10ES-43 CONTROL SYSTEMS ( ECE A B&C Section) Faculty : Shreyus G & Prashanth V Chapter Title/ Class # Reference Literature Topic to be covered Part A No of Hours:52 % of Portions covered Reference Cumulative Chapter Unit 1: Modelling of Systems 1 T1 Ch 1.1, Mathematical models of physical system. Differential equations of physical mechanical 2 T1 Ch 2.1 systems.friction, Translational 15% 15% systems 3 T1 Ch 2.2 Rotational systems 4 T1 Ch 2.2 Gear trains 5 T1 Ch 2.7 Electrical systems 6 T1 Ch 2.7 Analogous systems Unit 2:Block Diagrams and Signal Flow Graphs 7-10 T1 Ch 2.4,2.5 Transfer functions, Block diagrams algebra 12% 27% 11-13 T1 Ch 2.6,2.7 Signal flow graphs; Unit 3:Time response of feed back control systems Standard test signals,unit step 14-15 T1 Ch 5.1,5.2 response of first and second order systems 16-17 T1 Ch 5.3 Time response specifications 15% 42% Time response specifications of 18 T1 Ch 5.4 second order systems 19-20 T1 Ch 5.5 Steady state errorsand error constants. Unit 4:Stability analysis 21-22 T1 Ch 6.1,6.2 Concept of stability, Necessary conditions for stability 23-24 T1 Ch 6.4,6.5 Routh-stability criterion 20% 62% 25-26 T1 Ch 6.6 More on the routh stability criterion Part B Unit 5:Root Locus Technique 27-28 T1 Ch 7.1 Introduction; 29-32 T1 Ch 7.2,7.3 Properties and construction of 15% 77% the root loci; Problems Unit 6: Stability in the Frequency Domain 33-34 T1 Ch 9.1 Mathematical preliminaries, 35-37 T1 Ch 9.2 Nyquest stability criterion 38-39 T1 Ch 9.3-9.4 Assessment of relative stability using Nyquest criterion 23% 100%
Unit 6:Frequency domainanalysis 27-28 T1 Ch 7.1 Introduction; 29-32 T1 Ch 7.2,7.3 Properties and construction of 15% 77% the root loci; Problems Unit 8: Introduction to state variable analysis 33-34 T1 Ch 9.1 Mathematical preliminaries, 35-37 T1 Ch 9.2 Nyquest stability criterion 38-39 T1 Ch 9.3-9.4 Assessment of relative stability using Nyquest criterion 23% 100% Text Book: 1. J.Nagarath and M.Gopal, Control systems Engineering New AgeInternational (p) Limited,Publishers, 4 th Edition-2005 Reference Books: 1. Modern Control Engineering, K.Ogata,Pearson Education Asia/PHI, 4 th Edition,2002 2. Concepts of ControlSystems,P.S. Satyanarayana: Dynaram publishers,bangalore,2001 3. Control systems- Principaes and design, M.Gopal,TMH.1999 4. Feedback control system analysis and synthesis,j.j.d Azzo and C.H.Houpis;McGraw Hill,International student Edition.
Question Bank Chapter 1: Modeling of Systems 1) What is control system? Explain different types of Control system. 2) What are the advantages and disadvantages of open loop and closed loop system? 3) Explain the comparison between open loop and closed loop system. (A) Electrical System 4) Find the Transfer function of the Electrical network system.. 5) Find the Transfer function of the Electrical network system R1 Vi C R2 Vo 6) Find the Transfer function of the Electrical network system 7) Find the Transfer function of the Electrical network system.. 8) Determine the transfer function relation Vo(s) to Vi(s) for the network shown in fig below. Calculate output voltage t 0 for a unit step voltage input at t=0.
