Controller Design and Stability Analysis for Some Linear Systems Using Pulse-Width-Modulation

Digital control is a branch of control theory that uses a computer processor to control and drive a continuous-time system so that it operates in a desirable way over time. Accuracy, flexibility, performance, and low cost have led to an increased usage of digital controllers.

Digitally controlled systems require digital-to-analog (D/A) and analog-to-digital (A/D) converters to translate signals between the plant and digital controller. D/A conversion is often accomplished using Zero-Order-Hold (ZOH), but another method of D/A conversion can be performed using Pulse-Width-Modulation (PWM). PWM based control systems have gained much attention due to their versatility and usage in many practical applications ranging from household appliances to jet engines. Stability analysis of a control system is a highly studied topic, and PWM based control systems present challenges due to the nonlinearities introduced by the discontinuous PWM signal.

This thesis is focused on presenting a new Lyapunov stability analysis for some systems under PWM control. Different from the existing results, the proposed procedure is developed based on Zero-Order-Hold (ZOH), yielding a sufficient condition for the switching period of the PWM signal. The effectiveness of the proposed result will be demonstrated in application to a group of linear systems with simulations results.