Homework Answers
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For this underdamped system: 12.5 GS=2 so +0.24s +101 1) Derive a state space equation for...
A process has the state model described by: a. Is the system fully state controllable or...
A process has the state model described by:
a. Is the system fully state controllable or not? Explain why or
why not.
b. Is the system fully observable or not? Explain why or why
not.
c. Design an observer with damping ratio , and the natural
frequency rads/sec n
d.Using the Luenberger gain matrix determined in Part c,
determine the error
response state model.
Problem 1: A process has the state model described by '11(0 a. Is the system fully...
The system has a steady-state gain of K = 23.8 rad/s/ and a time constant of...
The system has a steady-state gain of K = 23.8 rad/s/ and a time constant of t = 0.1 seconds. Let us further assume that you are required to design a PD position controller that has an overshoot of less than 5% and a peak time of no more than 0.2 seconds. 1. Using Equations 4 and 5 determine the required natural frequency (wn) and damping ratio (7) that will satisfy the overshoot and rise time requirements of the controller....
could you please answer this question QUESTION 2 Consider a system with an open-loop trans fer function given by Y(s) s+7 U(s) s2 +3s-8 (a) (8 marks) Derive a state-space model for the system in...
could you please answer this question
QUESTION 2 Consider a system with an open-loop trans fer function given by Y(s) s+7 U(s) s2 +3s-8 (a) (8 marks) Derive a state-space model for the system in canonical form. (b) (4 marks) Check the observability of the system. (c) 8 marks) Design a suitable full-order state observer for the system. Explain your choice of the observer's poles. d) (10 marks) Design a PI controller for the system so the output of the...
3.7 Underdamped free vibrations (e.g. a vibrating beam or slinky in damp air A system whose...
3.7 Underdamped free vibrations (e.g. a vibrating beam or slinky in damp air A system whose response is governed by the following constant-coefficient, is performing underdamped free vibrations if oc 1 (underdamped ). (Seetion 6.7). linear, 2td order, ODE ) and 1t)- (freei (a) After assuming a solution t)et where C and p are conustants, show every step that proves yit) can be expressed in terms of the yet-to-be-determined constants A and B and he constant wa (defined above) called...
5. For each of the following, determine if the system is underdamped, undamped, critically damped or overdamped ad sket...
5. For each of the following, determine if the system is underdamped, undamped, critically damped or overdamped ad sketch the it step response (a) G (s) = (c) G(s)-t 2+68+ (d) G (s) = 36 6. The equation of motion of a rotational mechanical system is given by where θ° and θί are respectively, output and input angular displace- ments. Assuming that all initial conditions are zero, determine (a) the transfer function model. (b) the natural frequency, w natural frequency,...
Please derive the equations and draw simulink model. For the vibration absorber model below. (a) ma is selected to be 5% of main mass m, what should the value of ka be so the vibration of the main...
Please derive the equations and draw simulink
model.
For the vibration absorber model below. (a) ma is selected to be 5% of main mass m, what should the value of ka be so the vibration of the main mass is eliminated? (b) What are the natural frequencies of the system? (c) Adding a damper to the absorber such that the absorber has a damping ratio of 0.5, how much would the main mass vibrate now? What if the excitation frequency...
PD & PID controller design Consider a unity feedback system with open loop transfer function, G(s)...
PD & PID controller design Consider a unity feedback system with open loop transfer function, G(s) = 20/s(s+2)(8+4). Design a PD controller so that the closed loop has a damping ratio of 0.8 and natural frequency of oscillation as 2 rad/sec. b) 100 Consider a unity feedback system with open loop transfer function, aus. Design a PID controller, so that the phase margin of (S-1) (s + 2) (s+10) the system is 45° at a frequency of 4 rad/scc and...
5. For each of the following, determine if the system is underdamped, undamped, critically damped or...
5. For each of the following, determine if the system is underdamped, undamped, critically damped or overdamped ad sketch the it step response (a) G (s) = (c) G(s)-t 2+68+ (d) G (s) = 36 6. The equation of motion of a rotational mechanical system is given by where θ° and θί are respectively, output and input angular displace- ments. Assuming that all initial conditions are zero, determine (a) the transfer function model. (b) the natural frequency, w natural frequency,...