(B) Mechanical System 9) Write the mechanical network for the following mechanical system K X M f(t) B 10) Write the mechanical network for the following mechanical system K D1 M1 D2 X2 M2 X1 f(t)
11) Write the mechanical network for the following mechanical system B3 X2 Xo X1 M2 K2 B2 f(t) M1 K3 K1 12) Write the differential equations governing the mechanical system show in fig. Find T.F K1 M1 X1 B M1 X f(t) K B1 B2 13) Determine the transfer function X1(s) F(s) and X2(s)/F(s) for the system shown in fig below. X1 X2 f(t) K1 B12 K2 M1 M1 B1 B2
14) Obtain the Mechanical circuit for the following Mechanical system and Find X1(s)/F(s) D1 K1 X1 M1 B2 K2 M2 f(t) (C) Analogous System 15) For the Mechanical system given find a) Write the Differential equations b) Draw the Mechanical network c) Draw the F-V and F-I analogous circuit B3 X2 Xo X1 M2 K2 B2 f(t) M1 K3 K1 16) For the Mechanical system given find a) write the Differential equations b) Draw the Mechanical network c) Draw the F-V and F-I analogous circuit K D1 M1 D2 X2 M2 X1
17) For the Mechanical system given find a) Write the Differential equations b) Draw the Mechanical network c) Draw the F-V and F-I analogous circuit B3 B1 M1 M2 f(t) 18) For the Mechanical system given find a) Write the Differential equations b) Draw the Mechanical network c) Draw the F-V and F-I analogous circuit K2 M2 X2 K3 B2 M3 X3 B3 f(t) M1 X1 K1 B1
(D) Rotational Motion 19) Write the differential equations governing the mechanical rotational system shown in fig.obtain the transfer function of the system. K J1 J2 T θ1 θ B 20) Write the differential equations governing the mechanical rotational system shown in fig. Obtain the transfer function of the system 2(s)/T(s) K J1 J2 T θ1 B12 θ B 21) Write torque current and torque voltage analogy Ko K1 K2 J1 J2 J3 T θ1 B1 B2 B3
22) S.T the system shown in figure are analogue systems Xi R2 K1 B1 1 o B2 Xo Ei C2 R E K2 Y C1 23) For the Mechanical system shown>draw the force voltage analogous network. Find the transfer function X2(s)/X1(s) L2 L1 X2 B1 K2 M2 X1 M1 B2 f(t)
24) Define transfer function, obtain the transfer function of an armature controlled D.C motor Ra La If=constant V e eb T θm Jm,Bm 25) Obtain the transfer function of a field controlled D.C. motor Rf Ea=Constant T
Assignment question 1) If C=1 f in the circuit shown in fig what values of R1 and R2 will give T=0.6sec and a=0.1 R1 Vi Vo T.F=a (1+ST) C R2 1+aST 2) Find the Transfer function of the network shown in fig below R i1 i2 Vi(t) C C Vo(t) R 3) Write the differential equations for the electrical network shown L1 R1 L2 i1(t) i2(t) + V C R2-4) Write the mechanical network for the following machine system X3 K2 B1 X2 K1 X1 M1 M2 f(t) B2
5) Write the equations of motion in S-domain for the system shown in fig below. Determine the transfer function of the system X1(t) X(t) K M f(t) B2 B1 6) For the Mechanical System given find a) Write the differential equations b)draw the Mechanical network c) Draw the F-V and F-I analogous circuit X3 K2 B1 X2 K1 X1 M1 M2 f(t) 7) Write torque current and torque voltage analogy J1 B2 K1 K2 K3 K4 J2 J3 J4 θ2 θ3 θ4 T θ1 B3 B4 8) S.T the two systems shown in fig (a) & (b) are analogous systems by comparing this T.F X2(s)/X1(s) Vi R V2 K X1 f(t) C B X2
9) Write torque current and torque voltage analogy K K1 J1 T θ1 θ2 B θ3 J2 K2 10) Draw the analogues circuit also Write the Differential equation for the Mechanical system. K L1 f (t) L2 f(t) M X(t) B Chapter 2: Block diagram reduction and Signal floe graph I) using block diagram reduction technique find closed loop transfer function of the system 1) H3 G1 G2 G3 H2 H1
2) G1 G2 H1 H2 H3 3) G4 G1 G2 G3 H2 H1 4) H2 G1 G2 G3 H1 G4
5) G3 H2 G1 G2 H2 6) G4 H1 G1 G2 G3 H2 H3 7) G1 G2 G3 H3 H2 H1
8) G3 G1 G2 H2 H1 9) G1 G2 G3 G4 G5 G6 G7 G5 10) H1 G1 G2 G3 G4 G5 H2
11) 1/Ra Rc 1/Ro 1/Rb Rd II Block diagram reduction of multiple inputs. 1) For the system represented by the block diagram shown in fig. Evaluate the closed loop transfer function when the input R is (a) At Station I (b) At Station II H3 G1 G2 G3 H1 H2
2) Find the transfer function C1/R1 and C2/R2 + - R1 + G1 G2 G3 C1 + H2 H1 2 R2 + + + - G4 G5 G6 C 3) A multi-input and multi output system is shown in fig determine the following transfer function C1/R1 when R2=0, C2/R1 when R2=0, C1/R2 when R1=0 and C2/R2 when R1=0 R1 + G1 C1 - G4 G2 - R2 - + R2 G3
