425 Can a tank with the outflow rate fixed by a constant speedl pump reach a steady state if the inlet flow rate undergoes a step change? Why, or why not? If the transfer function is G'S-K/s is it possible to calculate a steady-state gain? ner
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G / 4.18/A process has the transfer function Y(s) U(s) G(s) = 2s + 1 (a) For a step change in the...
Problem 3. (40 points) For the process described by the transfer function 10(1-2s)e2s Y(s) U(s) (...
Problem 3. (40 points) For the process described by the transfer function 10(1-2s)e2s Y(s) U(s) (10s+1)(4s+ 1)(s +1) (a) Find an approximate transfer function of first-order-plus-time-delay form that describes this process (b) Determine and plot the response y(t) of the approximate model, obtained in part (a), for a unit ramp using Skogestad's "Half Rule"; change in u(t) (U(s)
Problem 3. (40 points) For the process described by the transfer function 10(1-2s)e2s Y(s) U(s) (10s+1)(4s+ 1)(s +1) (a) Find an approximate...
3. For the transfer function give by, Y (s) U(s) Find the steady-state value of y(t)...
3. For the transfer function give by, Y (s) U(s) Find the steady-state value of y(t) for a unit step input in U. Use the final values theorem
7.22 A simple 1-DOF mechanical system has the following transfer function Y(s) 0.25 U(s) s +2s...
7.22 A simple 1-DOF mechanical system has the following transfer function Y(s) 0.25 U(s) s +2s +9 where the position of the mass y0) is in meters. The system is initially at rest, y(O) (0) 0, and the applied force is a step function u(t0 4N Copyrighto Problems 243 a. Accurately sketch the system response y() and label all important performance criteria on your sketch b. Use MATLAB or Simulink to verify your sketch in part (a). Plot y(o) from...
A chemical process unit exhibits an underdamped second order behavior as given by the transfer function:...
A chemical process unit exhibits an underdamped second order behavior as given by the transfer function: Y(s) U(s) 18 s2 + 3s + 9 Calculate the process gain, natural period of oscillation and damping factor for the system. (3m) b. If a step change in the input with the magnitude of 3 is introduced, i. Determine the step response (5m) ii. Estimate the new steady-state value of y. (2m)
The transfer function of a linear system is G(s) = Y(s) S-1 U(s) 5? + 4s...
The transfer function of a linear system is G(s) = Y(s) S-1 U(s) 5? + 4s +3 a. Express this system in the modal form. b. Express this system in the standard controllable form (SCF). (Parts d, e, f, and g use this system) c. In the standard controllable form, suppose the output is replaced by y=[-1 a] | [x2] Give a value for a which makes the system unobservable. d. What is y(t) if y(0-)=-3, ay = 6 and...
a system is given by the following transfer function Y(s)/u(s) = 1/(s^2-16) a)find the output in...
a system is given by the following transfer function Y(s)/u(s) = 1/(s^2-16) a)find the output in time domain Y(t) if the input u(t) is a unit step. (Hint the transfer function of the unit step function is 1/s) b)what is Y(t) as t goes to infinity
The Chosen Kp = 1.3 ----TOPOLO The pump transfer function has been step-input tested and found...
The Chosen Kp = 1.3
----TOPOLO The pump transfer function has been step-input tested and found to be 0.005 2s +1 The proportional control loop is therefore X + 0.005 *D K 0.005 2s +1 Using your chosen value of Ky 0.005 2s +1 1. Find the cltf 2. Calculate the expected rise time (5 time constants) 3. Calculate the steady-state output and steady-state error.
4. Consider the transfer function, Y(s)_ 3 F(s) + s(s2 + 2s + 4) (a) Qualitatively,...
4. Consider the transfer function, Y(s)_ 3 F(s) + s(s2 + 2s + 4) (a) Qualitatively, what is the time response y(t) if f(t) represents a unit-step input? What is the value of y(t) when time is sufficiently large? What is the time constant that we may use to evaluate the "speed" of response? (b) Repeat step (a) if f(t) represents an impulse input. What is y(t) when time is sufficiently large?
C(8) for the system shown in Figure 1. R(S Find the equivalent transfer function, Geg (s)...
