ECE-320 Lab 6: PI-D and I-PD Control with Dynamic Prefilters Overview In this lab you will be controlling the one degree of freedom systems you previously modeled using PI-D and I-PD controllers with and without dynamic prefilters. You will need your Simulink model and the closedloop_driver.m file from your homework for this lab. Design Specifications: For each of your systems, you should try and adjust your parameters until you have achieved the following: Torsional Systems (Model 205) • Settling time less than 1.0 seconds. • Steady state error less than 2 degrees for a 15 degree step, and less than 1 degree for a 10 degree step (the input to the Model 205 must be in radians!) • Percent Overshoot less than 25% Rectilinear Systems (Model 210) • Settling time less than 1.0 seconds. • Steady state error less than 0.1 cm for a 1 cm step, and less than 0.05 cm for a 0.5 cm step • Percent Overshoot less than 25% As a start, you should initially limit your gains as follows: 0.550.01pidkkk≤≤≤ Your memo should include four graphs for each of the 1 dof systems you used (one PI-D and one I-PD controller with and without dynamic prefilters.) Be sure to include the values of , , and in the captions for each figure. Your memo should compare the difference between the predicted response (from the model) and the real response (from the real system) for each of the systems. How does the use of a dynamic prefilter change the response? Attach your Matlab driver file closedloop_driver.m pkikdk 1Background: While PID controllers are very versatile, they have a number of drawbacks. One of the major drawbacks is that for a unit step input, the control effort can be infinite at the initial time. This is referred to as a set-point kick. There are two commonly used configurations of PID controls schemes that utilize a different structure, the PI-D and the I-PD controllers. These are a bit more difficult to model using Matlab’s sisotool, but it can be done and we get to explore more of sisotool. ()ut The PI-D controller avoids the set-point kick by putting the derivative in the feedback path, while the I-PD controller avoids the set-point kick by placing both the derivative and proportional terms in the feedback path. Both types of controllers can be implemented using the following Simulink model, which you should construct and name appropriately: For the PI-D controller, we have 1()ipkCs ks=+, 2()1150dksCss=+ while for the I-PD controller we have 1()ikCss=, 2()1150dpksCs ks=++ Note that for both controllers we continue to use a lowpass filter (with a cutoff of 50 rad/sec) in series with a differentiator. For both of these controllers, if we ignore the prefilter (assume it is unity), the transfer function from input to output is 121() ()()()1 ()() ()()pppCsG sYsRs C sG s C sG s=++ 2Next we need to use sisotool to help determine reasonable values for , , and . pkikdk When you start sisotool, you need to click on Control Architecture to get the proper configuration. Be sure that sisotool uses negative feedback for both loops. Click here to change the control architecture 3Next we need to select the correct architecture. Select the following architecture and be sure that sisotool uses negative feedback for both loops. Click on OK and when the previous window appears, select Loop Configuration. In the block Open-loop configuration for: select Open Loop Output of C1 and select Open for Output of Block C2. In the block Open-loop configuration for: select Open Loop Output of C2 and select Open for Output of Block C1. The following figures demonstrate what you are to do. Note that this step is not really necessary, but I find it a bit less confusing. The controllers in each window may not be exactly what you are expecting, but it is easier to visualize this way. 45Next, go back to our design window, and select View, then Design Plots Configuration. Then choose to plot the Root Locus plot for both Open Loop 1and Open Loop 2, as the following window shows: You should now have a design window with two (empty) root locus plots and we are ready to start. For practice, let’s assume our plant is 2938.4()1.25 329.8pGsss=++ .When we import the plant, we should get a design window that looks like the figure on the following page. Each window shows the root locus for the plant and two identical proportional controllers. 6I Let’s initially assume we want to use a PI-D controller. In this case, for simulation purposes, we have (we won’t worry about the lowpass filter here). We will start off asuming , but this is just a guess! To assign this to controller C2, in the design window we select Designs, the Edit Compensator, then select C2 in the compensator window, and enter the controller. 2()dCs ks=0.01dk = 7Next we’ll enter the PI part of the controller into . As a starting point, let’s assume 1()Cs10.15( 15)()sCss+= and enter this into C1. If you have done this correctly, you should get the following root locus plots. The step response for this controller configuration is shown on the next page: 8Note that, compared to a normal PID controller, the control effort is not infinite at 0, and actually builds as time goes on (like an integral controller). At this point we might want to go back modify our controllers C1 and C2 to see if we get acceptable performance. Note that we can modify the two controllers (and gains) independently. Now we’ll assume we want to control the same plant, but this time use an I-PD controller. We first have to guess a PD controller. For the systems I tired, I found that the zero should be fairly small, between -1 and -5. As a start, we’ll try the following PD and I controllers 121.5() , () 0.01( 1)Cs Cs ss==+ If you enter these controllers, you should get the following root locus plots: 9The step response for this system is plotted on the following page. Again, you can change the controllers independently to try to obtain an acceptable response. 10Now we want to design and implement these types of controllers for your systems. You should go through the following steps for each of your systems. 11Step 1: Set up the 1 dof systems exactly the way they were when you determined their model parameters. Step 2: Modify closedloop_driver.m to read in the correct model file and implement the new structure. In particular, it must now determine C1(s) and C2(s), as