Control Systems Question Bank PDF

\[Educational Service: SNR Sons Charitable Trust\] \[Autonomous Institution, Reaccredited by NAAC with 'A+' Grade\] \[Approved by AICTE and Permanently Affiliated to Anna University, Chennai\] \[ISO 9001:2015 Certified and all eligible programmes Accredited by NBA\] VATTAMALAIPALAYAM, N.G.G.O. C...

\[Educational Service: SNR Sons Charitable Trust\] \[Autonomous Institution, Reaccredited by NAAC with 'A+' Grade\] \[Approved by AICTE and Permanently Affiliated to Anna University, Chennai\] \[ISO 9001:2015 Certified and all eligible programmes Accredited by NBA\] VATTAMALAIPALAYAM, N.G.G.O. COLONY POST, COIMBATORE -- 641 022. **Department of ­­­­­­Electronics and Instrumentation Engineering** **QUESTION BANK** ---------------------------------------------------- --------- -------------- ------- **Department** **EIE** **Semester** **V** **Course Code &Title: 20EE205 -- Control Systems** **MODULE 1 -- Modeling of Control System** **PART A -- 3 MARKS** +-----------------------------------------------------------------------+ | 1. List the analogous electrical elements in force voltage analogy | | for elements of mechanical translational systems | +-----------------------------------------------------------------------+ | 2. Signal flow graph is a better mathematical operation for finding | | the transfer function than the block diagram approach. Justify | | it. | +-----------------------------------------------------------------------+ | 3. Distinguish between open loop and closed loop systems. | +-----------------------------------------------------------------------+ | 4. Negative feedback is invariably preferred in closed loop system. | | Justify? | +-----------------------------------------------------------------------+ | 5. List out the major advantages and disadvantages of open - loop | | systems. | +-----------------------------------------------------------------------+ | 6. Outline the advantages of closed loop system over the open loop | | system. | +-----------------------------------------------------------------------+ | 7. Express the force balance equation of ideal dashpot and ideal | | spring. | +-----------------------------------------------------------------------+ | 8. List out any two dynamic models used to represent control system. | +-----------------------------------------------------------------------+ | 9. Recall primary feedback ratio, in block diagram representation of | | a closed loop system. | +-----------------------------------------------------------------------+ | 10. List out the effect of positive feedback on stability. | +-----------------------------------------------------------------------+ | 11. List the characteristics of negative feedback. | +-----------------------------------------------------------------------+ | 12. Label the components of feedback control system. | +-----------------------------------------------------------------------+ | 13. Compare mechanical translational system and mechanical rotational | | system | +-----------------------------------------------------------------------+ **PART B -- 10 MARKS** +-----------------------------------------------------------------------+ | 12. Determine the overall transfer function of the system whose | | signal flow graph is shown in Figure 1 | | | | Figure 1 | +=======================================================================+ | 1. Develop the differential equations governing the mechanical | | system shown in Figure 2. Draw the force-voltage electrical | | analogous circuit and verify by writing mesh equation. | | | |  | | | | Figure 2 | +-----------------------------------------------------------------------+ | 2. Develop the differential equations governing the mechanical | | system shown in Figure 3. Draw the force-current analogous | | circuits and verify by writing node equations. | | | | Figure 3 | +-----------------------------------------------------------------------+ | 3. Determine the overall gain for the signal flow graph shown in | | Figure 4. | | | |  | | | | Figure 4 | +-----------------------------------------------------------------------+ | 4. Construct the differential equations governing the mechanical | | system shown in Figure 5. Draw the force-voltage electrical | | analogous circuit and verify by writing mesh equation. | | | | C:\\Users\\User\\Desktop\\cs pic\\Capture 8.JPG | | | | Figure 5 | +-----------------------------------------------------------------------+ | 5. Develop the differential equations governing the mechanical | | rotational system shown in Figure 6. Draw the torque-voltage and | | torque-current analogous circuits and verify by writing mesh and | | node equations. | | | |  | | | | Figure 6 | +-----------------------------------------------------------------------+ | 6. Determine the differential equations governing the mechanical | | rotational system shown in Figure 7. Draw the torque-voltage and | | torque-current analogous circuits and verify by writing mesh and | | node equations. | | | | Figure 7 | +-----------------------------------------------------------------------+ | 7. Using block diagram reduction technique, Analyse the closed loop | | transfer function of the system whose block diagram is shown in | | Figure 