4. The de servo system shown in Figure Q4.1 is required to have a transient step response speci fication with a peak time of 0.58 seconds or better, and a +2% setting time of 1.7 seconds or better 01(s) K (s)G(s) s(s 1 (s 5) Figure Q4.1 The Bode diagram of the open-loop system is shown in Figure Q4.2 on page 8. This Bode diagram shows the uncompensated system (when K(s) 1, shown as a dashed line) and also shows the effect of including a particular lead compensator (shown as a solid line) (a) Translate the transient specification into an equivalent frequency response specification. 5Marks (b) The effect of a particular lead compensator is shown in Figure Q4.2 (page 8). Measure the gain crossover frequency of the compensated system and, assuming that the maximum phase advance mar has been added at this frequency, take measurements from the diagram in order to deduce the particular lead compensator transfer function. Include a gain parameter in your solution. Annotate Figure Q4.2 as appropriate Hint: You should not use the specification of part (a) in order to determine the compensator 6 Marks (c) Use MATLAB® to estimate the compensated system gain and phase margins, and also to produce a closed-loop step response for the compensated system. Include the MATLAB code used and the appropriate graphs. Explain any differences between the achieved per- formance and the specification of part (a) [4 Marks] (d) An improved specification requires that the settling time is halved, whilst maintaining the same damping ratio. Take appropriate measurements from Figure Q4.2 to help reveal why the standard design method will not succeed in this case, and suggest a way in which the compensator could be modified to enable a successful design to be carried out. You do not need to design any new compensator for part (d) 5 Marks] (e) What is the closed-loop compensated system steady-state error to a unit ramp input de- mand, with the compensator of part (b)? What further modification to the compensator might be required to further reduce this steady-state error without having an adverse effect on the achieved frequency response specification from part (a)? Do not design any new compensator for this part. 5 Marks]
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Bode Diagram 10 10 Frequency (rad/s) Bode Diagram 100F 140 10 10 Frequency (rad/s) Figure Q4.2 4. The de servo system s...
Consider the system shown as below. Draw a Bode diagram of the open-loop transfer function G(s).
1 Consider the system shown as below. Draw a Bode diagram of the open-loop transfer function G(s). Determine the phase margin, gain-crossover frequency, gain margin and phase-crossover frequency, (Sketch the bode diagram by hand) 2 Consider the system shown as below. Use MATLAB to draw a bode diagram of the open-loop transfer function G(s). Show the gain-crossover frequency and phase-crossover frequency in the Bode diagram and determine the phase margin and gain margin. 3. Consider the system shown as below. Design a...
5. Consider the feedback system in Figure 4 where! G(s) = 26+10% Figure 4 The Bode...
5. Consider the feedback system in Figure 4 where! G(s) = 26+10% Figure 4 The Bode plot of G is shown in Figure 5. Boda Diagram Magnitude (dB) -100- -156 -135 -root -225 10 Frequency radici Figure 5: Bode plot of G (a) [2 marks] Find the phase margin, gain margin and gain crossover frequency (approximate as needed) for the case when C(s) = 1. PM = GM = wc = You are asked to design a feedback controller C(s)...
Determine the shape in the frequency plane and the Bode diagram for the transfer function K(s...
Determine the shape in the frequency plane and the Bode diagram for the transfer function K(s + 2) GH- s?(s + 4)(s + 6) For a plant that has a diagram like the one shown in the figure, design a lead compensator so that the system has a maximum elongation of 15%. 5+2 K 5 + P CONTROL 6 s(s+2) PLANTA Construct the Bode diagram for the frequency response function: 2 GH(jw) - jw (1 + jw/2)(1 + jw/5) Design...
C(s) G(s) Figure 1: A block diagram for Problems 1-4 For the given unity feedback system with G(s...
C(s) G(s) Figure 1: A block diagram for Problems 1-4 For the given unity feedback system with G(s) - s 5)3' (a) Find the location of the dominant poles to yield a 1.2 second settling time and overshoot of 15% (b) If a compensator with a zero at-1 is used to achieve the conditions of Part a, what must be the angular contribution of the compensator pole be? (c) Find the location of the compensator pole. (d) Find the gain...
Y(s) C(s) G(s) R(S) Figure 1: Closed-loop system Q2 Consider the setup in Figure 1 with S s1 (i) ...
Y(s) C(s) G(s) R(S) Figure 1: Closed-loop system Q2 Consider the setup in Figure 1 with S s1 (i) Design a K,τ, α in the lead compensator 1TOS so that the closed-loop system shown in Figure 1 has a steady state error of.0 for a unit ramp reference input at R and a phase margin of about 45 degrees K, α, τ without Bode plots. When you add phase with the lead compensator add an additional 10 degrees of phase....
Write a MATLAB program that w design a PD compensator assuming second-order approximations as fol...
Write a MATLAB program that w design a PD compensator assuming second-order approximations as follows. . Allow the user to input the desired percent overshoot, peak time and gain required to meet a steady-state error specification Display the gain-compensated Bode plot . Calculate the required phase margin and bandwidth. . Display the pole, zero, and gain of the PD compensator. Display the compensated Bode plot ·Output the step response of the PD-compensated system to test your second-order approximation. [Implement your...
You may prepare your answer in softcopy, print out and submit or use hardcopy approach. Put...
