Abstract
An improved analytical tuning rule of a Proportional-Integral-Derivative (PID) controller for integrating systems with time delay is proposed using the direct synthesis method and multiple dominant pole-placement approach. Different from the traditional multiple dominant pole-placement method, the desired characteristic equation is obtained by placing the third-order dominant poles at −1/λ and placing the second-order non-dominant poles at −5/λ (λ is the tuning parameter). According to root locus theory, the third-order dominant poles and the second-order non-dominant poles are nearly symmetrically located at the two sides of the fifth-order dominant poles. This makes the third-order dominant poles closer to the imaginary axis than the fifth-order dominant poles, which means that, possibly, better performances can be achieved. Analytical formulas of a PID controller with a lead-lag filter are derived. Simple tuning rules are also given to achieve the desired robustness, which is measured by the maximum sensitivity (Ms) value. The proposed method can achieve better performances and maintain better performances when there exist parameters’ perturbation compared with other methods. Simulations for various integrating processes as well as the nonlinear continuous stirred tank reactor (CSTR) model illustrate the applicability and effectiveness of the proposed method.
Highlights
Integrating systems have become a study hot topic in terms of automatic control.These types of systems have at least one pole at the origin, which is regarded as the characterization of the open-loop instability [1]
The following integral systems can be divided into two types: a pure integral plus time delay system (PIPTD), a double integral plus time delay system (DIPTD), a stable first-order plus integral time delay system (FOPTDI) and an unstable first-order integral time delay system (UFOPTD) [3]
Inspired by the method of Anil [37], this paper provides a straightforward analytical adjusting rule of a robust PID controller for integral time delay systems based on the modified multiple dominant pole-placement method
Summary
Integrating systems have become a study hot topic in terms of automatic control. On the basis of comparing the expected characteristic equation with the closed-loop characteristic equation, the PID tuning rules of various forms of time delay integral systems are given in Ch. Anil [37]. Literature review shows that many PID parameter tuning methods are proposed for integral systems with time delay, there is still scope for improving performance and robustness. Inspired by the method of Anil [37], this paper provides a straightforward analytical adjusting rule of a robust PID controller for integral time delay systems based on the modified multiple dominant pole-placement method. The required characteristic equations are derived from the MDP method, which divides all the poles into the third-order dominant poles and the second-order non-dominant poles based on the idea of placing as many closed-loop poles as possible in the controller parameters.
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