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Rose-Hulman ECE 520 - State Variable Feedback

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ECE-520 Lab 5 State Variable Feedback and Integral Control For One and Two Degree of Freedom Systems Overview In this lab you will be utilizing state variable feedback control to place the poles in a closed loop system to improve the performance of your open loop one and two degree of freedom systems. In addition, you will be incorporating integral control to try and produce zero steady state error for a step input. For each of the systems you use in this lab (and for the remainder of the labs in this course) you will go through the following basic procedure: 1) Modify the Simulink driver you are using to load the mathematical model file (.mat file) that corresponds to the way you have the system configured. 2) Simulate the system to determine if your model meets the desired specifications. If it does not, modify the pole locations until it does meet the specifications. In addition, you need to be sure the control effort does not reach the saturation level. The simulated control effort for the discrete-time system does not model the real control effort as well as it does for the continuous time system. Hence, if your control effort is near the saturation level it is not likely to work well. 3) You may reduce the sampling interval if necessary to achieve better results, but this often leads to increased control effort. 4) Once you have simulated the system all of the variables you used are in Matlab’s workspace. Now compile the correct ECP driver file that replaces the model of the ECP system with the ECP system driver (and the real ECP system). Reset the ECP system, and run the system. 5) Finally, compare the predicted response (from your mathematical model) with the real response (from the ECP system). A graph showing the predicted and real response is to be included in your memo (as an attachment) for each system you simulate. 1Notes and Guidlines: • Although it should not matter, only use positive pole locations. Apparently the ECP system are not particularly happy with negative pole locations. • Start with poles at around 0.5 or 0.6, and then move them in closer once you see how the system is responding. We are not trying to make the systems go particularly fast here, but just see how discrete-time control systems work. • The ECP systems really do not like poles at the origin, so don’t put any poles there (no deadbeat control.) • Run the systems for at least one second, but don’t run the system so long most of your graph shows the system at steady state. • Reset the system each time before you run it. • As soon as you start you controller (click on play) be prepared to stop the system. In particular, listen for vibrations that are growing louder and stop the system as soon as possible after this. Design Specifications For each of your systems try and have the simulated systems meet the following design specifications a) Settling time less than or equal to one second b) Steady state error is zero for a 1 cm step input (or a 15 degree step input) c) Percent overshoot less than 20% You should try for the 1cm (or 15 degree) inputs, but if your system is unwilling to cooperate try a 0.5 cm input (or a 10 degree input). This is particularly true when trying to control the position of the second cart/disk. You system should (eventually) reach the correct steady state level. It won’t be exact due to measuring errors, but it should be close. Remember we are only guaranteed a zero steady state error at some point in time, it may take a while for the system to actually get to steady state. 2Part A: One Degree of Freedom Rectiliner Systems a) Load the files from the Lab 4 folder into a folder for Lab 4. b) Configure your one degree of freedom system the way you did in Lab 1. c) Modify the Matlab driver file DT_sv1_servo_driver.m to read in the appropriate mathematical model. d) Use state variable feedback coupled with an integral controller to place the poles in such a way that you think you will meet the system requirements given above. Remember there is usually a tradeoff between speed of response and the required control effort, which is limited by our motors. e) Run the simulation for at least one second (Tf should be at least one second). This is because the ECP systems tend to hang up if they run for less than a second. f) Simulate the systems, check to see that they meet the design requirements and the control effort does not reach the saturatation level. If there is a problem, go to step (e) and try a different set of pole locations. g) Create the file Model210_DT_sv1_servo.mdl to implement the controller. The easiest way to do this is as follows: • open up your file DT_sv1_servo.mdl and then save it as Model210_DT_sv1_servo.mdl. • replace (copy and paste) the mathematical model of the system used in Model210_DT_sv1_servo.mdl with the ECP drivers from Model210_DT_sv1.mdl • edit the outputs of Model210_DT_sv1_servo.mdl so the states and time do not have the `m’ prefix. h) Reset the ECP system. i) Connect Model210_DT_sv1_servo.mdl to the ECP system and run it. j) Use the program Compare_DT1.m to produce a plot comparing the predicted response using the mathematical model of the system with the real response of the system. Note that the third state is not plotted since it is not really all that important. k) Copy and paste this graph into your Word document that will eventually become your memo for this lab. It is a real good idea to write a short caption at this time so you don’t forget what you just did. 3Part B: Two Degree of Freedom Rectiliner Systems For this system you need to basically go through the same steps you used in PART A, except you will need to use the programs DT_sv2_servo.mdl and DT_sv2_servo_driver.m you wrote for your homework. You will need to copy the program Model210_DT_sv1_servo.mdl to Model210_DT_sv2_servo.mdl and then modify the program Model210_DT_sv2_servo.mdl to work with the two degree of freedom system (you need to change the outputs of the demux). Configure your two degree of freedom system the way you did in Lab 2. Assume we are trying to control the position of the first cart, and then we are trying to control the position of the second cart. You should compare the predicted response with the response of the real system. Hence you will have two plots (each showing all four states) as you analyze your system. Part C: One Degree of Freedom


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