Optimal and Robust Control

Knowledge (I memorize and understand)

1. Explain how the peak in the sensitivity and complementary sensitivity functions relate to gain and phase margins.
2. Explain the concept of a bandwidth. Shall we define it using the sensitivity or the complementary sensitivity functions?
3. Give the two "waterbed effect" integral formulas. You do not have to remember the formulas exactly but at least the essence.
4. Give the SISO version of interpolation conditions of internal stability. Namely, assuming that the transfer function of the system vanishes at z in the right half plane of the complex plane, it must hold that S(z) = 1. Similarly, for an unstable pole p of the system, it must hold that T(p) = 1. 
5. Give the lower bound on the peaks in the weighted sensitivity function in presence of poles and/or zeros in the right half plane.
6. How does the time delay in the system affects the achievable bandwidth?
7. How does the presence of disturbance affect the achievable bandwidth?
   
8. What conditions on system transfer function(s) are imposed by the saturation of actuators? More accurately, under which conditions is it guaranteed that the actuators do not saturate?
9. Explain the concept of directionality in MIMO systems.
10. Explain the condition number of the matrix of transfer functions. How can it be computed? Perhaps only approximately.
11. How does the presence of input multiplicative uncertainty affect the achievable behaviour of the closed-loop transfer functions?

Skills (I can use the knowledge to solve a problem)

1. Analyze the provided linear model of dynamics of the system to be controlled in order to learn the limitations on achievable performance such as bandwidth, resonant peak, steady-state regulation error etc.