【正文】 , 1997. [12] Owens, . Multivariable and Optimal Press: London, 1981. [13]Boyd, S., et. al. LMIs in System and Control Theory. SIAM: Philadelphia, PA, 1994. Figure 1. User interface control for minimum control energy problem Figure 2. User interface control for fixed final state LQ regulator. 。 when a user chooses an object there is an expectation that a certain kind of action will take place. In MATLAB the GUI is implemented using user interface (UI) 1 shows the application of user interface in minimum control energy for a scalar system with fixed final state. The system model and performance index are given by ???????102012nk kkkkuJuxx r ba (7) where xk and uk denote the state and control input,respectively. r is a positive scalar weighting factor. This program will produce plots of the state and the optimal input vs. time. The sliders will allow the user to change the system parameters and observe the resulting changes. Figure 2 illustrates the use of user interface control in a discretetime fixed final state linear quadratic regulator. The system model and performance index are given by 0,0,0,)(2121,11?????????? ??? RQNRQNSikBANik kTkkTkxTNixkk uuxxNxJ uxx (8) and the optimal control law equations given by ,1 11)( AkT SBRBSBK kTk ????? sN given rPVKxVPVKKUBRBSBKPVBRBSBVPPCVVKBAVkSASNkkukKTkkkukkkTukNkTTkkkTNkTkkkTkkTkTBkQBA11111111111)(10,1,)()()()(????????????????????????????? rN given The system parameters are specified in continuous time and are discretized based on the sampling period T. The program produces plots of output and control input for optimal and suboptimal regulator. The value of T and the final time ??ft can be changed with the slider bars. The A, B, and C buttons allow the user to change the system parameters. The system button prints system parameters in continuous and discretetime, sampling period, poles of the system, and the final time. The recalc button updates the plots based on the parameter changes. Although, the GUI is very useful for presenting the changes in system response due to parameter variations, the implementation is very time consuming and requires an extensive knowledge of MATLAB. Conclusion In this paper, we have presented the use of MATLAB and some of its panion toolboxes in our graduate curriculum, at Penn State University and the University of Arkansas. Several of the advantages provided by puter simulation packages, such as MATLAB, include a reinforcement of student understanding of theoretical principles, allowing assignment of larger, and more plex designs, increased student attentiveness, and enhanced professional development. The main disadvantages of using puter simulation packages are the extra work required of students and instructors, the maintenance and operation of these packages on an accessible puter system, and assuring that the packages are inserted in the baseline curriculum as part of the required course material. Due to the variety of student backgrounds (at Penn State Great Valley Campus), some students have had no prior exposure to the MATLAB which made it difficult for them to finish all the assignments. Using user interface controls will reduce this problem but at the same time will place more burden on the instructor. The general student reaction to the use of and MATLAB has been very positive. References [1] Martin, ., Azemi, A., Hewett, D., Schneider,., “PSpice in Electrical Engineering Laboratories,” Proceedings of the ASEE Annual Conference, 1992, pp. 13071308. [2] Andrews, D., Azemi, A., Charlton, S., Yaz, E.,“Computer Simulation in Electrical Engineering Education,” Proceedings of the ASEE GulfSouthwest Section Meeting, 1994, pp. 7782. [3]Azemi, A., Yaz, E., “Utilizing SIMULINK and MATLAB in a Graduate Nonlinear Systems Analysis Course,” Proc. of the 26th Frontier in Education Conference, vol. 1, 1996, pp. 595599, Salt Lake, UT. [4]Azemi, A., Stook, C., “Utilizing MATLAB in Undergraduate Electric Circuits Courses,” Proc. Of the 26th Frontier in Education Conference, vol. 1,1996, pp. 599603, Salt Lake, UT. [5] Yaz, E., Azemi, A., “Utilizing MATLAB in two Graduate Electrical Engineering Courses,” Proceedings of the 25th Frontiers in Education Conference, 1995, pp. . [6] Dorf, R., Bishop, . Modern Control Systems,s