Homework Answers
d) step response:
clc;
clear all;
s=tf('s');
g=15/(s*(s+2.5)); % plant
gc=4.775*0.349*(1+0.1*s);%controller
step(feedback(g*gc,1));grid% step response
legend('compensated system')
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The servomechanism is to be controlled by inserting a proportional-plus-derivative (PD) 2. compensator immediately after the amplifier a. Verify that the system can be represented by the block diagra...
Please solve parts (a) and (b) neatly and show problem solving. Ignore reference to part 1, but please still plot the root loci. For the system given in Figure 1 a) Design a PD compensator with the t...
Please solve parts (a) and (b) neatly and show problem solving.
Ignore reference to part 1, but please still plot the root
loci.
For the system given in Figure 1 a) Design a PD compensator with the transfer function: to give a dominant root of the closed-loop characteristic equation of the compen- sated system at s -1+j1 (i.e., a settling time Ts of less than 6 seconds and a maximum overshoot Mo of less than 10%). Required Pre-Practical work] (b)...
2. Controller Design For each of the following plants G, design a compensator G, so that the closed loop system KG, G (1 + KG, G has two dominant poles near 2 ± i Plot a root locus plot for the s...
2. Controller Design For each of the following plants G, design a compensator G, so that the closed loop system KG, G (1 + KG, G has two dominant poles near 2 ± i Plot a root locus plot for the system before adding the compensator and another plot for after. Use the simplest G that you can find. Determine the gain K that will achieve the desired poles 142
2. Controller Design For each of the following plants G,...
Question 1 (60 points) Consider the following block diagram where G(s)- Controller R(s) G(s) (a) Sketch the root locus assuming a proportional controller is used. [25 points] (b) Design specifica...
Question 1 (60 points) Consider the following block diagram where G(s)- Controller R(s) G(s) (a) Sketch the root locus assuming a proportional controller is used. [25 points] (b) Design specifications require a closed-loop pole at (-3+j1). Design a lead compensator to make sure the root locus goes through this point. For the design, pick the pole of the compensator at-23 and analytically find its zero. (Hint: Lead compensator transfer function will be Ge (s)$+23 First plot the poles and zeros...
2. Consider the closed-loop system shown below Here Kp represents the gain of a proportional controller, and the proces...
2. Consider the closed-loop system shown below
Here Kp represents the gain of a proportional controller, and
the process transfer function is given by
.
(a) Sketch the locus of the closed-loop poles as the
proportional gain, Kp, varies from 0 to ∞. Be sure to clearly mark
poles, zeros, asymptotes, angles of arrival/departure,
break-in/away points, and real axis portion of the locus.
(b) Using Routh's array, determine the range of the proportional
gain, Kp, for which the closed-loop system...
i am needing help with a b c o chris question thanks 1000 O(s) Gc(s) s(s2 110s 1250) Figure 2: Disc Drive System Block D...
i am needing help with a b c o chris question thanks
1000 O(s) Gc(s) s(s2 110s 1250) Figure 2: Disc Drive System Block Diagram We will now try to design a compensator with the requirements that Overshoot 10% ii. Ts S 100ms II. eramp(oo) s 0.001 Do the following (you may use MATLAB at your leisure, but be sure to explain your logic for your design choices) a) Use MATLAB to draw the root locus when Gc K. Augment...
Recall the disc drive problem from Tutorials, where we demonstrated that the system can be written as e(s)+ 1000 Ge...
Recall the disc drive problem from Tutorials, where we demonstrated that the system can be written as e(s)+ 1000 Ge(s) s(s2 110s 1250) Figure 2: Disc Drive System Block Diagram We will now try to design a compensator with the requirements that i. Overshoot 1096 ii. Ts S 100ms ii. eramp() s 0.001 Do the following (you may use MATLAB at your leisure, but be sure to explain your logic for your design choices) a) Use MATLAB to draw the...
Consider the automobile cruise-control system shown below: Engine ActuatorCarburetor 0.833 and load 40 3s +1 Compensator R(s)E(s) Ge(s) s +1 -t e(t) Sensor 0.03 1) Derive the closed-loop transfer fun...
Consider the automobile cruise-control system shown below: Engine ActuatorCarburetor 0.833 and load 40 3s +1 Compensator R(s)E(s) Ge(s) s +1 -t e(t) Sensor 0.03 1) Derive the closed-loop transfer function of V(s)/R(s) when Gc(s)-1 2) Derive the closed-loop transfer function of E(s)/R(s) when Ge(s)-1 3) Plot the time history of the error e(t) of the closed-loop system when r(t) is a unit step input. 4) Plot the root-loci of the uncompensated system (when Gc(s)-1). Mark the closed-loop complex poles on...
1 CONTROL SYSTEM ANALYSIS & DESIGN Spring 2019 HW 7 Due 4/4/2019, Thursday, 11:59pm 1. Design...
1 CONTROL SYSTEM ANALYSIS & DESIGN Spring 2019 HW 7 Due 4/4/2019, Thursday, 11:59pm 1. Design a lead compensator for the closed-loop (CL) system whose open loop transfer function is given below. Design objectives: reduce the time constant by 50% while maintaining the same value of the damping ratio for the dominant poles. Please note that H(s)-1. Please use the method based on root locus plot. G(s) 2 [s(s+2)] Please include detailed step Obtain the location of the desired dominant...
A system having an open loop transfer function of G(S) = K10/(S+2)(3+1) has a root locus...
