-aided design techniques6, 7 onboard missiles. Three different discrete-time control system design techniques have been investigated in the present research. All of them are discrete-time analogs of continuous-time nonlinear system design techniques discussed in the literature. The first approach is the discrete-time version of the state-dependent Riccati equation (SDRE) technique discussed in References 8 and 9. The second design technique is a discrete-time version of the recursive backstepping10 methodology, and employs discretized system dynamics. The third technique is the discrete-time version of the feedback linearization design approach. In this last technique, the system dynamics is first transformed into a linear, time-invariant form through the definition of state variable feedback. The transformed model is then converted into discrete-time form by defining sample-holds at the input and the outputs. The discretized is linear model is then used for control system design. All three techniques have been employed for the design of missile flight control systems. Section II will present each of the design techniques in detail.