Abstract
This paper describes an approximated-scalar-sign-function-based anti-windup digital control design for analog nonlinear systems subject to input constraints. As input saturation occurs, the non-smooth saturation constraint is modeled with the approximated scalar sign function which is a smooth nonlinear function. The resulting nonlinear model is further linearized at any operating point with the optimal linearization technique, and Linear Quadratic Regulator (LQR) is then applied for a state-feedback controller optimal for each operating point. As input saturation is encountered, an iterative procedure is developed to adjust control gains by systematically updating LQR weighting matrices until the inputs lie within the saturation limits. Through global digital redesign, the analog LQR controller is converted to an equivalent digital one for keeping the essential control performance, and moreover, delay compensation is taken into account during digital redesign for compensating the potential time delays in a control loop. The swing-up and stabilization control of single rotary inverted pendulum system is used to illustrate and verify the proposed method.
Highlights
Various types of hardware limitations always exist in practical control systems with potential effects on the final control performance
Most of them are proposed for linear systems, like the extensively-studied two-phase approach [1,2,3,4] and Linear Matrix Inequalities (LMI)-based methods [5,6,7]
This paper proposes an approximated-scalar-sign- anti-windup design, including approximated scalar sign function-based anti-windup technique for analog nonli- function, optimal linearization and Linear Quadratic Regulator (LQR)
Summary
Various types of hardware limitations always exist in practical control systems with potential effects on the final control performance. The approximated scalar sign function are differentiable, as optimal linearization in [17] is applied for the local linear model at any operating point and a state-feedback sign( z) = z z2. In addition to input constraints, time-delayed systems are another practical concern in the proposed design This concern arises from the fact that in a sampled-data control system which is a popular control scheme nowadays due to the advance of computer technology, some fundamental operations like controller computation, A/D and D/A conversions, sensing and actuation etc, could cause time delays in the control loop. It can be shown that the j-th truncation (5) gives the signed control so it is of practical interest to extend the better approximation of (3) as the value of j approaches developed anti-windup methodology to time-delayed the infinity, i.e. systems. The weighting matrices Q and R should be tuned to make the resulting analog controller (20) give a desired control performance in the delay-free case
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