ECE451/551 Matlab and Simulink Controller Deign Project Aim: Ue Matlab and Simulink to build and imulate variou control configuration a dicued in the Modern Control ection (chapter 18-23) in the intructor book Claical and Modern Control Deign which i available on the cla webpage. The ytem to be conidered i the C1 dc-to-dc voltage converter. The function of thi ytem i to convert a dc voltage level to a lower dc voltage level with high power efficiency. Thi converter chematic and model i given in the following page and wa dicued in cla. The tate pace ytem repreentation i provided by uing the State Space Averaged model which i given in the following page and dicued in chapter 18 of the book. The converter will be ued to convert 28 V at the input to 15 V at the output acro an R 3 load. The component value are L1 130 H, L2 1 mh, C1 500 F and C2 100 F. The voltage converion V ratio V f out g D where D i the teady tate duty ratio. Although not needed for our model, we will ue 1 100 khz. T In thi project you will examine the imulation reult uing both Matlab (a done in the book for another converter) and alo confirm thee reult with Simulink. Ue of the Matlab code provided in the book, but uitably modified for the C1 converter, i permitted. The tranient imulation reulting from input voltage change of V 28V 30V will be examined for variou configuration correponding to the following for the converter examined in the book: 1) Open loop, Fig. 18.2 Fig. 18.3 2) Full tate feedback, Fig 19.5 Fig. 19.3 and Fig. 19.6 3) Full tate feedback with integral control, Fig. 20.2 Fig 20.4 and Fig. 20.6 4) Full tate feedback with integral control and full order oberver, Fig. 21.1 Fig. 21.2 and Fig. 21.4 5) Full tate feedback with integral control and reduced order oberver, Fig. 21.6 Fig. 21.7 6) LQR: Linear Quadratic Regulator (note: no oberver), ue Fig. 19.5 Fig. 22.3 and Fig. 22.1 7) LQG (Linear Quadratic Gauian) = LQR+LQE: Linear Quadratic Regulator (LQR) and Linear Quadratic Etimator (LQE) (note: full order oberver), ue Fig. 21.1 Fig. 22.4 and Fig. 22.6 8) LQG/LTR: Linear Quadratic Gauian with Loop Tranfer Recovery (note: reduced order etimator), ue Fig. 21.6 Fig. 23.8 You are free to chooe your own pole location for the variou configuration. Guideline for thi are given the book and in the Matlab code in the book. For each of the configuration, your Matlab and Simulink imulation hould agree with each other. g
For Matlab code: Modify the Matlab code provided in the book appropriately for the C1 converter. Store thee file in a directory correponding to the configuration. More on thi below. For Simulink: The mot tructured way to run the individual configuration of the project i to: 1) Write a Matlab m file which when run introduce the variable, that are ued by Simulink, into the workpace. 2) In Simulink ue imple ymbol (a ued in the conceptual block diagram) to intantiate Simulink block value. Your Simulink block diagram hould ue to workpace block to feed output into the Matlab workpace. Run Simulink. 3) Ue an appropriate plot command in Matlab to plot the reult that have been written to the workpace. If the above i followed then there i generally no need for further documentation to be provided. So, in your report, for each of the above ubection, provide the 1) Matlab input file, 2) Simulink block diagram with all block clearly labeled, and 3) the Matlab plot file along with the actual plot. At the end of the report provide a concluion which indicate how cloely your Matlab and Simulink imulation agree with each other. Submit an electronic verion of your report along with all your *.m and *.mdl file in a zipped file. Confining your file for different configuration to their own appropriately named ubdirectorie will implify running of your project (if neceary). Email to tymerki@ee.pdx.edu.
C1 dc-to-dc voltage converter: Topology and Model The chematic of the C1 dc-to-dc voltage converter i hown in Figure 1. Fig. 1: C1 converter. The witche Q and P operate cyclically with period T. During the firt part of the period of length DT, where D i the teady tate duty ratio, where 0 D 1, witch Q in ON and witch P if OFF. Thi reult in a circuit configuration which can be decribed in tate pace by the quadruple A, B, C, E. Note we 1 1 1 1 will ue the ymbol E in the tate pace output equation here rather than D which ha been reerved to repreent duty ratio. During the remainder of the period of length (1 DT ), witch Q in OFF and witch P if ON. The correponding tate pace quadruple i A, B, C, E. Henceforth we will ue for convenience the following: D' 1 D. State Space Averaging (SSA) Model: The large ignal model i given by: 2 2 2 2
A i uual practice, the tate variable are given by the inductor current and capacitor voltage:
SSA matrice: For the tranient imulation we will ue the mall-ignal SSA model: xˆ Axˆ Buˆ B ˆ dd yˆ Cxˆ Euˆ E ˆ dd where matrice A, B, C and E where previouly defined and where B ( A A ) X ( B B ) U d 1 2 1 2 E ( C C ) X ( E E ) U d 1 2 1 2 Term with a caret ^, repreent mall deviation away from the teady tate value.