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Unformatted text preview: 16 CONTROL FUNDAMENTALS 16.1 Introduction 16.1.1 Plants, Inputs, and Outputs Controller design is about creating dynamic systems that behave in useful ways. Many target systems are physical; we employ controllers to steer ships, ﬂy jets, position electric motors and hydraulic actuators, and distill alcohol. Controllers are also applied in macro- economics and many other important, non-physical systems. It is the fundamental concept of controller design that a set of input variables acts through a given “plant” to create an output. Feedback control then uses sensed plant outputs to apply corrective inputs: Plant Inputs Outputs Sensors Jet aircraft elevator, rudder, etc. altitude, hdg altimeter, GPS Marine vessel rudder angle heading gyrocompass Hydraulic robot valve position tip position joint angle U.S. economy fed interest rate, etc. prosperity inﬂation, M1 Nuclear reactor cooling, neutron ﬂux power level temp., pressure (Continued on next page) 16.2 Representing Linear Systems 77 16.1.2 The Need for Modeling Effective control system design usually benefits from an accurate model of the plant, although it must be noted that many industrial controllers can be tuned up satisfactorily with no knowledge of the plant. Ziegler and Nichols, for example, developed a general recipe which we detail later. In any event, plant models simply do not match real-world systems exactly; we can only hope to capture the basic components in the form of differential or integro- differential equations. Beyond prediction of plant behavior based on physics, the process of system identification generates a plant model from data. The process is often problematic, however, since the measured response could be corrupted by sensor noise or physical disturbances in the system which cause it to behave in unpredictable ways. At some frequency high enough, most systems exhibit effects that are diﬃcult to model or reproduce, and this is a limit to controller performance. 16.1.3 Nonlinear Control The bulk of this subject is taught using the tools of linear systems analysis. The main reason for this restriction is that nonlinear systems are diﬃcult to model, diﬃcult to design controllers for, and diﬃcult overall! Within the paradigm of linear systems, there are many sets of powerful tools available. The reader interested in nonlinear control is referred to the book by Slotine and Li (1991). 16.2 Representing Linear Systems Except for the most heuristic methods of tuning up simple systems, control system design depends on a model of the plant. The transfer function description of linear systems has already been described in the discussion of the Laplace transform. The state-space form is an entirely equivalent time-domain representation that makes a clean extension to systems with multiple...
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This note was uploaded on 02/27/2012 for the course MECHANICAL 2.154 taught by Professor Michaeltriantafyllou during the Fall '04 term at MIT.
- Fall '04