A system having an open loop transfer function of G(S) = K10/(S+2)(3+1) has a root locus plot as shown below. The location of the roots for a system gain of K= 0.248 is show on the plot. At this location the system has a damping factor of 0.708 and a settling time of 4/1.5 = 2.67 seconds. A lead compensator is to be used to improve the transient response. (Note that nothing is plotted on the graph except for that...
Problem 2 Wis) R(s) U(s) Gol (s) D a (s) E(s) H(s) Given a system as in the diagram above, use MATLAB to solve the problems: Assume we want the closed-loop system rise time to be t, 0.18 sec S + Z H(...
Problem 2 Wis) R(s) U(s) Gol (s) D a (s) E(s) H(s) Given a system as in the diagram above, use MATLAB to solve the problems: Assume we want the closed-loop system rise time to be t, 0.18 sec S + Z H(s) 1 Gpl)s(s+)et s(s 1) s + p a) Assume W(s)-0. Draw the root locus of the system assuming compensator consists only of the adjustable gain parameter K, i.e. Dct (s) Determine the approximate range of values of...
Please solve parts (a) and (b) neatly and show problem solving.
Ignore reference to part 1, but please still plot the root
loci.
For the system given in Figure 1 a) Design a PD compensator with the transfer function: to give a dominant root of the closed-loop characteristic equation of the compen- sated system at s -1+j1 (i.e., a settling time Ts of less than 6 seconds and a maximum overshoot Mo of less than 10%). Required Pre-Practical work] (b)...
2. Controller Design For each of the following plants G, design a compensator G, so that the closed loop system KG, G (1 + KG, G has two dominant poles near 2 ± i Plot a root locus plot for the system before adding the compensator and another plot for after. Use the simplest G that you can find. Determine the gain K that will achieve the desired poles 142
2. Controller Design For each of the following plants G,...
Question 1 (60 points) Consider the following block diagram where G(s)- Controller R(s) G(s) (a) Sketch the root locus assuming a proportional controller is used. [25 points] (b) Design specifications require a closed-loop pole at (-3+j1). Design a lead compensator to make sure the root locus goes through this point. For the design, pick the pole of the compensator at-23 and analytically find its zero. (Hint: Lead compensator transfer function will be Ge (s)$+23 First plot the poles and zeros...
2. Consider the closed-loop system shown below
Here Kp represents the gain of a proportional controller, and
the process transfer function is given by
.
(a) Sketch the locus of the closed-loop poles as the
proportional gain, Kp, varies from 0 to ∞. Be sure to clearly mark
poles, zeros, asymptotes, angles of arrival/departure,
break-in/away points, and real axis portion of the locus.
(b) Using Routh's array, determine the range of the proportional
gain, Kp, for which the closed-loop system...
i am needing help with a b c o chris question thanks
1000 O(s) Gc(s) s(s2 110s 1250) Figure 2: Disc Drive System Block Diagram We will now try to design a compensator with the requirements that Overshoot 10% ii. Ts S 100ms II. eramp(oo) s 0.001 Do the following (you may use MATLAB at your leisure, but be sure to explain your logic for your design choices) a) Use MATLAB to draw the root locus when Gc K. Augment...
Recall the disc drive problem from Tutorials, where we demonstrated that the system can be written as e(s)+ 1000 Ge(s) s(s2 110s 1250) Figure 2: Disc Drive System Block Diagram We will now try to design a compensator with the requirements that i. Overshoot 1096 ii. Ts S 100ms ii. eramp() s 0.001 Do the following (you may use MATLAB at your leisure, but be sure to explain your logic for your design choices) a) Use MATLAB to draw the...
Consider the automobile cruise-control system shown below: Engine ActuatorCarburetor 0.833 and load 40 3s +1 Compensator R(s)E(s) Ge(s) s +1 -t e(t) Sensor 0.03 1) Derive the closed-loop transfer function of V(s)/R(s) when Gc(s)-1 2) Derive the closed-loop transfer function of E(s)/R(s) when Ge(s)-1 3) Plot the time history of the error e(t) of the closed-loop system when r(t) is a unit step input. 4) Plot the root-loci of the uncompensated system (when Gc(s)-1). Mark the closed-loop complex poles on...
1 CONTROL SYSTEM ANALYSIS & DESIGN Spring 2019 HW 7 Due 4/4/2019, Thursday, 11:59pm 1. Design a lead compensator for the closed-loop (CL) system whose open loop transfer function is given below. Design objectives: reduce the time constant by 50% while maintaining the same value of the damping ratio for the dominant poles. Please note that H(s)-1. Please use the method based on root locus plot. G(s) 2 [s(s+2)] Please include detailed step Obtain the location of the desired dominant...
A system having an open loop transfer function of G(S) = K10/(S+2)(3+1) has a root locus plot as shown below. The location of the roots for a system gain of K= 0.248 is show on the plot. At this location the system has a damping factor of 0.708 and a settling time of 4/1.5 = 2.67 seconds. A lead compensator is to be used to improve the transient response. (Note that nothing is plotted on the graph except for that...
Problem 2 Wis) R(s) U(s) Gol (s) D a (s) E(s) H(s) Given a system as in the diagram above, use MATLAB to solve the problems: Assume we want the closed-loop system rise time to be t, 0.18 sec S + Z H(s) 1 Gpl)s(s+)et s(s 1) s + p a) Assume W(s)-0. Draw the root locus of the system assuming compensator consists only of the adjustable gain parameter K, i.e. Dct (s) Determine the approximate range of values of...
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