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Session 1448

Teaching State Variable Feedback to Technology Students Using MATLAB and SIMULINK

Kathleen A.K. Ossman, Ph.D. University of Cincinnati

I. Introduction

This paper describes a course and laboratory in State Variable Feedback developed as a t echnical elective for students in the Electrical and Computer Engineering Technology (ECET) program at the University of Cincinnati. Students pursuing the EET degree are required to take courses in Signals and Systems and Feedback Controller Design. They learn to design lead, lag, and proportional-integral-derivative controllers (both analog and digital) for single-input single- output systems. The technical elective in State Variable Feedback allows students to explore the added benefits of a state variable controller when applied to multi-input multi-output systems and/or systems where constraints are imposed on the controller (i.e., tracking in minimum time or tracking with minimum control effort expended). In the past, a course in State Variable Feedback would have been too mathematically rigorous to include in a technology program. However, with the use of MATLAB and SIMULINK1, students are able to design state variable feedback controllers and simulate the system responses without getting caught up in complicated matrix manipulations and integral calculations.

II. Modeling Systems

The course begins with modeling of several types of systems including electrical circuits, mechanical translational systems, motors, a robot gripper, an inverted pendulum on a cart, and pitch control for a helicopter using both differential equations and state variable models 2,3. Students have been exposed to system modeling using differential equations and transfer functions in the pre-requisite courses, but state equations are an entirely new concept. In course assignments and in lab, students build models of systems in SIMULINK using both transfer function blocks and state space blocks in order to better understand the similarities between these system models. In MATLAB, the functions ss2tf and tf2ss are introduced as tools for switching between the two types of system models for single-input-single-output (SISO) systems.

As an example, one of the systems explored in lab is the two-mass system shown in Figure 1.

y1(t) y 2(t)

f(t) Spring, K Applied Force

Rolling Friction = B (constant) Figure 1: Two-mass System

Proceedings of the 2002 American Society for Engineering Education Annual Conference & Exposition Copyright © 2002, American Society for Engineering Education

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Ossman, K. (2002, June), Teaching State Variable Feedback To Technology Students Using Matlab And Simulink Paper presented at 2002 Annual Conference, Montreal, Canada. 10.18260/1-2--11014