Prove analytically that control loop of an ideal second order process (K/(As2+Bs+1)) controlled by a proportional...
Prove analytically that control loop of an ideal second order process (K/(As2+Bs+1)) controlled by a proportional controller is always stable.
Prove analytically that a typical first order process (Ke-Ls/(Ts+1)) with delay in the same control loop may not be stable.
Useful information:
A, B, T, L always have positive values.
e-a = (1-a/2)/(1+a/2)
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Prove analytically that control loop of an ideal second order
process (K/(As2+Bs+1)) controlled by a proportional...
1. Consider the usual unity-feedback closed-loop control system with a proportional-gain controll...
1. Consider the usual unity-feedback closed-loop control system with a proportional-gain controller Sketch (by hand) and fully label a Nyquist plot with K-1 for each of the plants listed below.Show all your work. Use the Nyquist plot to determine all values of K for which the closed-loop system is stable. Check your answers using the Routh-Hurwitz Stability Test. [15 marks] (a) P(s)-2 (b) P(s)-1s3 (c) P(s) -4-8 s+2 (s-2) (s+10)
1. Consider the usual unity-feedback closed-loop control system with a...
I am stuck on how to create the transfer function to be suitable for a bide plot, then actually plotting the Bode diagram Question 3 A third order process is to be controlled by a proportional con...
I am stuck on how to create the transfer function to
be suitable for a bide plot, then actually plotting the Bode
diagram
Question 3 A third order process is to be controlled by a proportional controller (Kp) and is to havea unity feedback closed loop arrangement. The process consists of three first order lags that have the following parameters GP1-1s+1) GP2 8/(s+2) GP3 5(s+0.2) A) Draw the system closed block diagram 3 marks B) Using the Log-Linear graph paper...
Given the control loop above, determine the overall gain K for the Gc(s) for a given G(s) and design requirements. Peak Time (Tp) = 0.2 second Settling time (Ts) = 0.25 second G(s) = 1/ ( s^2 + 10s +...
Given the control loop above, determine the overall gain K for
the Gc(s) for a given G(s) and design requirements.
Peak Time (Tp) = 0.2 second
Settling time (Ts) = 0.25 second
G(s) = 1/ ( s^2 + 10s + 221)
Design a Dual PD controller to have two-distinct roots. Assume
the angle for (one zero) Z1 = 10 degrees.
R(s) C(s) G(s) G(s) Given the control loop above, determine the overall gain K for the Gc(s) for a given...
1. Consider the usual unity-feedback closed-loop control system with a proportional-gain controller: 19 r - PGS-Try...
1. Consider the usual unity-feedback closed-loop control system with a proportional-gain controller: 19 r - PGS-Try P(s) Draw (by hand) and fully label a Nyquist plot with K = 1 for each of the plants listed below. Show all your work. Use the Nyquist plot to determine all values of K for which the closed-loop system is stable. Check your answers using the Routh-Hurwitz Stability Test. [15 marks] (a) P(s) = (b) P(s) = s(s+13 (6+2) (©) P(s) = 32(6+1)
A second-order process is described by its transfer function G(s) = (s+1)(843) and a PI controlle...
A second-order process is described by its transfer function G(s) = (s+1)(843) and a PI controller by Consider feedback control with unit feedback gain as shown in Figure 1 A disturbance D(s) exists, and to achieve zero steady-state error, a small integral component is applied. Technical limitations restrict the controller gain kp to values of 0.2 or less. The goal is to examine the influence of the controller parameter k on the dynamic response. D(s) Controller Process X(s) Y(s) Figure...
PROBLEM 4 Suppose that a system is shown in Figure 4. There are three controllers that might be incorporated into this system. 1. Ge (s)-K (proportional (P) controller) 2. GS)K/s (integral (I) contro...
PROBLEM 4 Suppose that a system is shown in Figure 4. There are three controllers that might be incorporated into this system. 1. Ge (s)-K (proportional (P) controller) 2. GS)K/s (integral (I) controller) 3. G (s)K(1+1/s) (proportional, integral (PI) controller) The system requirements are T, < 10 seconds and P0 10% for a unit step response. (a) For the (P) controller, write a piece of MATLAB code to plot root locus for 0<K<,and find the K value so that the...
Problem 1 Open-loop tersus Closed-loop control: Consider a first-order system Σ' with inputs (d,u) and output...
Problem 1 Open-loop tersus Closed-loop control: Consider a first-order system Σ' with inputs (d,u) and output y, governed by Z(t) y(t) ar(t1+hd(t)+5a1(t), cr(t) = = (a) Assume Σ is table (ie, a < 0). For Σ, what is the steady-state gain fron u to y (assuming d 0)? What is the steady-state gain from d to y (assuming t. 0)? These are the open-loop steady-state gains. Call these SSGy and SSGgby respectively (b) Σ is controlled by a "proportional" controller...
QUESTION 3 Copy of R(s) C(s) G(s) Given the control loop above, determine the overall gain K for the Gc(s) for a given G(s) and design requirements. Peak Time (Tp) 0.2 second Settling time (Ts)-0.12...
QUESTION 3 Copy of R(s) C(s) G(s) Given the control loop above, determine the overall gain K for the Gc(s) for a given G(s) and design requirements. Peak Time (Tp) 0.2 second Settling time (Ts)-0.12 second G(s) 1/ (s24) Design a Dual PD controller to have two-distinct roots. Assume the angle for (one zero) Z1 60 degrees.
QUESTION 3 Copy of R(s) C(s) G(s) Given the control loop above, determine the overall gain K for the Gc(s) for a given...
Tutorial -On PID control (Control System: Instructor slides and lab) Consider a second order mass...
part 2 & part 3 please...
