Robust Simultaneous Stabilization Using Derivative State Feedback

Abstract

In simultaneous stabilization of continuous time switched linear system models of inertially coupled dynamic systems with bounded persistent external disturbance and internal parameter variations, the generalized proportional integral derivative (PID) controller suffers from a serious drawback. It loses the ability to guarantee exponential stability of the closed-loop error response, which is the difference between the actual and the desired closed-loop responses. The high value of the hardware gain has no control over the situation. On the contrary, the derivative state feedback (DSF) controller effectively employs the hardware gain in diminishing the effects of external and internal disturbances. These facts are proved and illustrated by suitable examples. The proposed method of simultaneous stabilization is shown to be an easier alternative to solve Diophantine equations encountered. The method for single input single output (SISO) systems is also shown to extend seamlessly to the control of multiple input multiple output (MIMO) square models with equal number of inputs and outputs. The shortcoming of the method is pointed out when the models are not square. The advantages of the proposed methodology over the existing methods are outlined. Finally, an efficient time domain simulation scheme is presented for the numerical study of such models in time and transfer function domain with nonzero initial conditions.