Reference no: EM133187630

Frequency domain control design methods

Problem 1: Let G be a plant with the transfer function G.s/ D 1=.s - 1/. The goal is to stabilize it with minimum control effort, measured by a size of the control sensitivity transfer function, T_c(s) = R(s)/1 - G(s)/R(s).

Question 1. What is the smallest attainable ||Tc||_∞ What controller R(s) attains it?

Question 2. Assume that the bound |T_c (jω)| ≤ 1 has to be met for all ω > ω₀ for some ω₀ > 0. What is the lower bound on ||T_c||_∞ in this case ? Plot this bound as a function of ω₀.

Question 3. Construct generalized plants for the standard H_∞ problem corresponding to the problems in items 1 and 2.

Problem 2. Consider the DC motor from HW1, now with the parameters

(the difference is hat L_a = 0 now). The requirements remain the same:
• an integral action in R(s),
• high-frequency roll-off of at least 1 for R(s),
• µm ≥ 0:5 <=> |S.jω| ≤ 2 for all ω,
• |Tc(jω)| ≤ 1 for all ω.

Using the H_∞ loop-shaping procedure, design a controller satisfying these requirements. Try to maximize the resulting crossover frequency ω_c. Explain your design choices.

Besides a brief file with explanations, submit a MyName.mat (with your name in place of "MyName") file having LTI 3 systems in it:
• the plant, named G
• the controller, named R
• the final weight used in the design, named W