Lab_1_s08 - EE 429 DIGITAL CONTROL SYSTEMS Spring 2008...

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EE 429 DIGITAL CONTROL SYSTEMS Spring 2008 Laboratory #1: Sampled-Data Transformation of an Analog Controller Introduction In this laboratory you will replace an analog phase-lead controller for a magnet suspension system with a adat- sampled system . You will then consider several different techniques for approximating the analog controller with a data sampled control system. In particular, you will consider the backward rectangular rule, the trapezoidal rule (also known as the bilinear method or the Tustin transformation), and the step-invariance method. Using the data acquisition system, you will be able to record and compare the step-responses obtained using the analog controller and each of the digital controllers. Objectives The objectives of Experiment #1 are to: 1 Approximate an analog phase-lead controller with a data sampled control system using the following methods: (a) backward rectangular rule (b) trapezoidal rule (c) step invariance 2 Compare the performance of the analog controller to each of the digital controllers designed in part (1). 1
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Part I: Theoretical Background There are two general approaches for designing a digital control system. If the plant is already equipped with an analog controller, one method is to approximate the analog controller using a data sampled system. If the performance of the original analog controller is not acceptable, or if an analog controller is unavailable, then the second method is to directly design a digital control system based on a discrete-time model of the continuous-time process. The direct design of digital controllers will be considered in a later experiment. For now, we consider the ±rst approach. This leads us to the central question of this laboratory exercise: given the controller transfer function C ( s ), what discrete transfer function will have approximately the same characteristics? We consider two different methods for approximating an analog controller: Method 1: numerical integration Method 3: hold equivalence Each of these methods are now considered. Additional detail can be found in Chapter 11 of Phillips and Nagle.
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Lab_1_s08 - EE 429 DIGITAL CONTROL SYSTEMS Spring 2008...

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