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By Yu, Cheng-Ching

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Additional info for Autotuning of PID Controllers [electronic resource]: A Relay Feedback Approach

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2 always produce a monotonic response, where, at t = 0 , the response from the model starts at the lowermost (or uppermost) point (A or B) and, at t = Pu / 2 , it ends at the other extreme point (B or C). 10. e. n  3 ). 10. 10 shows the correctness of the derived mathematical models. If the relay height is other than unity, then the model for the relay output response will be just multiplied by actual value of relay height h . 4 Conclusion In this chapter the relay feedback test is introduced and the steps required to perform the experiment are also given.

For example, if the K u and  u in the previous example are close to the true values, then we will not have errors in the steady state gains and time constant for model 1. 16 can deviate significantly from the true system parameters. This implies the observed ultimate period Pˆu and the computed ultimate gain are not the true values. In order to have a better approximation of the transfer function, fundamental analysis of the relay feedback system is necessary. First, one would like to know what the period of oscillation from the relay feedback experiment really represents.

3. Design the IMC controller as Gc = G 1 F . g. F = 1/( s + 1) n .  is the user-specified tuning parameter. 4. Tranform the IMC controller Gc(s) into a controller K(s) in the conventional  ). g. e. K (s ) = Gc /(1  GG c The IMC approach offers a systematic way to identify the controller structure, and, probably more importantly, it can also be used to derive tuning parameters for the PID controller [8], usually known as IMC-PID tunings. g. g. imaging high-order derivatives of measurement noises.

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