Question

Design a PID controller with filter for the following system:

G(s) = 2/2ˢ+1
1. Choose the desired closed-loop characteristic polynomial as (s² + 22ξwns + wₙ²)² where § = 0.707 and un= 3. What are the values of Kc, u, tp and y?

Answer 1

To design a PID controller with a filter for the given system, we need to calculate the values of Kc, u, tp, and y. The closed-loop characteristic polynomial and transfer function are provided. By equating coefficients, we can solve for the unknowns.

Step-by-step explanation:

A PID controller is a popular control algorithm used in engineering systems to regulate and control the output of a system. The controller consists of three components: the proportional, integral, and derivative terms. The filter in the controller is used to smooth the control signal and reduce noise.

To design a PID controller with a filter for the given system, first, we need to calculate the values of Kc, u, tp, and y. For the closed-loop characteristic polynomial, (s² + 22ξwns + wₙ²)², where ξ = 0.707 and wn = 3, we can match the coefficients with the given transfer function, G(s) = 2/(2s+11).

By equating the coefficients, we can solve for Kc, u, tp, and y.