C(8) for the system shown in Figure 1. R(S Find the equivalent transfer function, Geg (s) 1 Cix) Figure 1. Block diagram 2s+1 s(5s+6Ge(s) = and Figure 2 shows a closed-loop transfer function, where G(s) 2. proper H(s) K+s. Find the overall closed-loop transfer function and express is as rational function. C(s) Ea (s) Controller R(s) +/ Plant G(s) Ge (s) Feedback H(s) Figure 2. Closed loop transfer function Construct the actuation Error Transfer Function associated with the system shown...
Suppose that the zero-state response to the step input for a plant with transfer function G0(s)...
Suppose that the zero-state response to the step input for a plant with transfer function G0(s) is given by y0(t) for each t 0. Answer the following questions. Your answers are expected to be expressed in terms of y0. 1) What is the zero-state response to the same plant but for the input given by u(t) = t for each t 0 and u(t) = 0 for each t < 0? 2) Consider now the transfer function G(s) = s2G0(s)...
Problem 3. (40 points) For the process described by the transfer function 10(1-2s)e2s Y(s) U(s) (10s+1)(4s+ 1)(s +1) (a) Find an approximate transfer function of first-order-plus-time-delay form that describes this process (b) Determine and plot the response y(t) of the approximate model, obtained in part (a), for a unit ramp using Skogestad's "Half Rule"; change in u(t) (U(s)
Problem 3. (40 points) For the process described by the transfer function 10(1-2s)e2s Y(s) U(s) (10s+1)(4s+ 1)(s +1) (a) Find an approximate...
3. For the transfer function give by, Y (s) U(s) Find the steady-state value of y(t) for a unit step input in U. Use the final values theorem
7.22 A simple 1-DOF mechanical system has the following transfer function Y(s) 0.25 U(s) s +2s +9 where the position of the mass y0) is in meters. The system is initially at rest, y(O) (0) 0, and the applied force is a step function u(t0 4N Copyrighto Problems 243 a. Accurately sketch the system response y() and label all important performance criteria on your sketch b. Use MATLAB or Simulink to verify your sketch in part (a). Plot y(o) from...
A chemical process unit exhibits an underdamped second order behavior as given by the transfer function: Y(s) U(s) 18 s2 + 3s + 9 Calculate the process gain, natural period of oscillation and damping factor for the system. (3m) b. If a step change in the input with the magnitude of 3 is introduced, i. Determine the step response (5m) ii. Estimate the new steady-state value of y. (2m)
The transfer function of a linear system is G(s) = Y(s) S-1 U(s) 5? + 4s +3 a. Express this system in the modal form. b. Express this system in the standard controllable form (SCF). (Parts d, e, f, and g use this system) c. In the standard controllable form, suppose the output is replaced by y=[-1 a] | [x2] Give a value for a which makes the system unobservable. d. What is y(t) if y(0-)=-3, ay = 6 and...
The Chosen Kp = 1.3
----TOPOLO The pump transfer function has been step-input tested and found to be 0.005 2s +1 The proportional control loop is therefore X + 0.005 *D K 0.005 2s +1 Using your chosen value of Ky 0.005 2s +1 1. Find the cltf 2. Calculate the expected rise time (5 time constants) 3. Calculate the steady-state output and steady-state error.
4. Consider the transfer function, Y(s)_ 3 F(s) + s(s2 + 2s + 4) (a) Qualitatively, what is the time response y(t) if f(t) represents a unit-step input? What is the value of y(t) when time is sufficiently large? What is the time constant that we may use to evaluate the "speed" of response? (b) Repeat step (a) if f(t) represents an impulse input. What is y(t) when time is sufficiently large?
C(8) for the system shown in Figure 1. R(S Find the equivalent transfer function, Geg (s) 1 Cix) Figure 1. Block diagram 2s+1 s(5s+6Ge(s) = and Figure 2 shows a closed-loop transfer function, where G(s) 2. proper H(s) K+s. Find the overall closed-loop transfer function and express is as rational function. C(s) Ea (s) Controller R(s) +/ Plant G(s) Ge (s) Feedback H(s) Figure 2. Closed loop transfer function Construct the actuation Error Transfer Function associated with the system shown...
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