Control System Design — Winter 2024

Define the following terms: (i) Controllability (ii) Observability

Derive the state space model of series RLC circuit.

Explain Robust PID controller design in detail.

List the properties of state transition matrix.

Write the steps to design lag compensator in frequency domain.

Obtain the state space model of field controlled DC motor.

x Obtain the time response of the system described by [ 1] = x2 [ 0 1 ][ x 1 ]+[ 1 ]u with the initial conditions [ x 1 (0) ] = −1 −2 x 2 −1 x 2 (0) 0 x 1 [ ],y = [0 1][ ] 1 x

Find the dimensions of the system matrix, input matrix, output matrix and feedforward matrix for the system having three state variables, two input variables and one output variable.

Derive the equation to obtain the transfer function from the state space model.

Explain Linear Quadratic Regulator for optimal control.

Define the following terms: (i) state (ii) state vector (iii) state space

Obtain the diagonal canonical form for the system having following transfer function C(s) (s+3) = R(s) (s+1)2(s+2)

Describe the procedure to design a full-state feedback controller.

State the procedure to check observability of a system in state space.

Explain need of compensation and types of compensation.1

Aunity feedback system with the forward transfer function G(s) = K is operating with a closed-loop step response that has 15% s(s+7) overshoot. Evaluate the settling time and Design a lead compensator to decrease the settling time by three times. Choose the compensator’s zero to be at -10.

Draw the pole- zero diagram of lead compensator and lag compensator in s-plane.

−2 0 1 Consider the system given by x = [ ]x+ ⌊ ⌋u and y = d −3 0 [0 1]x. Determine the condition of controllability for this system.

Consider the system given by G(s) = 1 . Design a lag s(s+1)(0.5s+1) compensator such that static velocity error constant Kis 5 sec-1, the v phase margin is at least 40° and the gain margin is at least 10 dB.

What is the goal of robust system design? When any control system is said to be a robust system?

Draw an electrical network realizing lead compensator. Also derive its transfer function.

2 3 0 Consider the second order system given by x = [ ]x+ ⌊ ⌋u −1 4 1 and y = [1 0]x. Design the state observer for the given system such that rad ζ = 0.8 and 𝜔 = 10 . n sec

What are the considerations that are to be kept in mind while designing the robust control system?

0 1 0 Consider the system having A = [ 0 0 1 ] and C = −a −a −a012 [1 0 0]. Determine the observability of this system.

With the help of illustrative bode diagram, discuss the basic characteristics of lead compensator.