General Algorithm for Autotuning of Proportional-Integral-Derivative Controllers by the Relay Feedback Test

Abstract

Generalized algorithms are of great importance because they eliminate the need to switch between methods and strategies for various cases; in fact, the same structure is useful after little modification. In this paper we introduce a scheme for modeling and controlling self-regulating systems. The purpose is to achieve a general but not optimal proportional-integralderivative (PID) autotuner for firstand second-order transfer functions with or without time delays. A modeling algorithm based on a single run of the relay feedback test is proposed. The general procedure can be applied to derive up to five unknown parameters for various cases. After the relay parameters are assigned, there is no need for a human operator; this feature as well as a short test time is the major advantage of the modeling phase of autotuning. A generalization of direct synthesis for disturbance rejection is proposed for tuning a PID controller. The algorithm is modified to a 2 degrees of freedom structure so it can provide a good set-point response and controller effort as well. The advantage of the structure as a general method is the need for only one design parameter related to performance and robustness characteristics. Systematic ways to choose the design parameter will eliminate the need for a human operator, which makes the scheme suitable for the tuning phase of autotuning. Simulation examples for the identification phase show the accuracy of the identified models. Additionally, illustrative simulations show the effectiveness of the generalized tuning method for low-order transfer functions. Also, examples clarify the priority of the method to the well-known tuning method, internal model control, with the same degree of robustness. The autotuner is a general, unified structure that unlike the previous methods does not alter modeling and tuning methods for various cases of low-order transfer functions.

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“…Giả sử, điều kiện thiết lập của động cơ là bằng không, hàm truyền mô tả mối quan hệ giữa vị trí góc của động cơ (θ) và điện áp điều khiển (V) được thể hiện bằng phương trình dưới đây [12] (2) Trong đó, e(t) = y r (t) -y(t), e(t) -là tín hiệu vào, u(t) -là tín hiệu ra ; K p , τ I , τ D -lần lượt là các hằng số tỷ lệ, hằng số thời gian tích phân, và hằng số thời gian vi phân. Đã có nhiều nghiên cứu trong vấn đề tự chỉnh các tham số của bộ điều khiển PID để hệ thống thu được đáp ứng mong muốn, một trong các phương pháp phổ biến được sử dụng là phương pháp rơle [13][14][15][16].…”