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Uestion Two ) Consider a second order system whose transfer function, H(s), is given by: s+5 A(s)...
Question One (a) The Impulse Response of a second order system is given by h(t) where: h(t) 4000e...
Question One (a) The Impulse Response of a second order system is given by h(t) where: h(t) 4000e 3000 c0, where the time, t, is given in milliseconds (ms) and h(t) is considered to be the resulting voltage in volts. 0) Derive the Transfer Function, the Laplace Transform H(s) of h(t). () Using part (0). write out the Frequency Response, HGo), of the second order (ii) Express the Frequency Response obtained in part (i) as a single response system. and...
2- The following requirements are given for a second-order system that is described by the transfer...
2- The following requirements are given for a second-order system that is described by the transfer function s2+25Wnstwa Maximum overshoot: 5% <P.0.< 15% Settling time: 5s < 75% < 10s Peak time: tp < 2s (a) Describe and sketch the s-plane regions of the pole locations satisfying the requirements. (20pts) (b)Determine the largest and smallest possible peak time of a system with the poles satisfying the requirements. (10pts) Hints: Im(s) cos =-5 10, vi Res P.O.=100e 1-3 16 wn, tp
uestion 3: (10 points) n the RC circuit in the figure, Ri = 10 KQ, R2...
uestion 3: (10 points) n the RC circuit in the figure, Ri = 10 KQ, R2 = 30 KO, and C 6 uF. aswer the following questions, ) What is the equivalent resistor R12 to R and R2? 2) Find the differential equation relating the output voltage Vout to the input voltage 3) What is the order of the system? 4) What is the time constant t? 5) For step input Vin = 10V, find an expression for the output...
Question One (a) The Impulse Response of a second order system is given by h(t) where: h (t) 4000...
Question One (a) The Impulse Response of a second order system is given by h(t) where: h (t) 4000 e 3000 e20 where the time, t, is given in milliseconds (ms) and h(t) is considered to be the resulting voltage in volts. (0) Derive the Transfer Function, the Laplace Transform H(s) of h(t). (i) Using part (0, write out the Frequency Response, H(jo), of the second order (ii) Express the Frequency Response obtained in part (i) as a single response...
5 Problem 4.41 Consider the second-order plant with transfer function: 1 G(s) = (s1)(5s 1) and...
5 Problem 4.41 Consider the second-order plant with transfer function: 1 G(s) = (s1)(5s 1) and in a unity feedback structure 1. Determine the system type and error constant with respect to tracking polynomial reference inputs of the system for P (i.e., De = kp), PD (i.e., Dc = kp+kps), and PID (i.e., De=kp +ki/s+ kps) controllers. Let kp = 19,ki 0.5,kp = 4/19. 2. Determine the system type and error constant of the system with respect to disturbance inputs...
5. Draw the magnitude characteristic of the Bode plot of the following transfer function: H(s)10(10s +11...
5. Draw the magnitude characteristic of the Bode plot of the following transfer function: H(s)10(10s +11 (S + 200)2 Identify the poles and zeros Sketch the magnitude plot. The y-axis should be in dB. The x-axis should logarithmic, but labeled in rad/sec e) f) g) Use MATLAB to draw the complete Bode plot and check your answer. h) If the input current is VIN(t)-10 cos(t+35"),what is the output voltage. Use your MATLAB Bode plot to answer this.
b) Given a second order system with the following open loop transfer function where damping ratio,...
b) Given a second order system with the following open loop transfer function where damping ratio, } = 0.707 and natural frequency, Wn= 2.5. wn? G(S) = S2 + 23wns +wn? i. Determine the steady state error to an appropriate input via a calculation method using the transfer function. Compare your answer with the steady state error from the exact frequency response for this system given in Figure Q4(b). (5 marks) ii. Evaluate the difference of the exact frequency response...
= 2s +1 Consider the continuous-time LTI causal system with Transfer function H(s) $? + 5s...
= 2s +1 Consider the continuous-time LTI causal system with Transfer function H(s) $? + 5s +6' a) Compute the ROC for H(s). (3 pts) b) Discuss the BIBO stability of the system. (2pts) c) Compute the system output when the input is x(t) = 8(t) (Dirac's delta). (5 pts)
Consider the system with open-loop transfer function s+2 G(s) = k 82 4 Show the type...
Consider the system with open-loop transfer function s+2 G(s) = k 82 4 Show the type of poles that the close-loop system has (real, imaginary, or repeated) for the different values ofk in [0 +00). Sketch the root locus of the close-loop system's poles when the gain k takes values in [0 +oo). Show clearly the break points of the loci, and calculate analytically the values that the branches of the loci are converging when k o
Using MATLAB 4) Consider the stable second-order continuous transfer function (in s domain): H = S...