Signal Flow Graph: I Obtain the transfer function using Masons gain formula for the signal flow Graphs given below. 1) -H1 -H2 G1 G2 G3 G4 R 1 1 G5 G8 G6 G7 C -H3 -H4 2) -0.5 10 2 R 10 1 C 1 5 1-1 -2-1
3) -H1 G4 G2 G1 G8 G6 R(s) 1 1 C(s) G3 G5 G7 -H2 4) -H1 0.5 R(s) G2 G3 G4 C(s) -H2 G6 -H3 5) -H2 R(s) 1 G1 G2 G3 G4 C(s) -H1-1
6) Convert the block diagram to signal flow graph and determine the transfer fnction using Masons gain formula G4 R(s) + + + + + G1 G2 G3 - - - H2 H1 C(s) R(s) 7) Convert the block diagram to signal flow graph and determine the transfer function using Masons gain formula H2 - + + + G1 G2 G3 C(s) - - - H1 G4 Assignment Questions I Determine the overall transfer function C(s)/R(s) for the following system R(s) 1) H2 - + G1 + + G2 G3 G4 C(s) H1 2) + G1 + C(s) G2 R(s) - H2 H1
3) H3 + + + + R(s) G1 G2 G3 - + H4 G4 C(s) H1 H2 4) G4 R(s) + C(s) G1 G2 + - H3 + G4 H2 + H1 Chapter 3: Time domain Analysis of Control System 1)For a second order system subjected to unit step input,determine tr,tp,mp and settling time ts given ζ=0.6 w n =5 r/s 2) A unity feed back control system is characterized by an open-loop transfer function G(s) H(s) = K S(S+10) Determine the gain K,so that the system will have a damping ratio of 0.5.For this value of K find the rise time, peak time and peak overshoot. Assume that the system is subjected to a step of 1V.
3) The open loop transfer function of a unity feedback system is given by G(s) = K S (ST+1) where K & T are +ve constant. By what factor should the amplifier gain K be reduced, so that the peak overshoot of unit step response of the system is reduced from 75% to 25%. 4) A unity feedback control system has an open loop transfer function G(s) = 10 Find the rise time, S(S+2) percentage overshoot, peak time and settling time for a step input of 12 units. 5) Measurements conducted an a servomechanism show the system response to be C(t)=1+0.2e -60t -1.2e 10t when subjected to a unit step input. Obtain an expression for closed loop transfer function, Determine the undamped natural frequency and damping ratio. 6) A unity feedback control system show in fig,find the transfer function of the prototype system used to model a second order system. 7) A unity feed back control system has an amplifier with gain KA=10 and gain ratio G(s) = 1 S(S+2) in the feedback forward path. A derivative feed back H(s) =SKo is introduced as a minor loop around G(s). Determine the derivative feedback constant Ko.So that the system damping factor is 0.6. 8) For servomechanism with open loop transfer function given below. Explain what type of input signal give rise to constant steady state errors and calculate their values. 9) Consider a unity feedback system with a closed loop transfer function C(s) KS+b R(s) S 2 +as+b Determine the open loop transfer function G(s).S.T the steady state error with unit ramp input is given by
a-k b 10) A unity feedback system has the forward transfer function G(s) = K 1 (2S+1) The input r(t)=1+6t is S (5S+1) (1+S 2 ) applied to the systems. Determine the minimum values of K1 if the steady error is to be less than 0.1 11) For a control system the open loop transfer function is G(s) = 40 Determine the steady (S+1) (S 2 +10S+6)) state error of the system. When the transfer function of the feed back path is H(s) = 4 (S+3) r(t)= t 2 /2 and the system input are (i) r(t)=4u(t) (ii)=5tu(t) (iii) 12) For the unity feed back system shown in fig find the steady state error for (i) a unit step input (ii) a unit step velocity input (iii) a unit step acceleration input 10 0.2S+1 20 0.4 13) A unity feed back Has G(s) = 40 (S+2) S(S+1) (S+4) Determine (i) Type of the system (ii) Steady state error for the input r (t) = 4t 14) For a unity system G(s) = 100 r(t)=6t. Determine steady state errors. S(S+8) If it is desired to reduce this existing error by 5%. Find new value of gain of the system. Assignment: 1) A unity feedback control system is characterized by the following open loop transfer function G(s) = 0.4S+1 Determine its transient response for unit step input and sketch the response, S(S+0.6) Evaluate the maximum overshoot and the corresponding peak time.