8 | | | |  | | | | Figure 8 | +-----------------------------------------------------------------------+ | 8. The signal flow graph for a feedback control system is shown in | | Figure 9. Determine the closed loop transfer function C(s)/R(s) | | | | C:\\Users\\User\\Desktop\\cs 2020\\New Doc 2019-12-27 | | 16.22.09\_14.jpg | | | | Figure 9 | +-----------------------------------------------------------------------+ | 9. Construct the closed loop transfer function of the system whose | | block diagram is shown in Figure 10 | | | |  | | | | Figure 10 | +-----------------------------------------------------------------------+ | | +-----------------------------------------------------------------------+ | Develop the differential equations governing the mechanical rotationa | | l system shown in | | --------------------------------------------------------------------- | | ----------------- | | | | Figure 12. Also draw the torque-voltage and torque current analogous | | circuits. | | | | Figure 12 | +-----------------------------------------------------------------------+ | 11. Convert the block diagram to signal flow graph shown in Figure 13 | | and determine the transfer function using Mason's gain formula | +-----------------------------------------------------------------------+ | | +-----------------------------------------------------------------------+ | | +-----------------------------------------------------------------------+ | | +-----------------------------------------------------------------------+ **MODULE 2 -- Time domain and Frequency Domain** **PART A -- 3 MARKS** +-----------------------------------------------------------------------+ | 16. List out the test signals used in control system | +=======================================================================+ | 1. State damping ratio in control systems | +-----------------------------------------------------------------------+ | 2. List out the classification of system depending on the value of | | damping | +-----------------------------------------------------------------------+ | +------------------------------------------------------------------+ | | | 15. Differentiate steady state error and steady state constants. | | | | | +==================================================================+ | | | 3. State generalized error coefficients | | | +------------------------------------------------------------------+ | | | 4. List out any two advantages of generalized error constants | | | | over static error constants. | | | +------------------------------------------------------------------+ | | | 5. Compare rise time and peak time. | | | +------------------------------------------------------------------+ | | | 6. List out the time domain specifications | | | +------------------------------------------------------------------+ | | | 7. Compare step signal and ramp signal | | | +------------------------------------------------------------------+ | | | 8. Recall steady state response | | | +------------------------------------------------------------------+ | | | 9. Infer damped frequency of oscillations in control systems | | | +------------------------------------------------------------------+ | | | 10. The closed loop transfer function of second order system is | | | | C(s)/R(s)=10/6S+10. Cite the type of damping in a system. | | | | | | | | +-------------------------------------------------------------+ | | | | | 14. A second order system has a damping ratio of 0.6 and | | | | | | natural frequency of oscillation is 10rad/sec. | | | | | | Determine the damped frequency of oscillation. | | | | | | | | | +=============================================================+ | | | | | 11. List out the drawbacks of static coefficients | | | | | +-------------------------------------------------------------+ | | | | | 12. List out the three constants associated with a steady | | | | | | state error. | | | | | +-------------------------------------------------------------+ | | | | | 13. State transient response. | | | | | +-------------------------------------------------------------+ | | | +------------------------------------------------------------------+ | +-----------------------------------------------------------------------+ **PART B -- 10 MARKS** 1. *Determine the gain K, so that the system will have a damping ratio of 0.5 for this value of K for a unit step input for the unity feedback system is characterized by an open loop transfer function G(s)=K/s(s+10).* 2. *Determine rise time, percentage overshoot, peak time and settling time for a step input of 12 units for the unity feedback control system has an open loop transfer function, G(s)=10/s(s+2).* *3. For a unity feedback control system the open loop transfer function, G(s)= 10(s+2)/s^2^(s+1).Represent* *a) the position, velocity and acceleration error constants.* *b) the steady state error when the input is R(s), where R(s)= 3/s -- 2/s^2^+ 1/3s^2^* *5. A positional control system with velocity feedback is shown in figure 14. Determine the response of the system for unit step input.* *6. A positional control system with velocity feedback is shown figure 15. Determine the response c(t) to the unit step input, rise time, peak time, maximum overshoot and settling time for damping ratio is 0.5.