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Ouestion 1: Design a backstepping controller for the system described belowto guarantee the asymptotic stability of...
The objective of the controller design in Fig. 1 is to find the controller Gc(s) such...
The objective of the controller design in Fig. 1 is to find the
controller Gc(s) such that I.)The closed-loop system is stable
ii.)The output of the system above (y(t)) can track the reference
input r(t) = At (A>0 is any real number). Use the Nyquist plot
and Nyquist criterion to show that: a.)The portional controller
Gc(s)=K can achieve asymptotic tracking of the ramp input r(t)=At
but cannot meet the stability requirement for 0<K<+inf. b.)
Can the PI controller Gc(s)=K(1+10/s) be...
a-represent system in state space form? b-find output response y(t? c-design a state feedback gain controller? 3- A dyn...
a-represent system in state space form?
b-find output response y(t?
c-design a state feedback gain controller?
3- A dynamic system is described by the following set of coupled linear ordinary differential equations: x1 + 2x1-4x2-5u x1-x2 + 4x1 + x2 = 5u EDQMS 2/3 Page 1 of 2 a. Represent the system in state-space form. b. For u(t) =1 and initial condition state vector x(0) = LII find the outp (10 marks) response y(t). c. Design a state feedback gain...
Design a phase lead controller using the Root Locus Method for the system described by G(s)....
Design a phase lead controller using the Root Locus Method for the system described by G(s). Ensure that there is a reduction of MORE than 40% of the original settling time, additionally, enure that an overshoot of 12% is not exceeded. G(s)=1/(s3+13s2+32s+20)
Question 4 (a) A feedback control system with a proportional controller is shown in Figure Q4...
Question 4 (a) A feedback control system with a proportional controller is shown in Figure Q4 (a). (i) Sketch the root locus of the system, (ii) Design the proportional controller (choose the value of K) such that the damping ratio does not exceed 0.5 and the time constant is less than 1 second. [All necessary steps of root locus construction and controller design must be shown). C(s) R(S) + s(s+4)(s + 10) Figure Q4 (a). A feedback control system [11...
Design Project #1 : Design of PID Controller Design a PID controller so that the step...
Design Project #1 : Design of PID Controller Design a PID controller so that the step response of the following closed-loop system satisfy (settling time) 3sec, POS(% overshoot) 20%, and steady state tracking error (ess)<0. R(s) Y(s) K, ss +1 If you can reduce both settling time and overshoot, then it would be much better. To verify your answer, you should use Matlab simulink and show that your answer is correct in your report. Describe the detailed design procedure (as...
Design Problems: (1) A robotic system is described by the transfer function P(s)=- 100 s(s +9.7)(s...
Design Problems: (1) A robotic system is described by the transfer function P(s)=- 100 s(s +9.7)(s + 51.2) Use the root locus method to design a lead controller that achieves a closed-loop step response with P.0.5 2.5 %, and a settling time T, < 0.25s (using the 2% criterion). Also, the steady-state error to a unit ramp should be ess < 0.15. (2) This system is open-loop unstable: P(S) = 500 (5 - 1)(s + 10) Using the root locus...
find the following: a)state transition matrix? b)output as function of time? c)design a state feedback controller to...
find the following:
a)state transition matrix?
b)output as function of time?
c)design a state feedback controller to place closed loop at (-3)
and (-5)
Question (: (10 hO Considering the following system, 01x + 0 t<0 tt t20 Where x(0)-L1] , u(t)-(% ,u(t) a) Find the state transition matrix. (3 marks) b) Find the output as a function of time. (3 marks) c) Design a state feedback controller to place the closed loop poles at (-3) and (-5). (4 marks)...
Option A: Select a suitable controller for a system of your choicepleade choose Procedure: oid uo...
Please take your time and answer in detail. Thank you.
Option A: Select a suitable controller for a system of your choicepleade choose Procedure: oid uontollor Select the system of your choice. Pid Con Identify variables and parameters of the system Derive mathematical models for the system Obtain the CLTF and OLTF of the system. Represent the system (BD) blou disg aw Determine the output without the controller. Find the output with the controller Inspect stability of the system (obtain...
5. A robotic arm is described by the first order transfer function G(s)A where Kp-1, however...
5. A robotic arm is described by the first order transfer function G(s)A where Kp-1, however it may change with respect to the arm's position. (a) Design a control system that will reject a disturbance signal d(t)=3+3cos(t-r) without steady-state error. All desired closed-loop poles are positioned at-λ where-λ= 1. (b) In order to guarantee the closed-loop stability for the variation of Kp the maximum and minimum values of Kp 1 need to be determined. Use Routh- Hurwitz stability criterion to...
