Embedded Digital Control with Microcontrollers

8Transfer Function Based Controller Design

The linear and time-invariant (LTI) system at hand may not satisfy the required design criteria. To solve this problem, a controller can be added to it as mentioned in Chapter 7. There, we picked predesigned controllers. In this chapter, we will explore the transfer function-based controller design methodology for this purpose. We will benefit from the closed-loop control strategy in the design phase throughout the chapter since it is applicable to a broader class of problems. As a reminder, the closed-loop controller feeds the output signal back to input. Hence, the reference and actual output signals are compared to generate the control signal. We will formalize the transfer function based controller design method this way. As for the controller structure, we will first introduce the proportional integral derivative (PID) controller and its versions as proportional (P) and proportional integral (PI) controllers. We will provide Python based design methods for these. Then, we will introduce the lag–lead controller and its versions as the lag and lead controllers. We will also provide their design methodology in MATLAB. As the end of chapter application, we will design transfer function-based controllers to the actual DC motor and observe their effects on the performance criteria.

8.1 PID Controller Structure

PID is one of the most popular controller design structure used in practical applications. The main reason for this popularity ...