State Feedback Control and Kalman Filtering with MATLAB/Simulink Tutorials

1State Feedback Controller and Observer Design

1.1 Introduction

State feedback control systems open up a different landscape to control system design for complex systems that have a higher order or have many input and output variables. For those of us who are familiar with the classical control systems designed using a Laplace transfer function model, the continuous‐time control systems using a state space model will be a natural extension. Therefore, it is easier to learn and master the design steps in the continuous‐time.

The chapter begins with a case study on the effectiveness of PID control of a system with interactions (see Section 1.2). This is to answer the question why to go beyond PID control because this question is urgent for some of us who work in the field of process control and use PID control as bread and butter for daily operations. In Section 1.3, the basic idea about state feedback control is illustrated using a simple analytical example and is followed by the introduction of controllability with an explanation what it means when a system loses its controllability. The concept of closed‐loop eigenvalues (or poles) is fundamental in state feedback control. By choosing a set of desired closed‐loop eigenvalues, a state feedback controller is designed (see Section 1.4). With a similarity transformation, this section takes us in a step‐by‐step manner for the design of a pole‐assignment controller. However, the pole‐assignment controllers have limitations when ...