EE 429
DIGITAL CONTROL SYSTEMS
Spring 2008
Laboratory #1: SampledData Transformation of an Analog Controller
Introduction
In this laboratory you will replace an analog phaselead 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 stepinvariance method. Using the data
acquisition system, you will be able to record and compare the stepresponses obtained using the analog controller
and each of the digital controllers.
Objectives
The objectives of Experiment #1 are to:
1 Approximate an analog phaselead 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
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentPart 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 discretetime model of the continuoustime 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.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 SCHIANO
 digital control, Tustin, ANALOG CONTROLLER, backward rectangular rule

Click to edit the document details