Using MATLAB
4) Consider the stable second-order continuous transfer function (in s domain): H = S +1 S2 + 3s + 2 Using the command Hd = c2d (H, Ts) with Ts = 0.1, convert H to the z domain. On the same Figure, plot the continuous impulse response of the system against the discrete one. Considering your work in problem 4, 5) Vary Ts (Ts = 0.7, 0.5, 0.3, 0.1) and observe the plot of the continuous impulse response...
Question One (a) The Impulse Response of a second order system is given by h(t) where: h(t) 4000e 3000 c0, where the time, t, is given in milliseconds (ms) and h(t) is considered to be the resulting voltage in volts. 0) Derive the Transfer Function, the Laplace Transform H(s) of h(t). () Using part (0). write out the Frequency Response, HGo), of the second order (ii) Express the Frequency Response obtained in part (i) as a single response system. and...
2- The following requirements are given for a second-order system that is described by the transfer function s2+25Wnstwa Maximum overshoot: 5% <P.0.< 15% Settling time: 5s < 75% < 10s Peak time: tp < 2s (a) Describe and sketch the s-plane regions of the pole locations satisfying the requirements. (20pts) (b)Determine the largest and smallest possible peak time of a system with the poles satisfying the requirements. (10pts) Hints: Im(s) cos =-5 10, vi Res P.O.=100e 1-3 16 wn, tp
uestion 3: (10 points) n the RC circuit in the figure, Ri = 10 KQ, R2 = 30 KO, and C 6 uF. aswer the following questions, ) What is the equivalent resistor R12 to R and R2? 2) Find the differential equation relating the output voltage Vout to the input voltage 3) What is the order of the system? 4) What is the time constant t? 5) For step input Vin = 10V, find an expression for the output...
Question One (a) The Impulse Response of a second order system is given by h(t) where: h (t) 4000 e 3000 e20 where the time, t, is given in milliseconds (ms) and h(t) is considered to be the resulting voltage in volts. (0) Derive the Transfer Function, the Laplace Transform H(s) of h(t). (i) Using part (0, write out the Frequency Response, H(jo), of the second order (ii) Express the Frequency Response obtained in part (i) as a single response...
5 Problem 4.41 Consider the second-order plant with transfer function: 1 G(s) = (s1)(5s 1) and in a unity feedback structure 1. Determine the system type and error constant with respect to tracking polynomial reference inputs of the system for P (i.e., De = kp), PD (i.e., Dc = kp+kps), and PID (i.e., De=kp +ki/s+ kps) controllers. Let kp = 19,ki 0.5,kp = 4/19. 2. Determine the system type and error constant of the system with respect to disturbance inputs...
5. Draw the magnitude characteristic of the Bode plot of the following transfer function: H(s)10(10s +11 (S + 200)2 Identify the poles and zeros Sketch the magnitude plot. The y-axis should be in dB. The x-axis should logarithmic, but labeled in rad/sec e) f) g) Use MATLAB to draw the complete Bode plot and check your answer. h) If the input current is VIN(t)-10 cos(t+35"),what is the output voltage. Use your MATLAB Bode plot to answer this.
b) Given a second order system with the following open loop transfer function where damping ratio, } = 0.707 and natural frequency, Wn= 2.5. wn? G(S) = S2 + 23wns +wn? i. Determine the steady state error to an appropriate input via a calculation method using the transfer function. Compare your answer with the steady state error from the exact frequency response for this system given in Figure Q4(b). (5 marks) ii. Evaluate the difference of the exact frequency response...
= 2s +1 Consider the continuous-time LTI causal system with Transfer function H(s) $? + 5s +6' a) Compute the ROC for H(s). (3 pts) b) Discuss the BIBO stability of the system. (2pts) c) Compute the system output when the input is x(t) = 8(t) (Dirac's delta). (5 pts)
Consider the system with open-loop transfer function s+2 G(s) = k 82 4 Show the type of poles that the close-loop system has (real, imaginary, or repeated) for the different values ofk in [0 +00). Sketch the root locus of the close-loop system's poles when the gain k takes values in [0 +oo). Show clearly the break points of the loci, and calculate analytically the values that the branches of the loci are converging when k o
Using MATLAB
4) Consider the stable second-order continuous transfer function (in s domain): H = S +1 S2 + 3s + 2 Using the command Hd = c2d (H, Ts) with Ts = 0.1, convert H to the z domain. On the same Figure, plot the continuous impulse response of the system against the discrete one. Considering your work in problem 4, 5) Vary Ts (Ts = 0.7, 0.5, 0.3, 0.1) and observe the plot of the continuous impulse response...
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