automatic control systems
QUESTION 3: (35 points) For the system having the transfer function: ?(?) = 10 (? + 2)(? + 3) a) Find the transition matrix ?(?)by Hand. (10pts) b) Find the transition matrix ?(?)by using Matlab (5pts) c) By using state space approach, find the unit step response of the system with initial values [1,0] by Hand, draw the response in Matlab. (10pts) d) Design a control law for the for the given system to make pole placements of your choice (you will choose the desired poles and tell the reason of your choices) (10pts)
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Consider the following transfer function of a linear control system Determine the state feedba...
Consider the following transfer function of a linear control
system
Determine the state feedback gain matrix that places the closed
system at s=-32, -3.234 ± j3.3.
Design a full order observer which produces a set of desired
closed loop poles at s=-16, -16.15±j16.5
Assume X1 is measurable, design a reduced order observer with
desired closed loop poles at -16.15±j16.5
We were unable to transcribe this image1 Y(s) U(s) (s+1)(s2+0.7s+2) Consider the following transfer function of a linear control system (a)...
Consider the following transfer function of a linear control system 1- Determine the state feedb...
Consider the following transfer function of a linear control
system
1- Determine the state feedback gain matrix that places the
closed system at s=-32, -3.234 ± j3.3.
2- Design a full order observer which produces a set of desired
closed loop poles at s=-16, -16.15±j16.5
3-Assume X1 is measurable, design a reduced order observer with
desired closed loop poles at -16.15±j16.5
We were unable to transcribe this image1 Y(s) U(s) (s+1)(s2+0.7s+2) Consider the following transfer function of a linear control...
' 1. Review Question a) Name three applications for feedback control systems. b) Functionally, ho...
' 1. Review Question a) Name three applications for feedback control systems. b) Functionally, how do closed-loop systems differ from open-loop systems? c) Name the three major design criteria for control systems. d) Name the performance specification for first-order systems. e) Briefly describe how the zeros of the open-loop system affect the root locus and the transient response. What does the Routh-Hurwitz criterion tell us? f) 2. Given the electric network shown in Figure. a) Write the differential equation for...
3. (20 pts.) Consider the system: where: C-1 0 0 -4 0 7 a) Analyze the...
3. (20 pts.) Consider the system: where: C-1 0 0 -4 0 7 a) Analyze the stability of the system. b) Design a regulator for this system using the pole-placement with observer approach. Assume that the desired closed-loop poles for the pole placement part are located at: The desired observer poles are: S--7 c) Obtain the transfer function of the observer controller. S--7
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...
Problem 2 design of state feedback controller using pole placement for multi-input systems. Consi...
Problem 2 design of state feedback controller using pole placement for multi-input systems. Consider the system-Ar-Bu with 1. design a state feedback control u-Kr, or the gain K, to place the closed loop poles at -2,-3,-4 2. Exploiting the structure of A and B, find a different feedback gain that place the poles in the same location. This steps shows that there are several ways to design K; by inspection for instance. 3. Use the Matlab command 'place' to generate...
Problem 4. Consider the control system shown below with plant G(s) that has time con- stants...
Problem 4. Consider the control system shown below with plant G(s) that has time con- stants T1 = 2, T2 = 10, and gain k = 0.1. 4 673 +1679+1) (1.) Sketch the pole-zero plot for G(s). Is one of the poles more dominant? Using MATLAB, simulate the step response of the plant itself, along with G1(s) and G2(s) as defined by Gl(s) = and G2(s) = sti + 1 ST2+1 (2.) Design a proportional gain C(s) = K so...
please show work thank you! Use Matlab to and the SISOTool construct the system for analysis...
please show work
thank you!
Use Matlab to and the SISOTool construct the system for analysis (You may want to preview the tf and sisotool commands from matlab by typing help tf or doc tf etc...) Each Block B1, B2, B3 and B4 will be constructed individually and then concatenated together As shown in the block diagram let K=0.1 Set B1 = 0.1 by typing in matlab >>B1=0.1 To assign the Blockl values use the TF command to construct a...