* *7. A unity feedback control system is characterized by the following open loop transfer function* *8. A unity feedback system has the forward transfer function G(s)= K1(2s+1)/s(5s+1)(1+s)^2^.When the input r(t)=1+6t, determine the minimum value of K1 so that the steady error is less than 0.1* **10.** *For servo mechanisms with open loop transfer function given below explain what type of input signal give rise to a constant steady state error* *a). 20(s+2)/s(s+1)(s+3) b).10/(s+2)(s+3)* *11. Determine the stability of the system represented by the characteristics equation, S^4^+8S^3^+18S^2^+16S+5=0. Comment on the location of the roots of characteristics equation.* *12. Determine the stability of the system with the number of roots lying on right half of s-plane, left half of s-plane and on imaginary axis whose characteristic equation is S^6^+2S^5^+8S^4^+12S^3^+20S^2^+16S+16=0.* *13. Determine the stability of the system with location of the roots of characteristics equation represented by the characteristic equation 9S^5^-20S^4^+10S^3^-S^2^-9S-10=0.* *14. A unity feedback control system has an open loop transfer function,* *15. Sketch the root locus of the system whose open loop transfer function is G(s) = K/s(s+2)(s+4).* **MODULE 3 -- Stability Analysis** **PART A -- 3 MARKS** +-----------------------------------------------------------------------+ | 16. Recall frequency response | +=======================================================================+ | 1. List out the different frequency domain specifications | +-----------------------------------------------------------------------+ | 2. Illustrate the correlation bettween the time and frequency | | response | +-----------------------------------------------------------------------+ | 3. List out advantages of bode plot | +-----------------------------------------------------------------------+ | 4. Outline the expression for resonant peak and resonant frequency | +-----------------------------------------------------------------------+ | 5. List out the advantages of frequency response analysis | +-----------------------------------------------------------------------+ | 6. Compare resonant frequency and resonant peak | +-----------------------------------------------------------------------+ | 7. List out frequency domain specifications | +-----------------------------------------------------------------------+ | 8. DIfferentiate gain margin and phase margin | +-----------------------------------------------------------------------+ | 9. The damping ratio and natural frequency of oscillation of a | | second order system is 0.5 and 8 rad/sec respectively. Cite the | | resonant peak and resonant frequency | +-----------------------------------------------------------------------+ | 10. Compare bode plot and approximate bode plot | +-----------------------------------------------------------------------+ | 11. Illustrate the value of error in the approximate magnitude plot | | of a first order factor at the corner frequency | +-----------------------------------------------------------------------+ | 12. The closed loop frequency response is determine from open loop | | frequency response using M and N circle. Justify | +-----------------------------------------------------------------------+ | 13. Draw the polar plot G(s)=1/(1+sT) | +-----------------------------------------------------------------------+ | 14. Draw the bode plot G(s)=1/(1+sT) | +-----------------------------------------------------------------------+ | 15. Compare minimum phase system and non-minimum phase system | +-----------------------------------------------------------------------+ **PART B -- 10 MARKS** 1. *Sketch bode plot for the following transfer function and the system gain K for the gain cross over frequency to be 5 rad/sec. G(s)=Ks^2^/(1+0.2s)(1+0.02s)* 2. *Sketch the bode plot for the following transfer function and phase margin and gain margin. G(s)= 75(1+0.2s)/s(s^2^+16s+100)* 3. *Sketch the bode plot for the transfer function, G(s)= Ke^-0.2s^/s(s+2)(s+8) with K so that the system is stable with a).phase margin equal to 45^0^ b). gain margin equal to 2db* 4. *The open loop transfer function of a unity feedback system is given by G(s)=1/s(1+s)(1+2s). Sketch the polar plot with gain margin and phase margin* 5. *The open loop transfer function of a unity feedback system is given by G(s)=1/s^2^(1+s)(1+2s). Sketch the polar plot with gain margin and phase margin* 6. *The open loop transfer function of a unity feedback system is given by G(s)=1/s(1+s^2^). Sketch the polar plot with gain margin and phase margin* 7. *Consider a unity feedback system having an open loop transfer function G(s)=K/s(1+0.5s)(1+4s).