CONTROL SYSTEMS Hand written Notes for Unit-I, II, III & IV

 The Notes cover the following topics

UNIT I BASIC CONCEPTS AND SYSTEM REPRESENTATION
Basic elements in control systems – Open and closed loop systems with example –
Mathematical model of Translational, Rotational & Electrical systems – Transfer function – Block
diagram reduction techniques – Signal flow graph.
UNIT II TIME RESPONSE ANALYSIS
Introduction – Time domain specifications – Types of test inputs –I and II order system response
– Steady state error – Error coefficients – Generalized error series – P, PI, PD, PID Controlled characteristics.
UNIT III FREQUENCY RESPONSE ANALYSIS AND DESIGN
Introduction – Frequency domain specifications – Bode plots and polar plots – Constant M and
N circles and Nichols chart – Correlation between frequency domain and time domain specifications.
UNIT IV STABILITY OF CONTROL SYSTEMS
Characteristics equation – Location of roots in s-plane for stability – Routh Hurwitz criterion –
Root locus construction – Gain margin and phase margin – Nyquist stability criterion.

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Control System - Anna University Question Paper

ANNA UNIVERSITY – COIMBATORE
B.E.\B.TECH.DEGREE-

EXAMINATION-DECEMBER 2008
FIFTH SEMESTER-ELECTRICAL &ELECTRONICS ENGG.
CONTROL SYSTEMS
PART A-(2*20=40)
1. Define transfer function.
2. Name two types of electrical analogous for mechanical system.
3. What is a signal flow graph.
4. What is servomechanism.
5. List the time domain specifications.
6. Define peak overshoot.
7. A unity negative feedback system has Kp=5. What steady state error can be expected for inputs of 6u(t) and 6t u(t).
8. Why derivative controllers is not used in control system.
9. Define gain margin.
10. What are the main advantages of Bode plot.
11. What are M circles.
12. List out the different frequency domain specifications.
13. State Nyquist stability criterion.
14. What are the main sequences of root locus.
15. What is limitedly stable system.
16. What is centroid. How the centroid is calculated.
17. What is a compensator.
18. When is the lag-lead compensator required.
19. Write the procedure for designing the lag compensator.
20. What are the advantages and disadvantages in frequency domain design.

PART B-(5*12=60)
21. Write the differential equations governing the mechanical rotational system shown in fig. Obtain the transfer function of the system.

22. Explain the construction and working principle of AC servomotor.
23. A) Write the standard test signals used in the control system. (4)
B) Obtain the unit ramp and unit impulse response of a first order system. (8)
24. Draw the Bode plot for the open loop transfer function G(s)= K/s(s+1)(0.1s+1). Determine phase margin and gain margin.
(i) find the value of k to give a gain margin 10db.
(ii) (ii) find the value of K to give gain margin 30db.
(iii) (iii) find the value of K to give a phase margin of 24o
(iv) (iv) the marginal value of k for stability.
25. A) Construct the routh array system for the equation: s4+8s3+16s+5=0 and comment on the stability of the system. (4)
B) Consider the closed loop transfer feedback system shown in fig. Determine the range of k for which the system is stable. (8)

26. Sketch the root locus plot for 0 (s+2)(s+4)
Find the following:
a) the gain k at the j?-axis crossing,
(b) the gain at that point where the locus crosses the 0.45 damping atio line.
27. The closed loop transfer function of certain unity feedback control system is given by G(s)=K/s(s+4)(s+80). It is desired to have the phase margin to be at least 330 and the velocity error constant Kv=30sec-1. Design a phase lag series compensator.
28. Consider the unity feed back system whose open loop transfer function is G(s)=K/s(s+3)(s+6). Design a lag-lead compensator to meet the following specifications.
(i) velocity error constant, Kv=80,
(ii) (ii) phase margin ?=35o.

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Control System - Unit -1 to 3 - Formulas

UNIT I   :  BASIC CONCEPTS AND SYSTEM REPRESENTATION

To solve problem in Electrical system

From question, we have electrical circuits in terms of mesh or loop

Procedure:

Step1:Assume polarity for every loop in circuit along clockwise direction  and mark direction of loop current

Step2:Apply KVL for each loop

Step3:We obtain the no of eqn = no of loop

Step4:Apply Laplace Transform on Both side (refer: Table of Laplace transform)

Step5: Find Input and Output Variable.

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Control System - 2 Mark Question & Answers

1. Define System?
A system is a combination or an arrangement of different physical components which act together as an enti
unit to achieve certain objective.
2. What is control system?
A system consists of a number of components connected together to perform a specific function. In a syste
when the output quantity is controlled by varying the input quantity then the system is called control system.
3. Define regulator system.
A regulator system is one in which the output is maintained at a prescribed level.
4. Define Plant?
The portion of a system which is to be controlled or regulated is called the plant or the process.
5. Define Controller?
The element of the system itself or external to the system which controls the plant or the process is call
controller.
6. Define Input.
It is an applied signal or an excitation signal applied to a control system from an external energy source in ord
to produce a specified output.

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