FEEDBACK DESIGN FOR UNSTABLE PLANTS WITH SATURATING NONLINEARITIES : SINGLE-INPUT, SINGLE-OUTPUT

Control systems are often required to operate in the presence of saturation nonlinearities, such as actuator displacement and rate limiting. Whereas the occurrence of saturation may possibly be minimized by the choice of closed-loop bandwidth, the nonlinearities themselves are essentially unavoidable, and system performance and even stability can be compromised when the nonlinearities are encountered. To address this problem, a design technique for improving the performance of single-input, single-output feedback systems operating in the presence of saturation nonlinearities is presented. The technique allows application to unstable plants and is an extension of that previously discussed in the literature for stable plants. A simple design example is provided that demonstrates the applicability of the methodology to a case of actuator rate limiting. Introduction and Background EEDBACK design techniques that explicitly consider the pos- sibility of control saturation are receiving increasing attention in the literature. Optimal control strategies for regulators employing inequality constraints on control and state variables are well known. * Techniques that attempt to minimize the adverse effects of saturation are also well established, e.g., antiwindup controllers.2 Feedback systems designed to avoid saturation have been discussed.3 Nonlin- ear feedback controllers designed with the goal of improved perfor- mance with state and control saturation have also been described.4 Finally, linear feedback schemes to improve the performance of systems with saturation nonlinearities have been formulated.5 The research to be described here falls into the last category. In particular, the treatment of actuator saturation as a nuisance nonlin- earity is pursued. This implies that the system in question experi- ences saturation relatively infrequently and that a nominal control system design was obtained ignoring any nonlinear actuation ef- fects. Such is the case for many aircraft flight control systems in which actuator saturation, either displacement or rate, is a relatively rare occurrence. The rarity of such occurrences is not accidental since the performance requirements of control surface actuators are typically an important part of flight control system specifications. Nonetheless, flight control actuator saturations do occur, typically, with high-performance aircraft.6"8 When conditionally stable sys- tems are involved (e.g., statically unstable aircraft), the results can be catastrophic.9-10 The design technique to be pursued is an extension of that devel- oped by Horowitz 5'11'12 and in Refs. 13 and 14 briefly outlined in the next section. Attention is focused on single-input, single-output (SISO) systems. The design equations are presented next, and the Horowitz technique is extended to unstable plants. The internal sta- bility and input-output stability of the resulting design approach are then discussed, and a simple example is presented which demon- strates the design approach.