2) For system shown in fig determine i) Wn ii) Wd iii) damping ratio ζ iv) rise time tr v) % peak overshoot approximate 5% settling time vi) input to the system may be assumed to be step input signal R(s) 9 S(S+3) C(s) 3) For the system shown below determine the value of K,Kh,Mp is 20% tp=1 sec. Obtain tr & ts R(s) K S(S+1) C(s) 1+Kh S 4) A unity feed back system has G(s)= 80 (S+1) Determine (i) Type of the system (ii) All error S(S+2)(S+4) Coefficients and (iii) Steady state errors for a ramp input r(t)=4t. 5) For the unity feedback system having open loop transfer function G(s)= K(S+1) S (S 3 +5 S 2 +6S) Determine (i)type of the system (ii) error constants (iii) Steady state error for unit parabolic input
6) For a system shown in fig determine the type of the system, error constants and the steady state error for the input r(t)=10+5t+3t 2 20 + + 25 1/4 R(s) - S(S+4)(S+ - 10) C(s) 10S 7) A unity feedback control system has the forward transfer function G(s) = K (2S+1) S (4S+1) (S+1) 2 Determine the value of the K to limit the steady state error to 0.2 when the input r(t)=1+5t is applied. 8) A unity feed back system has G(s) = K S(S+2) (S 2 +2S+5) i) For a unit ramp input, it is desired ess 0.2 find K ii) Determine ess if input r(t)=2+4t+t 2 /2 Chapter 4: Stability Analysis 1) Determine the stability of the system having following characteristic equation (i) F(s) =S 3 +20 (ii) F(s) =S 3 +6 S 2 +11S+6 (iii) F(s) =S 5 +2S 4 + 4S 3 +6S 2 +2S+5 (iv) F(s)=(S-2)(S+1)(S-3) 2) Determine the stability of the system having following characteristic equation (i) F(s) =S 5 +2S 4 + 3S 3 +6S 2 +2S+1
(ii) F(s) =S 5 +S 4 + 2S 3 +2S 2 +3S+5 3) Determine the stability of the system having following characteristic equation (i) F(s) =S 8 +5S 6 + 2S 4 +3S 2 +1 (ii) F(s) =S 5 +S 4 + 4S 3 +24S 2 +3S+63 (iii) F(s) =S 6 +2S 5 + 8S 4 +12S 3 +20S 2 +16S+16 (ii) F(s) =S 5 +2S 4 + 24S 3 +48S 2-25S-50 4) Find the range of K so that the system has the G(s)= K & H(s)=1 S (S 2 +S+1) (S+4) and the system will be stable. 5) A unity feed back system having 2 is marginally stable and S (S 2 +PS+4K) oscillates with frequency 2 r/s. Find K & P 6) An open loop transfer function has poles at S=0 & S=-2 and zero at S=-4 if H=1.Determine the range of K for stable system. 7) Find how many roots have real parts greater than -1 for S 3 +9 S 2 +30S+40=0 8) An unity feed back control system has open loop transfer function G(s) = K S(1+T 1 S) (1+T 2 S) Find the value of K, if the system is stable (T1 & T2>0) 9) Determine the range of K such that the roots of the characteristic equation F(s)=S(S+1)(S 2 +3S+2)+K=0 are more negative than -1 10) Find the range of K for stable feed back control system show in fig 5S+10 S+1 K S+1 5/ S 11) A system oscillates with a frequency of W, if it has poles at S=±jW and no poles in the right half of S- plane. Determine the values of K and a. So that the system shown in fig oscillates at a frequency of 2 r/s
K(S+1) S 3 +as 2 +2S+1 12) For a unity feed back system with G(s) = K using RH criterion find the range S(1+0.4S) (1+0.25S) of K for stability, marginal value of K and frequency of sustained oscillations. Assignment: 1) Determine the stability of the system having following characteristic equation (i) F(s) =S 4 +20S 3 +55S 2 +60S+34 (ii) F(s) = S 4 +4S 3 +3S 2 +10S+20 (iii) F(s) =S 5 +2S 4 +3S 3 +6S 2 +5S+6 (iv) F(s)= S 4 +2S 3 +6S 2 +8S+8 2) For the closed loop feedback system G(s) = K Determine the range of K for which the S 4 +5S 3 +5S 2 +4S+K system is stable and also the frequency of the sustained oscillation. 3) A unity feed back control system has G(s) = K(S+13) using the Routh s Criterion calculate the S(S+3) (S+7) range of K for which the system is (i) stable (ii) has its closed loop poles more negative than -1 4) A unity feed back control system has G(s) = K using the Routh s Criterion, find the range of S(S+2) (S+4) (S+6) K for stability. Also find K max & W max. 5) For the system represented by open loop transfer function G(s) H(s) = K using RH criterion (S+1) (S+2) (S+3) (i) Determine the range of K for which the system is stable. (ii) The value of K for which the system develops a sustained sinusoidal oscillations and corresponding frequency.