You may prepare your answer in softcopy, print out and submit or use hardcopy approach. Put all your MATLAB codes and Simulink Diagram under the appendix. The system below is to be compensated to achieve a phase margin of 50 degrees. s +3 x(t) 5+2s+ 2s E-KH. yệt) Design gain and phase-lead compensator to achieve the desired PM of 45 degrees. +PART A: Uncompensated system analysis % created by Fakhera 2020 Determine the uncompensated PM and GM s=tf('s'); g= (5+3)/...
4. Referring to the closed-loop system shown as below, design a lead compensator Ge(s) such that...
4. Referring to the closed-loop system shown as below, design a lead compensator Ge(s) such that the phase-margin is 45o, gain margin is not less than 8dB, and the static velocity error constant Ky is 4.0 sec1. Plot unit-step and unit-ramp response curves of the compensated system with MATLAB.
The transfer function of the given physical system is 2500 Gp(s)-T-1000 Part 3 1. Frequency response (a) Draw the bode...
The transfer function of the given physical system is 2500 Gp(s)-T-1000 Part 3 1. Frequency response (a) Draw the bode plot of open-loop transfer function when K (b) Use bode plot of open-loop transfer function to determine the type of system (do not use transfer function) (c) For what input the system will have constant steady-state error (d) for the unit input in item (c) calculate the constant steady-state error.(Use bode plot to calculate the error.) (e) Design a lead...
7. a) Sketch the root-locus Ris) C(s) diagram for the system S(5+) shown in figure when...
7. a) Sketch the root-locus Ris) C(s) diagram for the system S(5+) shown in figure when Ge=1. 6) Design phare- lead be compensator such that the system time constant is 0,25 see and != 0,45. Assume compensator at s=-4. Sketch the root-locus diagram of compensated system. c) Find the unit step responses of COMPENSATED and WN COMPENSATED systems and plot these responses. zero
5. Consider the feedback system in Figure 4 where! G(s) = 26+10% Figure 4 The Bode plot of G is shown in Figure 5. Boda Diagram Magnitude (dB) -100- -156 -135 -root -225 10 Frequency radici Figure 5: Bode plot of G (a) [2 marks] Find the phase margin, gain margin and gain crossover frequency (approximate as needed) for the case when C(s) = 1. PM = GM = wc = You are asked to design a feedback controller C(s)...
Determine the shape in the frequency plane and the Bode diagram for the transfer function K(s + 2) GH- s?(s + 4)(s + 6) For a plant that has a diagram like the one shown in the figure, design a lead compensator so that the system has a maximum elongation of 15%. 5+2 K 5 + P CONTROL 6 s(s+2) PLANTA Construct the Bode diagram for the frequency response function: 2 GH(jw) - jw (1 + jw/2)(1 + jw/5) Design...
C(s) G(s) Figure 1: A block diagram for Problems 1-4 For the given unity feedback system with G(s) - s 5)3' (a) Find the location of the dominant poles to yield a 1.2 second settling time and overshoot of 15% (b) If a compensator with a zero at-1 is used to achieve the conditions of Part a, what must be the angular contribution of the compensator pole be? (c) Find the location of the compensator pole. (d) Find the gain...
Y(s) C(s) G(s) R(S) Figure 1: Closed-loop system Q2 Consider the setup in Figure 1 with S s1 (i) Design a K,τ, α in the lead compensator 1TOS so that the closed-loop system shown in Figure 1 has a steady state error of.0 for a unit ramp reference input at R and a phase margin of about 45 degrees K, α, τ without Bode plots. When you add phase with the lead compensator add an additional 10 degrees of phase....
Write a MATLAB program that w design a PD compensator assuming second-order approximations as follows. . Allow the user to input the desired percent overshoot, peak time and gain required to meet a steady-state error specification Display the gain-compensated Bode plot . Calculate the required phase margin and bandwidth. . Display the pole, zero, and gain of the PD compensator. Display the compensated Bode plot ·Output the step response of the PD-compensated system to test your second-order approximation. [Implement your...
You may prepare your answer in softcopy, print out and submit or use hardcopy approach. Put all your MATLAB codes and Simulink Diagram under the appendix. The system below is to be compensated to achieve a phase margin of 50 degrees. s +3 x(t) 5+2s+ 2s E-KH. yệt) Design gain and phase-lead compensator to achieve the desired PM of 45 degrees. +PART A: Uncompensated system analysis % created by Fakhera 2020 Determine the uncompensated PM and GM s=tf('s'); g= (5+3)/...
4. Referring to the closed-loop system shown as below, design a lead compensator Ge(s) such that the phase-margin is 45o, gain margin is not less than 8dB, and the static velocity error constant Ky is 4.0 sec1. Plot unit-step and unit-ramp response curves of the compensated system with MATLAB.
The transfer function of the given physical system is 2500 Gp(s)-T-1000 Part 3 1. Frequency response (a) Draw the bode plot of open-loop transfer function when K (b) Use bode plot of open-loop transfer function to determine the type of system (do not use transfer function) (c) For what input the system will have constant steady-state error (d) for the unit input in item (c) calculate the constant steady-state error.(Use bode plot to calculate the error.) (e) Design a lead...
7. a) Sketch the root-locus Ris) C(s) diagram for the system S(5+) shown in figure when Ge=1. 6) Design phare- lead be compensator such that the system time constant is 0,25 see and != 0,45. Assume compensator at s=-4. Sketch the root-locus diagram of compensated system. c) Find the unit step responses of COMPENSATED and WN COMPENSATED systems and plot these responses. zero
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