State Feedback Control and Kalman Filtering with MATLAB/Simulink Tutorials

2Practical Multivariable Controllers in Continuous‐time

2.1 Introduction

One of the primary objectives in feedback control is to compensate unexpected disruptive events of system operations. These events (or disturbances) are either expected or unexpected, and for most times, they are not measured. For instance, an electrical machine has a sudden change of electrical load. The state feedback control systems introduced in Chapter 1 lack the capability to reject the disturbances. Therefore, in their present forms, they have limited applications to practical problems.

The objective of this chapter is to introduce two types of practical multivariable controllers. These controllers are capable of tracking step reference signals and rejecting low frequency disturbances. In order to have these capabilities, the multivariable controllers will have integral control in addition to having an anti‐windup implementation to deal with the events when the actuators reach their maximum or minimum values.

The chapter begins with the well‐known classical approach to include integral action using state space model (see Section 2.2.1). This design is intuitive and easy to understand. But it lacks of an anti‐windup mechanism when the control signal reaches its maximum or minimum limit, hence the integrator windup scenario occurring (see Section 2.2.2). The remainder of Section 2.2 is to modify the classical controller by considering the effect of disturbance in the controller design, leading to ...