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Problem 1. Consider the following mass, spring, and damper system. Let the force F be the...
3. Consider the following mass-spring-damper system. Let m= 1 kg, b = 10 Ns/m, and k...
3. Consider the following mass-spring-damper system. Let m= 1 kg, b = 10 Ns/m, and k = 20 N/m. b m F k a) Derive the open-loop transfer function X(S) F(s) Plot the step response using matlab. b) Derive the closed-loop transfer function with P-controller with Kp = 300. Plot the step response using matlab. c) Derive the closed-loop transfer function with PD-controller with Ky and Ka = 10. Plot the step response using matlab. d) Derive the closed-loop transfer...
This feedback control system represents Integral Control of a Mass-Spring-Damper system: Controller Mass-Spring-Damper R(S) + Y(s)...
This feedback control system represents Integral Control of a Mass-Spring-Damper system: Controller Mass-Spring-Damper R(S) + Y(s) 17 S2 + 2s +6 NOTE: 1) Integral control is being used here (i.e. C(s) = Determine the values of gain "K,” for which the closed-loop system (i.e. RS ) remains stable.
5. Consider the model of a spring-mass-damper system, where the following parameter values are as...
5. Consider the model of a spring-mass-damper system, where the following parameter values are assumed: m 1,b 2, k 2 a. Design a rate feedback controller to meet the following step response specifictions: ts 1 s, ζ 206. b. Compare the step response of the closed-loop systems in Probs. 3&5
5. Consider the model of a spring-mass-damper system, where the following parameter values are assumed: m 1,b 2, k 2 a. Design a rate feedback controller to meet the following...
Question #4 (25 points): Consider the open loop system that has the following transfer function 1 G(S) = 10s+ 35 Us...
Question #4 (25 points): Consider the open loop system that has the following transfer function 1 G(S) = 10s+ 35 Using Matlab: a) Plot the step response of the open loop system and note the settling time and steady state 15 pts error. b) Add proportional control K 300 and simulate the step response of the closed loop 15 pts system. Note the settling time, %OS and steady state error. c) Add proportional derivate control Kp 300, Ko 10 and...
Consider the following second-order ODE representing a spring-mass-damper system for zero initial...
Consider the following second-order ODE representing a spring-mass-damper system for zero initial conditions (forced response): where u is the Unit Step Function (of magnitude 1 a. Use MATLAB to obtain an analytical solution x() for the differential equation, using the Laplace Transforms approach (do not use DSOLVE). Obtain the analytical expression for ao. Also obtain a plot of x() (for a simulation of 14 seconds) b. Obtain the Transfer Function representation for the system. c. Use MATLAB to obtain the...
Spring 2019 3. Given a closed-loop control system with unity feedback is shown in the block...
Spring 2019 3. Given a closed-loop control system with unity feedback is shown in the block diagram. G(s) is the open-loop transfer function, and the controller is a gain, K. 1. (20) Calculate the open-loop transfer function tar →Q--t G(s) (10) Calculate the steady-state error to a step input of the open-loop system. 7. (in Bode Form) from the Bode plot. (10) Calculate the shortest possible settling time with a percentage overshoot of 5% or less. 8. 2. (10)Plot the...
3. A mass on frictionless rollers is attached to a wall using a spring-damper mechanism: 99m...
3. A mass on frictionless rollers is attached to a wall using a spring-damper mechanism: 99m where input u is force and output y is position. Consider a unity-feedback control scheme as shown in question 2, but where the controller and plant are the following: C(s)1 P(s) Note that the parameters M1 and K 2 have been substituted, but that damping coefficient B is unknown. Suppose the damper slowly wears out over time. Draw a root-locus plot illustrating how the...
A colleague gave you a Simulink model (figure 5) for a non-linear mass-spring-damper system but f...
A colleague gave you a Simulink model (figure 5) for a non-linear mass-spring-damper system but forgot to provide yo u with the corresponding equation. (i) Find the non-linear equation of the mass-spring-damper system (ii) Find the equilibrium position (iii Find the Jacobian (linearise the equation about ts equilibrium) (iv) Comment on the stability of the system. (v) Plot the response of the linearised and non-linear model. What is the difference in mag of the non-linear equation. nitude between the linear...
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...