B2 and B3 B. Controller Design Consider the positional robotic system and its BD. Assume: H-1...
B2 and B3
B. Controller Design Consider the positional robotic system and its BD. Assume: H-1 and G,-3/(s+4). B.1 Design a steady state error es10 % due to a unit step input. Initials: PD-type controller to ensure a time constant of 0.25 sec., and Controller Plant R G, G. H Sensor to ensure -0.5 and o,-10 rad/s. B2. Design a Pl-type controller B3. Design a PID-type controller to ensure co,-5 rad/s, E-0.5 and e2 % due to a unit ramp...
The objective of the controller design in Fig. 1 is to find the
controller Gc(s) such that I.)The closed-loop system is stable
ii.)The output of the system above (y(t)) can track the reference
input r(t) = At (A>0 is any real number). Use the Nyquist plot
and Nyquist criterion to show that: a.)The portional controller
Gc(s)=K can achieve asymptotic tracking of the ramp input r(t)=At
but cannot meet the stability requirement for 0<K<+inf. b.)
Can the PI controller Gc(s)=K(1+10/s) be...
a-represent system in state space form?
b-find output response y(t?
c-design a state feedback gain controller?
3- A dynamic system is described by the following set of coupled linear ordinary differential equations: x1 + 2x1-4x2-5u x1-x2 + 4x1 + x2 = 5u EDQMS 2/3 Page 1 of 2 a. Represent the system in state-space form. b. For u(t) =1 and initial condition state vector x(0) = LII find the outp (10 marks) response y(t). c. Design a state feedback gain...
Question 4 (a) A feedback control system with a proportional controller is shown in Figure Q4 (a). (i) Sketch the root locus of the system, (ii) Design the proportional controller (choose the value of K) such that the damping ratio does not exceed 0.5 and the time constant is less than 1 second. [All necessary steps of root locus construction and controller design must be shown). C(s) R(S) + s(s+4)(s + 10) Figure Q4 (a). A feedback control system [11...
Design Project #1 : Design of PID Controller Design a PID controller so that the step response of the following closed-loop system satisfy (settling time) 3sec, POS(% overshoot) 20%, and steady state tracking error (ess)<0. R(s) Y(s) K, ss +1 If you can reduce both settling time and overshoot, then it would be much better. To verify your answer, you should use Matlab simulink and show that your answer is correct in your report. Describe the detailed design procedure (as...
Design Problems: (1) A robotic system is described by the transfer function P(s)=- 100 s(s +9.7)(s + 51.2) Use the root locus method to design a lead controller that achieves a closed-loop step response with P.0.5 2.5 %, and a settling time T, < 0.25s (using the 2% criterion). Also, the steady-state error to a unit ramp should be ess < 0.15. (2) This system is open-loop unstable: P(S) = 500 (5 - 1)(s + 10) Using the root locus...
find the following:
a)state transition matrix?
b)output as function of time?
c)design a state feedback controller to place closed loop at (-3)
and (-5)
Question (: (10 hO Considering the following system, 01x + 0 t<0 tt t20 Where x(0)-L1] , u(t)-(% ,u(t) a) Find the state transition matrix. (3 marks) b) Find the output as a function of time. (3 marks) c) Design a state feedback controller to place the closed loop poles at (-3) and (-5). (4 marks)...
Please take your time and answer in detail. Thank you.
Option A: Select a suitable controller for a system of your choicepleade choose Procedure: oid uontollor Select the system of your choice. Pid Con Identify variables and parameters of the system Derive mathematical models for the system Obtain the CLTF and OLTF of the system. Represent the system (BD) blou disg aw Determine the output without the controller. Find the output with the controller Inspect stability of the system (obtain...
5. A robotic arm is described by the first order transfer function G(s)A where Kp-1, however it may change with respect to the arm's position. (a) Design a control system that will reject a disturbance signal d(t)=3+3cos(t-r) without steady-state error. All desired closed-loop poles are positioned at-λ where-λ= 1. (b) In order to guarantee the closed-loop stability for the variation of Kp the maximum and minimum values of Kp 1 need to be determined. Use Routh- Hurwitz stability criterion to...
B2 and B3
B. Controller Design Consider the positional robotic system and its BD. Assume: H-1 and G,-3/(s+4). B.1 Design a steady state error es10 % due to a unit step input. Initials: PD-type controller to ensure a time constant of 0.25 sec., and Controller Plant R G, G. H Sensor to ensure -0.5 and o,-10 rad/s. B2. Design a Pl-type controller B3. Design a PID-type controller to ensure co,-5 rad/s, E-0.5 and e2 % due to a unit ramp...
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