Define the closed-loop transfer function With the transfer function of the plant identified, the closed-loop transfer fu

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Define The Closed Loop Transfer Function With The Transfer Function Of The Plant Identified The Closed Loop Transfer Fu 1 (34.71 KiB) Viewed 46 times

Define The Closed Loop Transfer Function With The Transfer Function Of The Plant Identified The Closed Loop Transfer Fu 2 (33.75 KiB) Viewed 46 times

Define The Closed Loop Transfer Function With The Transfer Function Of The Plant Identified The Closed Loop Transfer Fu 3 (27.72 KiB) Viewed 46 times

Define The Closed Loop Transfer Function With The Transfer Function Of The Plant Identified The Closed Loop Transfer Fu 4 (24.5 KiB) Viewed 46 times

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Define the closed-loop transfer function With the transfer function of the plant identified, the closed-loop transfer function can be generated. You can derive this from the block diagram. Closed-loop C(s) R(s)0 E(s) Controller D() U(s) The closed-loop transfer function C can be easily derived from the block diagram to be C=Y DG Block diagram for the PID control feedback loop. The closed-loop transfer function C(s) encapsulates the entire feedback loop. The reference value denoted R(x) is the input of C and its output is Y(s)... R 1+ DG Plant G(a) D(s)-U(s) E(8) The plant transfer function G was identified in the previous section. The controller transfer function D must also be known APID controller computes the control signal as Y(*) I u(t)=ke+k₁ - Leve You can compute the controller transfer function D by taking the Laplace transform and then solving for the ratio of the input error, E(s), to the output control signal, U(s); e(t)dt+de +kde
Task 3. With the parameters k, = 1, k-0.1, and k=0.1, compute the PID transfer function D. Hint: define the transfer functions using s tf('s'). Then, use the variables with standard arithmetic operations to define D. Here is an example of this process to define R(x)=. =-0.3s: s R tf('s'); 3 define s 1/s^2 0.3's % define transfer function R * write your code to define D here Task 4. Compute the closed-loop transfer function C for the PID position control of the DC motor using the transfer functions G and D you defined in the previous two tasks. Note: It is possible to compute the closed-loop transfer function as CDG/(1+ DG). However, this formula will generate an unnecessarily complicated expression. Instead, use the feedback function. The syntax for feedback is sys feedback (sys1, sys?) sys1: the feedforward transfer function sys2: the feedback transfer function sys: the transfer function of the closed-loop system
8 9 e 1 These variables can be more easily understood in a block diagram. input o For this model, the feedback transfer function sys2 should be set to 1. % Use "feedback" to define c here sys sys1 08 sys2 Block diagram explanation of the syntax for the feedback function -o output Task 5. Compute and plot the step response of the closed-loop transfer function C using cep. If correct, your answer should appear as shown below. % write your code here Step Response
10 1 12 uiseControl.mlx Task 5. Compute and plot the step response of the closed-loop transfer function C using step. If correct, your answer should appear as shown below. write your code here i taskó apreday 08 06 04 02 01 0.2 Step Response 03 04 Time (seconds) 05 00 07 Step response of the closed-loop transfer function with k=1, k=0.1, and k=0.1. Task 6. Based on the step response you observed in Task 5, do you think the closed-loop transfer function is stable? 1
Task 7. Compute the poles of the closed-loop transfer function C. Computing the poles by hand is challenging. Instead, use the pole function. % write your code here Task 8. Based on the poles computed in Task 7, is the closed-loop transfer function stable? task8 - Task 9. It can be helpful to visualize the poles of the system in the complex plane. Use the pzmap function to plot the poles. Also, set the real and imaginary axis limits to [-10,10] using axis as: axis ([-10 10 10 10]) % Set the x- and y-axis limits to [-10,10] % write your code here