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Unformatted text preview: 4 Lab 1: PID Control 4.1 Outline In this experiment you will identify and design controllers for a “black box” with an unknown second order transfer function. The physical system is very close to linear as it is a simple op-amp based filter. By studying this you will be able to experimentally investigate system characteristics without being too concerned about the differences between your theoretical and experimental systems. The ugly aspects of reality will occur in later experiments. The first part of the experiment is spent in identifying your particular black box. Read Section 2.8 of the text before coming to the lab as that discusses some of the possible approaches to this problem. We will assume that the plants built into the box are of the form, P ( s ) = αω 2 n s 2 + 2 ζωs + ω 2 n . In the second part you will design and tune PID controllers to achieve various performance characteristics. A comparison between the observed responses and Matlab simulations will be useful. While doing this experiment bear in mind the possibility that the boxes might contain slightly more than second order filters. How would you know? Do you observe any characteristics that suggest perhaps a higher order filter or some nonlinearity? 4.2 Equipment Notes The black boxes each implement two transfer functions. The power connec- tions are: red (+12 volts), black (common), purple (-12 volts). Turn the power to the box off when making connections. 23 4.3 Experimental Procedure: Week 1 4.3.1 Prelab 1. List all of the characteristics of a second order system that you can measure experimentally. Describe how these quantities can be mea-measure experimentally....
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- Spring '07