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...
Questions 14-17: For the control system shown below Design the compensator so that the unit-step response...
Questions 14-17: For the control system shown below Design the compensator so that the unit-step response has a settling-time ofless then twe seconds, rise-time of less th 025seconds, and overshoot ofless than 29%1, adion maximum value ofthe actuator signal ) must be kept under five14) Indicate the allowable region of the complex plane for the closed-loop poles 15) Deterine K and a, the answers are nos unique). 16.) Use Matlab to plot the step-response of the control system using your...
Consider the following transfer function of a linear control
system
Determine the state feedback gain matrix that places the closed
system at s=-32, -3.234 ± j3.3.
Design a full order observer which produces a set of desired
closed loop poles at s=-16, -16.15±j16.5
Assume X1 is measurable, design a reduced order observer with
desired closed loop poles at -16.15±j16.5
We were unable to transcribe this image1 Y(s) U(s) (s+1)(s2+0.7s+2) Consider the following transfer function of a linear control system (a)...
Consider the following transfer function of a linear control
system
1- Determine the state feedback gain matrix that places the
closed system at s=-32, -3.234 ± j3.3.
2- Design a full order observer which produces a set of desired
closed loop poles at s=-16, -16.15±j16.5
3-Assume X1 is measurable, design a reduced order observer with
desired closed loop poles at -16.15±j16.5
We were unable to transcribe this image1 Y(s) U(s) (s+1)(s2+0.7s+2) Consider the following transfer function of a linear control...
' 1. Review Question a) Name three applications for feedback control systems. b) Functionally, how do closed-loop systems differ from open-loop systems? c) Name the three major design criteria for control systems. d) Name the performance specification for first-order systems. e) Briefly describe how the zeros of the open-loop system affect the root locus and the transient response. What does the Routh-Hurwitz criterion tell us? f) 2. Given the electric network shown in Figure. a) Write the differential equation for...
3. (20 pts.) Consider the system: where: C-1 0 0 -4 0 7 a) Analyze the stability of the system. b) Design a regulator for this system using the pole-placement with observer approach. Assume that the desired closed-loop poles for the pole placement part are located at: The desired observer poles are: S--7 c) Obtain the transfer function of the observer controller. S--7
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...
Problem 2 design of state feedback controller using pole placement for multi-input systems. Consider the system-Ar-Bu with 1. design a state feedback control u-Kr, or the gain K, to place the closed loop poles at -2,-3,-4 2. Exploiting the structure of A and B, find a different feedback gain that place the poles in the same location. This steps shows that there are several ways to design K; by inspection for instance. 3. Use the Matlab command 'place' to generate...
Problem 4. Consider the control system shown below with plant G(s) that has time con- stants T1 = 2, T2 = 10, and gain k = 0.1. 4 673 +1679+1) (1.) Sketch the pole-zero plot for G(s). Is one of the poles more dominant? Using MATLAB, simulate the step response of the plant itself, along with G1(s) and G2(s) as defined by Gl(s) = and G2(s) = sti + 1 ST2+1 (2.) Design a proportional gain C(s) = K so...
please show work
thank you!
Use Matlab to and the SISOTool construct the system for analysis (You may want to preview the tf and sisotool commands from matlab by typing help tf or doc tf etc...) Each Block B1, B2, B3 and B4 will be constructed individually and then concatenated together As shown in the block diagram let K=0.1 Set B1 = 0.1 by typing in matlab >>B1=0.1 To assign the Blockl values use the TF command to construct a...
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...
Questions 14-17: For the control system shown below Design the compensator so that the unit-step response has a settling-time ofless then twe seconds, rise-time of less th 025seconds, and overshoot ofless than 29%1, adion maximum value ofthe actuator signal ) must be kept under five14) Indicate the allowable region of the complex plane for the closed-loop poles 15) Deterine K and a, the answers are nos unique). 16.) Use Matlab to plot the step-response of the control system using your...
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