Process frequency response estimation from relay feedback

Department of Electrical Engineering, National University of Singapore, Singapore 119260
Control Engineering Practice (Impact Factor: 1.91). 09/1997; 5(9):1293-1302. DOI: 10.1016/S0967-0661(97)84368-7

ABSTRACT In this paper, a method for process frequency response identification is proposed, which can identify multiple points on process frequency response from a single relay feedback test. The process input and output transients resulting from a relay feedback cannot be directly converted to the frequency domain to obtain a process frequency response using FFT. A decay exponential is then proposed to modify the process input and output, so that the process frequency response can be identified with the help of FFT. Real-time testing of the method on various processes gives quite accurate process frequency responses, especially in the frequency range [0, ωc], which is important for control design and process modelling. The method inherits and extends the advantages of the original relay auto-tuning technique. It can be easily applied to PID auto-tuning and to transfer function modelling.

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    ABSTRACT: The well-known on/off relay-feedback identification test suffers from two imperfections. First, the parameters estimation does not bring a sufficient accuracy; second, a single test enables to quantify only two unknown model parameters. In this paper, two possible approaches dealing with these problems are attacked. Namely, the Autotune Variation Plus (ATV+) procedure introducing an additional artificial delay is utilized for a multiple-points model parameterization, and, the use of a saturation relay and a relay transient experiment with the Discrete Time Fourier Transform (DTFT) aid a better parameters estimation. The novelty of this contribution resides in that these methodologies are utilized with the combination with Linear Time-Invariant Time Delay Systems (LTI TDS) and their models. In our recent papers, theoretical aspects of the techniques were introduced and discussed, separately from other contributions dealing with a laboratory application of the saturation relay based approach. Both, theoretical and practical issues are summarized in this paper in a comprehensive presentation.
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    ABSTRACT: In the monograph PID Control algorithms for finite-dimensional, linear, continuous-time dynamical systems are studied. Mathematical models of such systems both using differential state equations and matrix transfer functions are presented and discussed. Next, PID control formulas are introduced and analysed. Special cases as P, PI and PD control algorithms are discussed and compared. The procedures for optimal control algorithms in closed-loop control systems are proposed and verified using numerical methods. Different types of feedback gains are proposed and compared using algebraic and optimization methods. For example static feedback with point delays is also considered. Design methods for multivariable PID control using Linear Matrix Inequality (LMI) approach are also presented and suboptimal control problems are solved. Pole placement problems are also stated and practically solved using algebraic methods. In the last chapter multivariable process identification is studied. Integral identification method is proposed both for single input – single output control systems with time delay and for multi input – multi output systems with multiple point delays in control variables. Finally, it should be pointed out, that the monograph contains many remarks and fruitful comments on PID control problems for linear systems. Moreover, it contains relationships to the similar results existing in the literature. The list of references has 229 positions, mainly published in the few last years. Summarizing the presented monograph contains comprehensive and detailed treatment of PID control for multivariable, continuous-time, finite-dimensional dynamical systems with constant coefficients. Both decentralized and centralized forms of PID controllers are discussed. Illustrative examples of different complexity are also presented.