DHANALAKSHMI COLLEGE OF ENGINEERING CHENNAI DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING YEAR/SEMESTER: II/IV IC6501 CONTROL SYSTEMS UNIT I SYSTEMS AND THEIR REPRESENTATION 1. What is the mathematical model of a system? (April - 2005) Mathematical model is the mathematical representation of the physical model of a system through use of appropriate physical laws. For most physical systems they are characterized by differential equations. A mathematical model may either be time variant or time invariant. 2. What is electrical analogous of a gear? (April - 2005) Transformer is electrical analogous of a gear. 3. Explain Mason s gain formula for signal flow graphs. (Nov 2003) (April 2004) According to Mason's Gain formula, Overall gain, T = PkΔk/Δ Where, T = transfer function of the system, Pk = forward path gain of kth forward path Δ = 1 - (sum of individual loop gain) + (sum of gain products of all possible Combinations of two non-touching loops) - (sum of gain products of all possible combination of three non- touching loops)+... ΔK = Δ of the Kth forward path. 4. What is the force voltage analogy of a mechanical spring? (Nov 2004) The force voltage analogy of mechanical spring is reciprocal of capacitance (1/C) 5. Mention the merit and demerit of closed loop system.(april 2000)(Nov 2012) Merits: (a)the controlled variable accurately follows the desired value. (b)effect on the controlled variable of external disturbances other than those associated with the feed back sensor are greatly reduced. (c)effect on variation in controller and process parameters on system performance is reduced to acceptable levels. (d)it improves the speed of its response. Demerits:
(a)by increasing the number of components of the system, it increases the complexity. (b)the gain of the system is reduced. (c)introduces the possibility of instability 6. Compare closed and open loop system (May 2013). Closed-loop control I. shows a closed-loop action (closed control loop); II. III. can counteract against disturbances (negative feedback); can become unstable, i.e. the controlled variable does not fade away, but grows (theoretically) to an infinite value. Open-loop control I. shows an open-loop action (controlled chain); II. can only counteract against disturbances, for which it has been designed; other disturbances cannot be removed III. cannot become unstable - as long as the controlled object is stable 7. State the basic elements for modeling in translational and rotational systems (May 2013). Mass, Dash pot and spring 8. Define transfer function. (Nov 2012). The transfer function of a linear, time-invariant system is defined as the ratio of the Laplace transform of the output (response function), to the Laplace transform of the input (driving function) under the assumption that all initial conditions are zero. 9. What is the principle of operation of closed loop systems? (Oct-2000) The closed loop system compares the actual output measured by the sensor with the desired output and produces the error signal or actuating signal. The actuating signal is applied to the process so as to influence the output in a manner, which tends to reduce the error. 10. What are the disadvantages of block diagram representation? (Nov 2004) 1. Reduction of block diagram is becoming tedious for complex systems. 2. It is time consuming. 3. Not suitable for MIMO system 4. Not suitable for nonlinear system
UNIT II TIME RESPONSE ANALYSIS PART - A 1. What are the standard test signals employed for time domain studies?(or) List the standard test signals used in analysis of control systems?-(april 2011) Step input, ramp input, parabolic input and impulse input signals. 2. What is steady state error?-(april 2011) The steady state error is the value of error signal e(t) when t tends to infinity. It is a measure of system accuracy. 3. State the effect of PI and PD controller on system performance. (May 2013) Effect of PI controller: 1. Improves steady state response of the system 2. Increases rise time 3. Reduces peak overshoot Effect of PI controller: 1. Improves transient response of the system 2. Reduces rise time. 3. Increases damping ratio as well as stability 4. Find The acceleration error coefficient for (May 2013) = + ( + ) ( + + ) Acceleration error constant (ka) = lim 0 2 1 + (1 + 2 ) 2( 2 + 4 + 20) = 10 5. Determine the type and order of the following system (Nov 2012) G(s) = K / (S+1) (S+2) Type 0.Order 2 6. What is meant by time constant of the system? (Nov 2012) The time in which a physical system's response to a step-wise change in an external variable reaches approximately 63% of its final (asymptotic) value. 7. What ate the types of controllers that are used in a closed loop system? (A-98) 1. Proportional 2. Integral 3. Proportional + Integral 4. Proportional +derivative 5. Proportional + Integral + Derivative
