root locus
4. Consider the system described by the following block diagram. In this block diagram \(G(s)=\frac{1}{s+1}, C(z)=\frac{K}{1-z^{-}}\) are the system model and the digital controller.
(a) Sketch the root locus diagram of the system, \(C(z) G(z)\).
(b) Determine the range of gain \(K\) for the stability using the root locus.
(c) Determine the value of gain \(\mathrm{K}\) to get around \(10 \%\) maximum overshoot when a step input is applied using the root locus. Verify your results with plotting the closed loop system for 20 seconds.
(d) Determine the range of gain \(K\) to produce step responses having no oscillation (overdamped) using the root locus.
(e) What is the type of the system? Find the steady-state errors for unit step and unit ramp inputs.Homework Answers
yUCni ias the block diagram shown below. Controller Process Sensor (a) (5%) Sketch the root locus of the closed-loop system. (b) (5%) Determine the range of K that the closed-loop system is stabl...
yUCni ias the block diagram shown below. Controller Process Sensor (a) (5%) Sketch the root locus of the closed-loop system. (b) (5%) Determine the range of K that the closed-loop system is stable. (c) (5%) Find the percentage of overshoot and the steady state error due to a unit step input of the open loop system process. (d) (5%) Find the steady-state error due to a unit step input of the closed-loop syste as a function of the design parameter...
[7] Sketch the root locus for the unity feedback system whose open loop transfer function is K G(s) Draw the root lo...
[7] Sketch the root locus for the unity feedback system whose open loop transfer function is K G(s) Draw the root locus of the system with the gain Kas a variable. s(s+4) (s2+4s+20) Determine asymptotes, centroid, breakaway point, angle of departure, and the gain at which root locus crosses ja-axis. A control system with type-0 process and a PID controller is shown below. Design the [8 parameters of the PID controller so that the following specifications are satisfied. =100 a)...
Problem 3 (25%): The closed-loop system has the block diagram shown below. Controlle Process Sensor s + l (a) (5%) Sketch the root locus of the closed-loop system. (b) (5%) Determine the range of...
Problem 3 (25%): The closed-loop system has the block diagram shown below. Controlle Process Sensor s + l (a) (5%) Sketch the root locus of the closed-loop system. (b) (5%) Determine the range of K that the closed-loop system is stable. (c) (5%) Find the percentage of overshoot and the steady state error due to a unit step input of the open loop system process. (d) (5%) Find the steady-state error due to a unit step input of the closed-loop...
% We can couple the design of gain on the root locus with a % step-response...
% We can couple the design of gain on the root locus with a
% step-response simulation for the gain selected. We introduce
the command
% rlocus(G,K), which allows us to specify the range of gain, K,
for plotting the root
% locus. This command will help us smooth the usual root locus
plot by equivalently
% specifying more points via the argument, K. Notice that the
first root locus
% plotted without the argument K is not smooth. We...
Automatic Control In unity feedback system with Gs) (s-IXs-2) With out controller, is this system stable, and why? For Gc K (proportional control) sketch the root locus. Find the range of K to mak...
Automatic Control
In unity feedback system with Gs) (s-IXs-2) With out controller, is this system stable, and why? For Gc K (proportional control) sketch the root locus. Find the range of K to make the system stable. Determine the range of K, so that the system has no overshoot Determine the range of K for steady state error to unit step input less than 20% a) b) c) d) e)
In unity feedback system with Gs) (s-IXs-2) With out controller,...
Lag Compensator Design Using Root-Locus 2. Consider the unity feedback system in Figure 1 for G(s...
Lag Compensator Design Using Root-Locus 2. Consider the unity feedback system in Figure 1 for G(s)- s(s+3(s6) Design a lag compensation to meet the following specifications The step response settling time is to be less than 5 sec. . The step response overshoot is to be less than 17% . The steady-state error to a unit ramp input must not exceed 10%. Dynamic specifications (overshoot and settling time) can be met using proportional feedback, but a lag compensator is needed...
Q4 For the following Proportional controller use the step response and root locus rules obtain the...
Q4 For the following Proportional controller use the step response and root locus rules obtain the root locus schematics for positive gain. (30 pts) Rs) ー10 a. Find the gain and frequency for marginal stability b. Find the gain for critical damping c. Find the real part and the gain ofthe CL pole for a =4 d. Find K that provides the system with 8 dB gain margin and find the complex poles for that gain e. Find the phase...
Question 2 System Stability in the s-Domain and in the Frequency Domain: Bode Plots, Root Locus...
Question 2 System Stability in the s-Domain and in the Frequency Domain: Bode Plots, Root Locus Plots and Routh- Hurwitz Criterion ofStability A unit feedback control system is to be stabilized using a Proportional Controller, as shown in Figure Q2.1. Proportional Controller Process The process transfer function is described as follows: Y(s) G(s) s2 +4s 100 s3 +4s2 5s 2 Figure Q2.1 Your task is to investigate the stability of the closed loop system using s-domain analysis by finding: a)...