Consider a single degree of freedom (SDOF) with mass-spring-damper system
Consider a single degree of freedom (SDOF) with mass-spring-damper system subjected to harmonic excitation having the following characteristics: Mass, m = 850 kg; stiffness, k = 80 kN/m; damping constant, c = 2000 N.s/m, forcing function amplitude, f0 = 5 N; forcing frequency, ωt = 30 rad/s. (a) Calculate the steady-state response of the system and state whether the system is underdamped, critically damped, or overdamped. (b) What happen to the steady-state response when the damping is increased to 18000 N.s/m? (Hint: Determine...
Do only parts C and D 1. A second-order system has the following transfer function that...
Do only parts C and D
1. A second-order system has the following transfer function that describes its response: F(s)- s2 +as + 9 A. For a -3, calculate the following performance specifications of the system: Natural frequency (on) Damping ratio( Estimated rise time and settling time with ±5% change (tr, ts) Estimated overshoot (MP) . B. Label (a) ±5% range of steady state, (b) tr, (c) ts, and (d) MP on the step response curve below (You may also...
A process has the state model described by:
a. Is the system fully state controllable or not? Explain why or
why not.
b. Is the system fully observable or not? Explain why or why
not.
c. Design an observer with damping ratio , and the natural
frequency rads/sec n
d.Using the Luenberger gain matrix determined in Part c,
determine the error
response state model.
Problem 1: A process has the state model described by '11(0 a. Is the system fully...
The system has a steady-state gain of K = 23.8 rad/s/ and a time constant of t = 0.1 seconds. Let us further assume that you are required to design a PD position controller that has an overshoot of less than 5% and a peak time of no more than 0.2 seconds. 1. Using Equations 4 and 5 determine the required natural frequency (wn) and damping ratio (7) that will satisfy the overshoot and rise time requirements of the controller....
could you please answer this question
QUESTION 2 Consider a system with an open-loop trans fer function given by Y(s) s+7 U(s) s2 +3s-8 (a) (8 marks) Derive a state-space model for the system in canonical form. (b) (4 marks) Check the observability of the system. (c) 8 marks) Design a suitable full-order state observer for the system. Explain your choice of the observer's poles. d) (10 marks) Design a PI controller for the system so the output of the...
3.7 Underdamped free vibrations (e.g. a vibrating beam or slinky in damp air A system whose response is governed by the following constant-coefficient, is performing underdamped free vibrations if oc 1 (underdamped ). (Seetion 6.7). linear, 2td order, ODE ) and 1t)- (freei (a) After assuming a solution t)et where C and p are conustants, show every step that proves yit) can be expressed in terms of the yet-to-be-determined constants A and B and he constant wa (defined above) called...
5. For each of the following, determine if the system is underdamped, undamped, critically damped or overdamped ad sketch the it step response (a) G (s) = (c) G(s)-t 2+68+ (d) G (s) = 36 6. The equation of motion of a rotational mechanical system is given by where θ° and θί are respectively, output and input angular displace- ments. Assuming that all initial conditions are zero, determine (a) the transfer function model. (b) the natural frequency, w natural frequency,...
Please derive the equations and draw simulink
model.
For the vibration absorber model below. (a) ma is selected to be 5% of main mass m, what should the value of ka be so the vibration of the main mass is eliminated? (b) What are the natural frequencies of the system? (c) Adding a damper to the absorber such that the absorber has a damping ratio of 0.5, how much would the main mass vibrate now? What if the excitation frequency...
PD & PID controller design Consider a unity feedback system with open loop transfer function, G(s) = 20/s(s+2)(8+4). Design a PD controller so that the closed loop has a damping ratio of 0.8 and natural frequency of oscillation as 2 rad/sec. b) 100 Consider a unity feedback system with open loop transfer function, aus. Design a PID controller, so that the phase margin of (S-1) (s + 2) (s+10) the system is 45° at a frequency of 4 rad/scc and...
5. For each of the following, determine if the system is underdamped, undamped, critically damped or overdamped ad sketch the it step response (a) G (s) = (c) G(s)-t 2+68+ (d) G (s) = 36 6. The equation of motion of a rotational mechanical system is given by where θ° and θί are respectively, output and input angular displace- ments. Assuming that all initial conditions are zero, determine (a) the transfer function model. (b) the natural frequency, w natural frequency,...
Do only parts C and D
1. A second-order system has the following transfer function that describes its response: F(s)- s2 +as + 9 A. For a -3, calculate the following performance specifications of the system: Natural frequency (on) Damping ratio( Estimated rise time and settling time with ±5% change (tr, ts) Estimated overshoot (MP) . B. Label (a) ±5% range of steady state, (b) tr, (c) ts, and (d) MP on the step response curve below (You may also...
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