8. What is the difference between type and order of a system? (O-97) Type: Number of poles of open loop transfer function located at the origin. Order: Highest power of s of the denominator of closed loop transfer function. i.e. the highest power of s of the characteristic equation. 9. Define settling time. (O-96) It is the time required for the step response curve of under damped second order system to reach and stay within a specified tolerance band. It is usually expressed as % of final value. The usual tolerable error is 2 % or 5 % of the final value. 10. What is meant by reset time? (A-97) In the integral mode of controller, the time during which the error signal is integrated is called the integral or reset time (Ti). In other words in PI control, the time taken by the controller to 'reset' the set point to bring the output to the desired value. U(s) = Kc (1+ (1/TiS)) E(s), where Ti is the integral (or) reset time. UNIT III-FREQUENCY RESPONSE PART A 1. List any two advantages of frequency response analysis. (April - 2005)(April 2011) (a)the absolute and relative stability of the closed loop system can be estimated from the knowledge of the open loop frequency response.(b)the practical testing of system can be easily carried with available sinusoidal signal generators and precise measurement equipments.(c )The transfer function of the complicated functions can be determined experimentally by frequency response tests.(d)the design and parameter adjustments can be carried more easily.(e)the corrective measure for noise disturbance and parameter variation can be easily carried.(f)it can be extended to certain non - linear systems 2. Define gain margin of a closed loop system. (April - 2005) The gain margin is the factor by which the system gain can be increased to drive it to the verge of instability. It may be defined as the reciprocal of the gain at the phase cross over frequency ( Gain margin GM = 1 / G (jω) H (j ω) at ω = ωpc. 3. How will you determine the closed-loop stability from the open-loop system? (Nov 2012) Through Nyquist stability criterion, we can determine the closed-loop stability from the openloop system. 4. What are the frequency domain specifications? Explain. (Nov 2003) The frequency domain specifications indicate the performance of the system in frequency domain, they are Resonant peak, Resonant frequency, Band width, Phase margin,gain margin
5. Define phase margin and gain margin. (May 2013) The phase margin is defined as the amount of additional phase lag at the gain crossover frequency (φgc) required to bring the system to the verge of instability. Phase margin γ = φgc + 180 6. Mention the use of Nichol s chart. (April 2004) (a)it is used to find the closed loop frequency response from the open loop frequency response.(b)it is used to determine the frequency domain specifications.(c )The gain of the system can be adjusted to satisfy the given specification. 7. Define Gain Crossover Frequency.(April 2011) The gain crossover frequency is the frequency at which the magnitude of open loop transfer function is unity. 8. Define phase cross over frequency. (O-2000) The phase cross over frequency is the frequency at which the phase of open loop transfer function is180. 9. Define resonant frequency. (Nov 2012) Resonant frequency is the frequency at which the resonance peak (Mr) occurs. This is related to the frequency of oscillation in the step response and thus is indicative of the speed of transient response. (Mr is the maximum value of the magnitude of the closed loop frequency response.) 10. What are constant M and N circles? (O-96) (O-2000) The magnitude M of closed loop transfer function with unity feed back will be in the form of circle in complex plane for each constant value of M. The family of these circles is called M circles.let N = tan α, Where α is the phase of closed loop transfer function with unity feed back. For each value of N, a circle can be drawn in the complex plane. The family of these circles is called N circles UNIT IV- STABILITY OF CONTROL SYSTEM PART A 1. How is pole locations and stability related?(nov 2012) (i) Poles are in left half of the s-plane system is stable. (ii) Poles are on imaginary axis, system is marginally stable. (iii) Poles are in right half of s-plane, system is unstable.