Chapter 5: Root Locus 1) A unity feed back control system has the forward transfer G(s) = K (S+2)(S+4) 2) Plot the root locus pattern of a system whose forward path transfer function is G(s) = K S(S+2) (S+3) 3) A negative feed back control system is characterized by G(s) H(s) = K S(S+1) (S+2) (S+3) Sketch the root locus plot for values of K ranging from 0 to.mark all the salient points on the root locus. 4) A unity feed back control system has G(s) = K Sketch the root locus has show on it S(S+2) (S+5) (a) Breakaway point (b) line for ζ=0.5 and value of K for this damping ratio (c) The frequency at which the root locus crosses the imaginary axis and the corresponding values of K. 5) Sketch the root locus plot for a negative feed back control system having an open loop transfer function G(s) H(s) = K S(S 2 +2S+2) 6) Sketch the root locus plot for unity feed back control system having an open loop transfer function G(s) H(s) = K S (S+4) (S 2 +4S+20) 7) For a system having loop transfer function G(s) H(s) = K Plot the root locus and find (S+3) (S 2 +4S+3) the values of K for marginal stability and corresponding frequency of oscillations.
K1 S+1 K2 S+3 8) Sketch the root locus of a feed back control system whose open loop transfer function is given by G(s) H(s) = K Determine the value of K for damping ratio ζ =0.5 S (S+3) (S 2 +2S+2) 9) Sketch the root locus of a feed K4 back control system whose open loop transfer function is given by G(s) = K(S+4) and S+4 H(s) =1. Determine the value of K for damping ratio ζ =0.707 S (S 2 +16S+13) 10) Sketch the root locus for positive values of K for the system G(s)H(s)= K(S+6) S(S+1) (S+2) Indicate all salient points and determine the range of K for which the system is stable also find the K value at BAP. 11) Sketch the root locus plot for a closed loop system having an open loop transfer function G(s) = K(S+2) S(S+1) For all values of K from 0 to. Comment on the stability of the system. Also show that a part of the root locus is a circle. 13) Sketch the root locus for a unity feed back control system with open loop transfer function G(s) = K(S+1) (S+3) S(S+1)
Assignment Questions 1) Draw the root locus and Determine the stability of the system with G(s) H(s) = K S(S+2) (S+8) 2) A unity feed back control system has an open loop transfer function G(s) = K S (S 2 +4S+13) Sketch the loop locus. 3) The open loop transfer function of a unity feed back system is given by G(s) = K (S+a) S (S 2 +4S+1) 4) Sketch the root locus for unity feed back system whose open loop transfer function is G(s) H(s) = K (S+1.5) S(S+1 (S+5) 5) Draw the root locus of a unity feed back control system given G(s) = K (S+1) S 2 (S+5) Chapter 5: Frequency Domain Analysis Bode Plot: 1) Explain the terms gain margin and phase margin as of a control system. 2) What the advantages are of bode diagrams? 3) Define the terms (i) Asymptotic plot (ii) Corner frequency (iii) Phase crossover frequency (iv) Gain crossover frequency. 4) Define and derive :Peak resonance Mp, Resonant frequency Wp, Band width Bw 5) Define cut off rate, cut off frequency. 6) The stability of a negative feed back control system whose open-loop transfer function is given by GH(s)= 50 S (0.5S+1) (0.05 S+1) 7) The loop transfer function of a system G(s) H(s) = 40 Determine gain and S(S+2) (S+5) Phase margin. Comment on the stability. 8) Sketch the Bode plot for the open loop transfer function G (jw) = 2 jw (1+i0.4w) (1+j0.1w) 9) Sketch the Bode plot for the open loop transfer function G (jw) = 160(S+2)
