Feedback Controller Design

Overview

Control systems are an ubiquitous part of our everyday life in this technologically driven era, be it a simple thermostat or a complicated robotic arm, control theory may be implemented to design stable and efficient systems.

In this project, I explored negative feedback control in electronic systems PID control and Lead-lag compensation. The electronic system employed for this project was a simple RLC circuit.

PID and Lead-Lag Compensator circuit designs were tested and tuned using MATLAB and LTSpice.

The tasks carried out in this project are:

• Analyzed open-loop system step response of the electronic system by modelling the system in MATLAB and LTSpice.

• Analyzed a closed-loop system without a controller/compensator by modelling the system in MATLAB and LTSpice.

• Studied the individual circuit implementations of Proportional, Integral and Derivative controllers. Followed by analysis of the combined PID controller circuit.

• Studied and implementated a Lead-lag compensator for the simple RLC electronic system, using Bode and Nyquist plots for the open-loop system.

The steps taken to complete the tasks above and the results obtained are analyzed in the attached report for anyone interested in designing a PID controller or a Lead-lag compensator.

Completion of this project has made me appreciate the usefulness of negative feedback in control systems. A feedback in a system paired with a controller/compensator, allows the system to keep track of the output error and compensate accordingly. Designing a controller specifically for a system allows you to control the response time and steady-state accuracy. Hence, a feedback system with a controller ensures optimal performance.

Moreover, the investigation carried out in the Lead-Lag Compensation has established a few key points that I will keep in mind when designing a lead-lag compensator. Namely, that the lag compensator’s purpose is to improve the steady-state accuracy and this can only be achieved by adding the lag compensator at low frequencies, while a lead compensator’s purpose is to improve the transient response and this is achieved by adding the lead compensator at high-frequencies. Finally, proportional gain is added to the system to push the improved transient and steady-state response, to the desired value. However, care needs to be taken to ensure that the added proportional gain is not greater than the gain margin of the improved system, as the system can become unstable.

Moving on to comparing PID control and Lead-lag compensation, it is safe to conclude that a lead compensator acts approximately as a PD controller as they both speed up the response of the system by improving the transient response of the system. Slowing down the transient response makes the system slower, which is approximately what a PI controller does to a system. Therefore, it is safe to conclude that Lag compensator acts approximately as a PI controller.

If you're interested in the design process I've attached a link to my detailed report on this project. Also, I'm more than happy to share my MATLAB and LTSpice files, shoot me a message!