Problem 3. For the above feedback system, the bode diagram of the stable open-loop transfer function...
Problem 3. For the above feedback system, the bode diagram of the stable open-loop transfer function G(s) is plotted below: (a) Find the approximate gain margin and phase margin of the system? Is the closed-loop system stable? (b) Suppose in the closed-loop system (s) is replaced with KG(8). What is the range of K so that the closed-loop system is stable? (C) Determine the system type of G(s). (d) Estimate the steady-state errors of the closed-loop system for tracking the...
3. Consider the following mass-spring-damper system. Let m= 1 kg, b = 10 Ns/m, and k = 20 N/m. b m F k a) Derive the open-loop transfer function X(S) F(s) Plot the step response using matlab. b) Derive the closed-loop transfer function with P-controller with Kp = 300. Plot the step response using matlab. c) Derive the closed-loop transfer function with PD-controller with Ky and Ka = 10. Plot the step response using matlab. d) Derive the closed-loop transfer...
This feedback control system represents Integral Control of a Mass-Spring-Damper system: Controller Mass-Spring-Damper R(S) + Y(s) 17 S2 + 2s +6 NOTE: 1) Integral control is being used here (i.e. C(s) = Determine the values of gain "K,” for which the closed-loop system (i.e. RS ) remains stable.
5. Consider the model of a spring-mass-damper system, where the following parameter values are assumed: m 1,b 2, k 2 a. Design a rate feedback controller to meet the following step response specifictions: ts 1 s, ζ 206. b. Compare the step response of the closed-loop systems in Probs. 3&5
5. Consider the model of a spring-mass-damper system, where the following parameter values are assumed: m 1,b 2, k 2 a. Design a rate feedback controller to meet the following...
Question #4 (25 points): Consider the open loop system that has the following transfer function 1 G(S) = 10s+ 35 Using Matlab: a) Plot the step response of the open loop system and note the settling time and steady state 15 pts error. b) Add proportional control K 300 and simulate the step response of the closed loop 15 pts system. Note the settling time, %OS and steady state error. c) Add proportional derivate control Kp 300, Ko 10 and...
Consider the following second-order ODE representing a spring-mass-damper system for zero initial conditions (forced response): where u is the Unit Step Function (of magnitude 1 a. Use MATLAB to obtain an analytical solution x() for the differential equation, using the Laplace Transforms approach (do not use DSOLVE). Obtain the analytical expression for ao. Also obtain a plot of x() (for a simulation of 14 seconds) b. Obtain the Transfer Function representation for the system. c. Use MATLAB to obtain the...
Spring 2019 3. Given a closed-loop control system with unity feedback is shown in the block diagram. G(s) is the open-loop transfer function, and the controller is a gain, K. 1. (20) Calculate the open-loop transfer function tar →Q--t G(s) (10) Calculate the steady-state error to a step input of the open-loop system. 7. (in Bode Form) from the Bode plot. (10) Calculate the shortest possible settling time with a percentage overshoot of 5% or less. 8. 2. (10)Plot the...
3. A mass on frictionless rollers is attached to a wall using a spring-damper mechanism: 99m where input u is force and output y is position. Consider a unity-feedback control scheme as shown in question 2, but where the controller and plant are the following: C(s)1 P(s) Note that the parameters M1 and K 2 have been substituted, but that damping coefficient B is unknown. Suppose the damper slowly wears out over time. Draw a root-locus plot illustrating how the...
A colleague gave you a Simulink model (figure 5) for a non-linear mass-spring-damper system but forgot to provide yo u with the corresponding equation. (i) Find the non-linear equation of the mass-spring-damper system (ii) Find the equilibrium position (iii Find the Jacobian (linearise the equation about ts equilibrium) (iv) Comment on the stability of the system. (v) Plot the response of the linearised and non-linear model. What is the difference in mag of the non-linear equation. nitude between the linear...
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...
Problem 3. For the above feedback system, the bode diagram of the stable open-loop transfer function G(s) is plotted below: (a) Find the approximate gain margin and phase margin of the system? Is the closed-loop system stable? (b) Suppose in the closed-loop system (s) is replaced with KG(8). What is the range of K so that the closed-loop system is stable? (C) Determine the system type of G(s). (d) Estimate the steady-state errors of the closed-loop system for tracking the...
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