Control System Theory — Winter 2022

Explain Standard Test Signals used in control system.

What are the limitations of open-loop systems over closed-loop systems? List the advantages of closed-loop system over open-loop system.

C Determine the overall transfer function for the system whose block R diagram is shown in fig. below using block diagram reduction technique.

Define the following: (1) Rise time (2) Delay time (3) Settling time.

X (s) X (s) Obtain the transfer function 1 and 2 of the mechanical system F(s) F(s) shown in fig. below.

K For the unity feedback control system with G(s)  . Find the s(s1)(s2) range of Kfor system that will cause the system to be stable, marginally stable and unstable. Make suitable comments.

Determine the stability of the system represented by the characteristic equation s6 3s5 5s4 9s3 8s2 6s40 by means of the Routh criterion. Determine the number of roots of the characteristic equation lying in the right-half of s-plane.1

Explain the terms with respect to root locus. (i) centroid (ii) angle of arrival and angle of departure (iii) breakaway and break in points.

State and explain nyquist stability criteria.

Sketch bode plot showing the magnitude in decibels and phase angle in degrees as a function of log frequency for the transfer function given below. Determine the gain cross over frequency.10 G(s)  s(10.5s)(10.01s)

Describe the steps to construct the polar plot.

Explain relationship between time and frequency response.

Consider a unity feedback control system with an open-loop transfer function. K(s1)(s2) G(s)H(s)  (s0.1)(s1) Draw the root locus of the system with the gain Kas a variable. Find from the root locus plot, the value of gain Kfor which a closed-loop system is critically damped.

Explain the effect of integral control action on system Performance.

What is compensation? What are the different types of compensations?

Draw the bode plot for phase-lead network and derive expression for the parameter α in terms of Φ . m

State limitations and effects of Lag compensator.

State the limitations of a single stage phase lead compensation.

Explain step by step Procedure for Phase Lag Network.

Explain the advantages of bode plot.

How will you define controllability and observability of the system?

Draw a series RLC circuit. Obtain its state space model considering current and capacitor voltage as state variables.

Define the following terms: Gain margin, phase margin, bandwidth, resonant peak

Explain the following terms: (i) State (ii) State Variables (iii) State Space (iv) State transition matrix

Alinear time-invariant system is described by the following state variable model: x  1 0 x  0 1  1  u         x   0 2 x  122 x  y(t)   1 2  1   x  2 Comment on the controllability and observability of the system.2