* **MODULE 4 -- Controllers** **PART A -- 3 MARKS** +-----------------------------------------------------------------------+ | 10. Sketch the step response of a P and PI controller | +=======================================================================+ | 1. Derivative controller is not used in control system. Justify | +-----------------------------------------------------------------------+ | 2. Outline the transfer function of PD and PI controller. | +-----------------------------------------------------------------------+ | 3. Differentiate type and order of a system | | | | +------------------------------------------------------------------+ | | | 9. List out the different types of controllers. | | | | | +==================================================================+ | | | 4. State the duality between controllability and observability | | | +------------------------------------------------------------------+ | | | 5. Recall the properties of eigen values | | | +------------------------------------------------------------------+ | | | 6. Show that the solution of homogeneous state equations | | | +------------------------------------------------------------------+ | | | 7. Illustrate eigen values and how eigen values are calculated, | | | | when eigen values are distinct | | | +------------------------------------------------------------------+ | | | 8. Model matrix is also called as vander monde matrix. Justify | | | +------------------------------------------------------------------+ | +-----------------------------------------------------------------------+ **PART B -- 10 MARKS** 1. **Consider the unity feedback system with open loop transfer function, G(s)= 100/(s+1)(s+2)(s+5). Design a PD controller, so that the phase margin of the system is 60^0^ at a frequency of 0.5 rad/sec.** 2. **Consider the unity feedback system with open loop transfer function, G(s)= 100/(s+1)(s+2)(s+10). Design a PID controller, so that the phase margin of the system is 45^0^ at a frequency of 4 rad/sec and the steady state error for unit ramp input is 0.6** 3. **Consider the unity feedback system with open loop transfer function, G(s)= 20/s(s+2)(s+4). Design a PD controller, so that the closed loop has a damping ratio of 0.8 and natural frequency of oscillation as 2 rad/sec.** 4. **Derive the transfer function for PID controller for industrial applications in control systems** 5. **Derive the transfer function for PD controller for industrial applications in control systems** **MODULE 5 -- State Space Representation** **PART A -- 3 MARKS** +-----------------------------------------------------------------------+ | 14. Illustrate the state model of nth order system | +=======================================================================+ | 1. List out the features of generalized error coefficients. | +-----------------------------------------------------------------------+ | 2. Sketch the block diagram representation of state model | +-----------------------------------------------------------------------+ | 3. Sketch the basic elements used to construct the block diagram of | | a state model | +-----------------------------------------------------------------------+ | 4. Draw the signal flow graph representation of state model | +-----------------------------------------------------------------------+ | 5. List out the advantages of state space modelling using physical | | variable | +-----------------------------------------------------------------------+ | 6. List out the advantages in chossing phase variables for state | | space modelling | +-----------------------------------------------------------------------+ | 7. List out the disadvantages in chossing phase variable for state | | space modelling | +-----------------------------------------------------------------------+ | 8. State transition matrix and how it is related to state of a | | system | +-----------------------------------------------------------------------+ | 9. Is state transition matrix is computed by canonical | | transformation. Justify | +-----------------------------------------------------------------------+ | 10. Outline the properties of state transition matrix | +-----------------------------------------------------------------------+ | 11. Classify the system depending on the value of damping. | +-----------------------------------------------------------------------+ | 12. Differentiate Controllability and Observability | +-----------------------------------------------------------------------+ | 13. State the condition for controllability by Gilberts method | +-----------------------------------------------------------------------+ **PART B -- 10 MARKS** 1. *The state model of the matrix is given by* 2. *Construct the state model of the electrical network shown in figure by choosing minimal number of state variables* 3. *Construct the state model of mechanical system shown in figure.* 4. *Obtain the state model of the mechanical system shown in figure by choosing a minimum of three state variables*  **Figure 18** 5. *Write state equations for the system shown in figure in which x1, x2 an x3 constitute the state vector. Determine whether the system is completely controllable and observable.* 6. *Consider the matrix A. Compute e^At^ by two methods.* 7. *A feedback system has a closed loop transfer function* *Construct three different state models for this system and give block diagram representation for each state model.* 8. *The state diagram of a linear system is given below Assign state variables and obtain the state model* A diagram of a function Description automatically generated **Figure 20** 9. *Construct the state model of the system whose transfer function is given as,* 10. *Construct a state model for a system characterized by the differential equation*