Design a discrete z-domain proportional plus integral plus

Question

1. Objective:

Design a discrete (Z-domain) proportional plus integral plus derivatives (PID) controller for the type-1 plant derived from Lab 2. The controller should satisfy the following specifications:

1. Steady-state error to a step input = 0

2. Percentage overshoot to a step input less than 5%

3. Setting time less than 1 second

Also the following specifications are required as they are good control system practice:

Gain margin greater than 15 dB

Phase margin greater than 45 degrees

2. Procedure:

Using continues plant model for the typw-1 system, design a discrete PID controller to meet the previous specifications. Begin by discretizing the plant (with the ZOH). Next, using pole-zero cancellation, select and place new poles and stimulate your responses with the controller designed. If the design specifications are not met, tweak the controller.

3. Requirement:

Pre-laboratory assignments should be typed and not handwritten. Also, provide justification of your design with figures and charts. The first step should be to show the response of the uncontrolled plant to a step input. From there, examine the dynamics and justify why a controller is needed. In this case, the system is type-1 but a PID controller is chosen to drive any steady-state error that may exist to zero.

Answer 1

In order to complete the assignment, you have to perform the following tasks accordingly as illustrated. Objective: Design a discrete or Z-domain proportional plus integral plus derivatives (PID) controller for the type-1 plant derived from the lab. The controller must satisfy the given conditions: 1) Steady-state error to a step input = 0 2) Percentage overshoot to a step input less than 5% 3) Setting time less than 1 second Requirement: The assignments must be typed and not handwritten. As well, give justification of your design with charts and figures. The primary step must be to show the response of the uncontrolled plant to a step input. From there, analyze the dynamics and validate why a controller is required. In this situation, the system is type-1 however a PID controller is selected to drive any steady-state error which might exist to zero.