Tutorial -On PID control (Control System: Instructor slides and lab) Consider a second order mass-force system to study its behavior under various forms of PID control xtn fon force In Disturbance force: 50) (i.e. wind force) Part I (dealing with the plant/process) 1. What is the model of this system, in other words, write the ODE of the system 2. Derive the transfer function of the above system from Fls) to X(s) 3. What...
QUESTION 3 Copy of R(s) C(s) G(s) G (s) Given the control loop above, determine the overall gain K for the Gc(s) for a given G(s) and design requirements. Peak Time (Tp) = 0.2 second Settling time (T...
QUESTION 3 Copy of R(s) C(s) G(s) G (s) Given the control loop above, determine the overall gain K for the Gc(s) for a given G(s) and design requirements. Peak Time (Tp) = 0.2 second Settling time (TS) = 0.12 second G(s) = 1/ (s^2 + .1s+4) Design a Dual PD controller to have two-distinct roots. Assume the angle for (one zero) Z1 - 60 degrees.
QUESTION 3 Copy of R(s) C(s) G(s) G (s) Given the control loop above,...
1. Consider the usual unity-feedback closed-loop control system with a proportional-gain controller Sketch (by hand) and fully label a Nyquist plot with K-1 for each of the plants listed below.Show all your work. Use the Nyquist plot to determine all values of K for which the closed-loop system is stable. Check your answers using the Routh-Hurwitz Stability Test. [15 marks] (a) P(s)-2 (b) P(s)-1s3 (c) P(s) -4-8 s+2 (s-2) (s+10)
1. Consider the usual unity-feedback closed-loop control system with a...
I am stuck on how to create the transfer function to
be suitable for a bide plot, then actually plotting the Bode
diagram
Question 3 A third order process is to be controlled by a proportional controller (Kp) and is to havea unity feedback closed loop arrangement. The process consists of three first order lags that have the following parameters GP1-1s+1) GP2 8/(s+2) GP3 5(s+0.2) A) Draw the system closed block diagram 3 marks B) Using the Log-Linear graph paper...
Given the control loop above, determine the overall gain K for
the Gc(s) for a given G(s) and design requirements.
Peak Time (Tp) = 0.2 second
Settling time (Ts) = 0.25 second
G(s) = 1/ ( s^2 + 10s + 221)
Design a Dual PD controller to have two-distinct roots. Assume
the angle for (one zero) Z1 = 10 degrees.
R(s) C(s) G(s) G(s) Given the control loop above, determine the overall gain K for the Gc(s) for a given...
1. Consider the usual unity-feedback closed-loop control system with a proportional-gain controller: 19 r - PGS-Try P(s) Draw (by hand) and fully label a Nyquist plot with K = 1 for each of the plants listed below. Show all your work. Use the Nyquist plot to determine all values of K for which the closed-loop system is stable. Check your answers using the Routh-Hurwitz Stability Test. [15 marks] (a) P(s) = (b) P(s) = s(s+13 (6+2) (©) P(s) = 32(6+1)
A second-order process is described by its transfer function G(s) = (s+1)(843) and a PI controller by Consider feedback control with unit feedback gain as shown in Figure 1 A disturbance D(s) exists, and to achieve zero steady-state error, a small integral component is applied. Technical limitations restrict the controller gain kp to values of 0.2 or less. The goal is to examine the influence of the controller parameter k on the dynamic response. D(s) Controller Process X(s) Y(s) Figure...
PROBLEM 4 Suppose that a system is shown in Figure 4. There are three controllers that might be incorporated into this system. 1. Ge (s)-K (proportional (P) controller) 2. GS)K/s (integral (I) controller) 3. G (s)K(1+1/s) (proportional, integral (PI) controller) The system requirements are T, < 10 seconds and P0 10% for a unit step response. (a) For the (P) controller, write a piece of MATLAB code to plot root locus for 0<K<,and find the K value so that the...
Problem 1 Open-loop tersus Closed-loop control: Consider a first-order system Σ' with inputs (d,u) and output y, governed by Z(t) y(t) ar(t1+hd(t)+5a1(t), cr(t) = = (a) Assume Σ is table (ie, a < 0). For Σ, what is the steady-state gain fron u to y (assuming d 0)? What is the steady-state gain from d to y (assuming t. 0)? These are the open-loop steady-state gains. Call these SSGy and SSGgby respectively (b) Σ is controlled by a "proportional" controller...
QUESTION 3 Copy of R(s) C(s) G(s) Given the control loop above, determine the overall gain K for the Gc(s) for a given G(s) and design requirements. Peak Time (Tp) 0.2 second Settling time (Ts)-0.12 second G(s) 1/ (s24) Design a Dual PD controller to have two-distinct roots. Assume the angle for (one zero) Z1 60 degrees.
QUESTION 3 Copy of R(s) C(s) G(s) Given the control loop above, determine the overall gain K for the Gc(s) for a given...
part 2 & part 3 please...
Tutorial -On PID control (Control System: Instructor slides and lab) Consider a second order mass-force system to study its behavior under various forms of PID control xtn fon force In Disturbance force: 50) (i.e. wind force) Part I (dealing with the plant/process) 1. What is the model of this system, in other words, write the ODE of the system 2. Derive the transfer function of the above system from Fls) to X(s) 3. What...
QUESTION 3 Copy of R(s) C(s) G(s) G (s) Given the control loop above, determine the overall gain K for the Gc(s) for a given G(s) and design requirements. Peak Time (Tp) = 0.2 second Settling time (TS) = 0.12 second G(s) = 1/ (s^2 + .1s+4) Design a Dual PD controller to have two-distinct roots. Assume the angle for (one zero) Z1 - 60 degrees.
QUESTION 3 Copy of R(s) C(s) G(s) G (s) Given the control loop above,...
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