Prob. 3-25 points For this problem, use the root locus features to solve all parts: comp For: comp = a proportional controller = a positive gain Kp and z (z-1)/(z2 + 16) sys a) Draw a rough sket...
Prob. 3-25 points For this problem, use the root locus features to solve all parts: comp For: comp = a proportional controller = a positive gain Kp and z (z-1)/(z2 + 16) sys a) Draw a rough sketch of the root-locus of the above system showing only the values of Kp at zeros and poles. b) 10 points: Find the range of Kp that makes the performance of the overall system underdamped. c) 10 points: Find the range of Kp...
course name: control system topic about root locus please show all your steps to make easier...
course name: control system
topic about root locus
please show all your steps to make easier for understanding.
1. Determine the stability condition of the systems describe in the first column below. Justify your answer with reason. show all your answers steps Justification Stability condition Systems description dy y +2 y x +3 dt dy -6y= x + dt2 dt provide special condition provide special condition 2. Given the closed loop system in the figure below, analysis the systems given...
yUCni ias the block diagram shown below. Controller Process Sensor (a) (5%) Sketch the root locus of the closed-loop system. (b) (5%) Determine the range of K that the closed-loop system is stable. (c) (5%) Find the percentage of overshoot and the steady state error due to a unit step input of the open loop system process. (d) (5%) Find the steady-state error due to a unit step input of the closed-loop syste as a function of the design parameter...
[7] Sketch the root locus for the unity feedback system whose open loop transfer function is K G(s) Draw the root locus of the system with the gain Kas a variable. s(s+4) (s2+4s+20) Determine asymptotes, centroid, breakaway point, angle of departure, and the gain at which root locus crosses ja-axis. A control system with type-0 process and a PID controller is shown below. Design the [8 parameters of the PID controller so that the following specifications are satisfied. =100 a)...
Problem 3 (25%): The closed-loop system has the block diagram shown below. Controlle Process Sensor s + l (a) (5%) Sketch the root locus of the closed-loop system. (b) (5%) Determine the range of K that the closed-loop system is stable. (c) (5%) Find the percentage of overshoot and the steady state error due to a unit step input of the open loop system process. (d) (5%) Find the steady-state error due to a unit step input of the closed-loop...
% We can couple the design of gain on the root locus with a
% step-response simulation for the gain selected. We introduce
the command
% rlocus(G,K), which allows us to specify the range of gain, K,
for plotting the root
% locus. This command will help us smooth the usual root locus
plot by equivalently
% specifying more points via the argument, K. Notice that the
first root locus
% plotted without the argument K is not smooth. We...
Automatic Control
In unity feedback system with Gs) (s-IXs-2) With out controller, is this system stable, and why? For Gc K (proportional control) sketch the root locus. Find the range of K to make the system stable. Determine the range of K, so that the system has no overshoot Determine the range of K for steady state error to unit step input less than 20% a) b) c) d) e)
In unity feedback system with Gs) (s-IXs-2) With out controller,...
Lag Compensator Design Using Root-Locus 2. Consider the unity feedback system in Figure 1 for G(s)- s(s+3(s6) Design a lag compensation to meet the following specifications The step response settling time is to be less than 5 sec. . The step response overshoot is to be less than 17% . The steady-state error to a unit ramp input must not exceed 10%. Dynamic specifications (overshoot and settling time) can be met using proportional feedback, but a lag compensator is needed...
Q4 For the following Proportional controller use the step response and root locus rules obtain the root locus schematics for positive gain. (30 pts) Rs) ー10 a. Find the gain and frequency for marginal stability b. Find the gain for critical damping c. Find the real part and the gain ofthe CL pole for a =4 d. Find K that provides the system with 8 dB gain margin and find the complex poles for that gain e. Find the phase...
Question 2 System Stability in the s-Domain and in the Frequency Domain: Bode Plots, Root Locus Plots and Routh- Hurwitz Criterion ofStability A unit feedback control system is to be stabilized using a Proportional Controller, as shown in Figure Q2.1. Proportional Controller Process The process transfer function is described as follows: Y(s) G(s) s2 +4s 100 s3 +4s2 5s 2 Figure Q2.1 Your task is to investigate the stability of the closed loop system using s-domain analysis by finding: a)...
Prob. 3-25 points For this problem, use the root locus features to solve all parts: comp For: comp = a proportional controller = a positive gain Kp and z (z-1)/(z2 + 16) sys a) Draw a rough sketch of the root-locus of the above system showing only the values of Kp at zeros and poles. b) 10 points: Find the range of Kp that makes the performance of the overall system underdamped. c) 10 points: Find the range of Kp...
course name: control system
topic about root locus
please show all your steps to make easier for understanding.
1. Determine the stability condition of the systems describe in the first column below. Justify your answer with reason. show all your answers steps Justification Stability condition Systems description dy y +2 y x +3 dt dy -6y= x + dt2 dt provide special condition provide special condition 2. Given the closed loop system in the figure below, analysis the systems given...
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