Control of dynamical systems using bounded feedback.
详细信息
文摘
High-gain and low-gain designs have been at the forefront of developing new nonlinear design methodologies.;While high-gain design has been intensively studied, its counterpart, low-gain design, received less attention. Motivated by results in stabilizing the well known ball-and-beam system, we introduce a family of low-gain designs, to extend the class of nonlinear systems stabilizable by state feedback.;Magnitude and/or rate constraints are the most frequently encountered nonlinearities in practical applications. Usually, design techniques that synthesize controllers to satisfy certain performance requirements do not take them a priori into account during the design phase. Additional concerns arise in the case when the linear plant has unstable modes. In this context, we address the problem of achieving maximum regions of attraction for unstable linear systems with inputs subject to magnitude limits and we apply our design to the longitudinal stabilization problem of an unstable aircraft.;Performance or stability degradation of the closed-loop system subject to input constraints has been referred to as the “windup” problem. To maintain stability and to avoid large changes in the desired performance introduced by actuator nonlinearities, “anti-windup” constructions have to be employed. These represent nominal controller modifications, in place when actuators saturate, to reduce the detrimental effects induced by the nonlinearities. Based on the “uniting local and global controllers” technique, we present an anti-windup compensator design for linear systems with exponentially unstable modes, in a non-local way. In particular, we address the problem of guaranteeing a large operating region for linear systems with exponentially unstable modes and give sufficient conditions to achieve local performance and global stability with large operating regions. The proposed scheme is applied to the linearized short-period longitudinal dynamics of an unstable fighter aircraft subject to rate and magnitude limits on the elevator deflection. The anti-windup design applied to this unstable linear system allows to achieve prototypical military specifications for small to moderate pitch rate pilot commands, while guaranteeing aircraft stability for all pitch rate pilot commands. Due to the large operating region achieved by the anti-windup scheme, the controlled aircraft allows the pilot to maneuver aggressively via large pitch rates during transients.