S 2 (S+8) (S+10) 10) Construct Bode Magnitude and phase diagrams GH(s) = 100 (0.1S+1) S(S+1) 2 (0.01S+1) Also comment on the stability of the system 11) Construct Bode Magnitude and phase diagrams GH(s) = 200 (S+2) S (S 2 +10S+100) Also comment on the stability of the system 12) Construct Bode Magnitude and phase diagrams GH(s) = 64 (S+2) S (S 2 +3.2S+64) (S+0.5) Also comment on the stability of the system 13) Find the open transfer function of the system whose Bode s magnitude is shown 0 db/dec -20 db/dec +20 db/dec 40 +20 db/dec 20 og w 1 10 100 1000 l
14) Find the open transfer function of the system whose Bode s magnitude is shown 40-40 db/dec 20 0.1 0.5 1 10-20 db/dec 50 100-20 +20 db/dec -40 db/dec -40 15) Find the open transfer function of the system whose Bode s magnitude is shown 40 30-20 db/dec 20 14 A -40 db/dec 0 50 Log W 0.1-20 db/dec -26 B -30 C -40 db/dec
16) A unity feedback control system has G(s)= K Determine the value of K so S (S+1) (1+0.1 S) that (i) Gain margin 12 db (ii) Phase margin=30 o 17) Sketch the Bode plots for the transfer function G(s)= KS 2 Determine the (1+0.2S) (1+0.02S) system gain K for the gain crossover frequency to be 5 rad/sec. 18) Sketch the Bode plots for the transfer function G(s)= KS+1) Determine the S (1+0.1S) 2 (1+0.02S) system gain K (i) for the gain margin of 20 db (ii) for a phase margin of 30 o 19) The open loop transfer function of a unity feedback control system is given by G(s) = K S (1+0.001S) (1+0.25S) (1+0.1S) Determine the value of K so that the system will have a phase margin of 40 o.what will be the gain margin? Use Bode plot. 20) The open loop transfer function of a unity feedback control system is given by G(s) = K S (S+2) (S+10) Determine the value of K so that the system will have a phase margin of 50 o and gain margin to be 10 db. Use Bode plot. Assignment questions: 1) Draw the Bode plot for a system having G(s) = K (1+0.2S) (1+0.025S) S 3 (1+0.001S) (1+0.005S) Show that the system is conditionally stable. Find the range of K for which the system is stable. 2) The open loop transfer function of a feedback control system is G(s)= 10 S (1+0.02S) (1+0.2S) Sketch the bode plot and determine gain margin and phase margin 3) The open loop transfer function of a feedback control system is G(s) = K S (1+S) (1+0.1S) (1+0.01S)
Determine the value of K 4) The open loop transfer function of a feedback control system is G(s)= 242(S+5) S (S+1) (S 2 +5S+121) Sketch the bode plot and determine gain margin and phase margin Nyquist Path and Stability Criterion: 1) State and explain Nyquist stability criterion. 2) Define gain margin and phase margin and explain how you measure them using Nyquist criterion 3) For the gain open loop transfer function G(s) H(s) = K of a system, sketch the S(S+2) (S+10) Nyquist plot and calculate the range of K for the system to be stable. 4) For the gain open loop transfer function G(s) H(s) = K of a system, sketch the S(S+1) (S+2) Nyquist plot and calculate the range of K for the system to be stable. 5) Find the range of values of K for which the closed loop control system is stable by using Nyquist criterion. G(s) H(s) = K(S+1) S(S-1) 6) Given that G(s) H(s) = K Determine the value of K for stability using Nyquist analysis. S(S+S 2) 7) Sketch the Nyquist plot of a unity feedback control system having the open loop transfer function G(s) = 5 Determine the stability of the system using Nyquist stability criterion. S (1-S) 8) Discuss the stability of a unity feed back control system having the open loop transfer function G(s) = 50 S (1+0.1S) (1+0.2S) Assignment questions: 1) The loop transfer function of a control system is G(s) H(s) = 40 Sketch the (S+4) (S 2 +2S+2) Nyquist stability plot. Find Gain margin and comment on stability.
2) The unity feedback control system has open loop transfer function G(s) = 2500 S (S+10) (S+5) Determine whether the system is stable or not.