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Unformatted text preview: Laboratory Assignment 6 System Identification using frequency response measurements 2.737 Mechatronics Dept. of Mechanical Engineering Massachusetts Institute of Technology Cambridge, MA-02139 1 Purpose System Identification Use of the HP3562A dynamic signal analyzer 2 Equipment HP3562A dynamic signal analyzer Protoboard with RC filter 3 Introduction There are two approaches to obtaining models of the physical systems that we aim to control : Theoretical models using physical laws Experimental models Theoretical models are very useful in that they provide you with a physical understanding of the operation of the system. However, theoretical models are usually obtained by recourse to idealization of actual system behavior. Such models prove to be very good at low frequencies and usually break down at higher frequencies. In such cases, recourse is usually made to experimental models of the plant. Also, most often before a final control design is made, it is prudent to verify the theoretical model with experimental data. Theoretical modeling is not to be belittled. In fact a sound understanding of the theoretical principles can lead to good experimental techniques and aid 1 in obtaining good models of the system. Modeling of most physical systems is done by systematic application of physical laws such as Newton’s laws of motion, Kirchoff’s laws, etc. The process of obtaining models of physical systems using experimental techniques is termed system identification. System identification is a very important task and has matured into an impor tant research area in its own right. This is all the more important in the current day scenario where a given system has to perform consistently in spite of changes in parameters and environment. In such cases the controller is tuned continuously to adapt to changes in operating parameters/environment leading to adaptive control. While, we do not want to get involved in the finer aspects of system identification, we want to provide you with a basic understanding of what system identification entails and what the common approaches to system identification are. 4 System Identification System identification is usually performed by injecting known signals into the plant to be charac terized (measured) and measuring the output. This leads to the input/output characteristics or the transfer function of the plant. Experimental data for generating such a model/transfer function are usually of four kinds : Transient (Step, Impulse etc.) Sinusoids of various frequencies and amplitudes Stochastic signals - from normal closed loop control signals etc. Pseudorandom (white) noise Each of these kinds of data has its own advantages and disadvantages. We have already done the transient and the frequency response measurements in Lab 4 when we measured the inductance of the transformer....
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- Spring '99
- Mechatronics, Low-pass filter, signal analyzer, Mechatronics Dept. of Mechanical Engineering Massachusetts Institute of Technology Cambridge