2. State and explain Nyquist stability criterion. (Nov 2003)(April 2011)(May 2013) N = - P If G(s)H(s) contour in the G(s)H(s) plane corresponding to Nyquist contour in s plane encircles the pt 1+ j0 in the anticlockwise direction as many times as the number of right half s plane poles of G(s)H(s), then the closed loop system is stable. 3. What is dominant pole pair? What is its significance? (O-98) (O-2000) The dominant pole is a pair of complex conjugate pole, which decides transient response of the system. In higher order systems the dominant poles are very close to origin and all other poles of the system are widely separated and so they have less effect on transient response of the system. 4. What is meant by characteristic equation? What is its significance? (O-98) The denominator polynomial of closed loop transfer function equated to zero is the characteristic equation. It tells about the stability of the system. 5. State the necessary condition for the Routh s criterion for stability. (A-96)(May 2013) A necessary and sufficient condition for stability is that all of the elements in the first column of the Routh array be positive. If this condition is not met, the system is unstable and the number of sign changes in the elements of the first column of the Routh array corresponds to the number of roots of the characteristic equation in the right half of the s plane. 6. What are the applications of root locus method? (Nov 2003) Used to study the dynamic response of a system, Visualizes the effects of varying various system parameters on root locations, Provides a measure of sensitivity of roots to the variation in the parameter being considered, It is applicable for single as well as multiple loop systems, Directly we can find the of closed loop response from the given open loop transfer function,we can find the range of open loop gain in which the system is stable in closed loop. 7. Define asymptotic stability. (April 2004) In the absence of the input, the output tends towards zero (the equilibrium state of the system) irrespective of initial conditions. This stability concept is known as asymptotic stability. 8. What are the characteristics of an unstable system? (Nov 2004) The system will give unbounded output for a bounded input, the system has roots with positive real part, the system has repeated roots on jω axis. 9. State the rule for finding out the root loci on the real axis. (April - 2005) A point on the real axis lies on the locus if the number of open loop poles plus zeros on the real axis to the right of this point is odd. 10. State the rule for finding the value of K at any point on the root locus diagram. (A-97) K = product of phasor lengths from any point S0 to open loop poles /Product of phasor lengths from any point S0 to open loop zeros
UNIT V- COMPENSATOR DESIGN PART - A 1.Discuss the effect of adding a zero to the open loop transfer function of the system?(april 2011) The addition of a zero to open loop transfer function of a system will improve the transient response, reduces the rise time. If the zero is introduced close to origin then the peak overshoot will be larger. If the zero is introduced far away then its effect is negligible. 2. Why is lag compensator not suitable for higher type systems? (Nov 2012) Stability condition cannot be attained for the higher type system using lag compensator. 3.Explain the basics of compensation with a lead network. (Nov 2003). A lead compensator is basically a high pass filter. It amplifies high frequency noise signals. If a zero in the system does not cancel the pole introduced by the compensator, then the lead compensation increases the order of the system by one. Lead compensation appreciably improves the transient response and there is a small change in steady state accuracy. It is employed to make an unstable system into a stable one. 4. Why compensation is necessary in feedback control systems?(april 2011) In feed back control systems compensation is required in the following situations. 1. When the system is absolutely unstable, then compensation is required to stabilize the system and also to meet the desired performance.2. When the system is stable, then compensation is required to meet the desired performance. 5. What is compensator? What are the different types of compensators?(may 2013) A device inserted into the control system for the purpose of satisfying the desired specifications is called compensator. Types: Lag, lead and lag lead compensators. 6. What is the need for lead and lag compensation? (Apr 2004) To improve the system performance lead and lag compensators are needed in control system. Lead compensators are used to improve transient performance. Lag compensators are used to improve the steady state performance. 7. Write the transfer function of a typical lag compensator.(may 2013) 8. Write the transfer function of a typical lead compensator and draw its pole-zero plot(april 2011)
9. Write the transfer function of a typical lag lead compensator. (April - 2005) 10. Draw the Bode plot of typical lead compensator. (April - 2005)