7. Repeat (6) with K+ = 40 and change Ky = 400, and 1600. What is your comment on the effect of Kp on the system in each

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7 Repeat 6 With K 40 And Change Ky 400 And 1600 What Is Your Comment On The Effect Of Kp On The System In Each 1 (51.9 KiB) Viewed 33 times

7. Repeat (6) with K+ = 40 and change Ky = 400, and 1600. What is your comment on the effect of Kp on the system in each case? 8. Repeat (6) with Kn = 800 and change K = 5 and 80. What is your comment on the effect of K, on the system in each case? 9. Bonus: Based on the results of (7) and (8) by trying different values of the controller constants, find the best value of Ky and K Note: • Special template will be used for this lab project. The template will be uploaded as a word document to use it as a template and type over it without changing its format. All your work should by typed Each section should have both analytical and programming solutions. It means that for each question the calculation and the code associated with the question should be placed in the space after the question. The MATLAB files should be also submitted to the dropbox to be tested. • The grade of this report is different than others, therefore, the rubric of this project is in the end of this document. Read it carefully to know how the report will be graded. • Screenshot or hand written work will not be graded. Equations that are not in the right format will not be graded. Equations should be typed using Equation editor • Acceptable form: y = 10e-3tu(t) (1) ) Not acceptable form: Y=10*e^-3*t (1) • No screenshot. Figures from MATLAB can be done using copy figure from Edit • Block diagrams should be done using the tools in word or other software but not sketched by hand |
Problem Description desired Speed Error Throttle Input Actual Speed Controller Engine Measured Speed Cruise control is a system, which automatically controls the speed of an automobile, The purpose of the cruise control system is to maintain a constant vehicle speed despite external disturbances, such as changes in wind or road grade. This is accomplished by measuring the vehicle speed, comparing it to the desired or reference speed, and automatically adjusting the throttle according to a control law. The cruise control system actually has a lot of functions other than controlling the speed of your car. It can accelerate or decelerate with the tap of a button. The cruise control system only controls the gas pedal. Cruise control system CCS is a closed feedback control system, and a simplified block diagram of a CCS is shown in Fig. 2. The speed of the vehicle is measured by a speed sensor and then compared to the specified desired speed. A controller receives and process the compared signals according to a control algorithm to manipulate the throttle which in turn adjust the gas flowing to the engine. In this project a simple a model of the vehicle dynamics are considered. Fig. 1 shows a vehicle and the forces acting upon it. For the simplified model it is assumed that the control force can be controlled directly and the dynamics of the power train, tires, etc., that go into generating the force are neglected. Speed Sensor . Fig. 2 1. Write the differential equation of the vehicle shown in Fig. 1 by summing forces in x-direction and applying Newton 20 law. f(t)and v(1) are the input and output of the system) 2. Drive the transfer function of the vehicle (s) using the differential cquation obtained in (1), then use MATLAB to express the transfer function. The MATLAB function can be used to express the transfer function. For more information about if-function: https://www.mathworks.com/help/control/reft.html 3. Using the transfer function () find the response to a constant input f(t) = 500 N. Find the response analytically and check your result by MATLAB then sketch the response v(t). This response is known as open-loop response. What is open-loop response? Solve it analytically and using MATLAB by m 4. Redo (3) for the input ) (500 Osts5 And sketch the response over 200 seconds. Solve it analytically and using MATLAB f(t) = 10 otherwise y = * 5. The transfer function of PI-Controller is - Ge(s) = K+ , Where, K, and K are the proportional and integral constants, respectively. Find the closed loop transfer function, where Vs) and V,(s) are the actual speed and the desired speed, respectively. Solve it , V(8) VEN V( analytically and using MATLAB Fig. 1. The parameters of the system are: Vehicle mass (m) = 1000 kg Damping coefficient (b) 50 N.s/m The variables of the system are: The displacement (x) The speed of the car (v) The force from the engine (1) The reference (desired speed):r = 10 m/s state 6. Find the closed response if Kp = 800 and K = 40 Express the output as a function of sand as a function of time. b. Find the steady-state error when there is a unit step change in the speed reference 6. If Ki=0, find the value of K, so that for a unit step input there will be a 0.05 error in the steady d. plot the response over 50 seconds. Show your analytical work and the MATLAB code used in this part.] 7. Repeat (6) with K = 40 and change K, = 400, and 1600. What is your comment on the effect of Ky on the system in each case? 8. Repeat (6) with K, = 800 and change Ki = 5 and 80. What is your comment on the effect of Ky on the system in each case? 9. Bonus: Based on the results of (7) and (8) by trying different values of the controller constants, find the best value of K, and K