Static anti-windup compensator design of linear Sliding Mode Control for input saturated systems

A feedback control system involving a linear Sliding Mode Controller (SMC) and an input saturated linear plant is considered here. The linear SMC is designed for linear plant without saturation on its input. The resulting feedback system will not necessarily show an intended performance if the control input to the plant is saturated. In addition, a directionality problem for multivariable input systems may occur during the saturation. As a result, transient response performance could be degraded and its control signals may not be stabilizing the feedback system anymore. In this case, a directionality compensator may be designed to overcome the problem while optimizing its performance. static anti-windup compensator as a directionality compensator is designed through a Linear Matrix Inequality (LMI)-based synthesis. The LMI conditions are derived based on a chosen Lyapunov function to ensure the stability of its closed loop system and an L₂-gain performance. The static anti-windup compensator is in fact a nonlinear algebraic loop and its implementation needs to be robust to delay. Therefore, an additional LMI constraint is also employed to guarantee the robustness. Two Input-Two Output (TITO) ill-conditioned plants are then considered to validate the effectiveness of the proposed design through simulations. Simulation runs have shown that the static anti-windup compensators effective in minimizing the performance degradation due to directionality problem while maintaining the stability of the input saturated closed loop system.