Design method of PID controllers for stabilizing single-input single-output multiple-time-lag system

Abstract

A design method of PID controllers for stabilizing a single-input single-output multiple-time-lag system comprises the following steps: firstly, an industrial control system is used for identifying a papermaking production process with low-concentration paper pulp delivered into a headbox serving as input and the thickness of manufactured finished product paper serving as output, so that a multiple-time-lag model of a controlled system is provided; secondly, a unit feedback control mechanism is adopted, a stabilization set of all the PID controllers which can guarantee stability of a closed-loop system is calculated in combination with a modified Nyquist stability criterion and a generalized Hermite theorem on the basis of model parameters of a controlled target, a frequency upper bound omega* which is large enough is selected first, the largest permitted stability range of a proportional gain kp is calculated, then, the largest permitted stability range of the proportional gain kp is traversed, a stability range of (kd, ki) is provided for each transversal point kp according to necessary and sufficient conditions for stabilizing the multiple-time-lag system, and therefore a stable set of (kp, ki, kd) is obtained. According to the design method of the PID controllers for stabilizing the single-input single-output multiple-time-lag system, the controller target can keep running in a stable state as long as control parameters are selected from the obtained stable set of the PID controllers and a PID control program is executed, and stable control over the system is realized.

Description

technical field [0001] The invention relates to a method used in the technical field of process control, in particular to a proportional-integral-derivative (PID) controller design method used in a papermaking production process control system. Background technique [0002] The papermaking process is a complex mass and heat transfer process, which is characterized by uncertainty, incomplete state, strong coupling between parameters, pure hysteresis and nonlinear characteristics, etc., and is a complex multivariable control object. In the papermaking process, in addition to the conventional thermal parameters that need to be tested and controlled, there are also some special and important parameters that need to be tested and controlled. For example, moisture is an important parameter in the papermaking process: if the moisture of the paper is too high or too low, the fluctuation of moisture will be large, which will reduce the tensile force and tension of the paper and cause...

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Problems solved by technology

[0005] 1. For linear time-delay systems, the optimal controllers obtained by using these methods are all rational structures, and often have a higher order, generally the same as the order of the controlled object, or even higher, so the implementation cost of the controller High, difficult to use in the paper industry;

[0006] 2. The traditional control method is based on the mathematical model describing the actual control object, but these models are generally obtained by using some approximation or simplification methods, so it is inevitable that there will be errors with the corresponding actual system

However, due to the existence of the approximation error of the time-delay term, adopting such a low-order controller design method may lead to instability of the closed-loop system, especially for a system with a large time-delay, the approximation error will be larger;

[0008] 4. Although there are some methods that can directly determine the stable set of PID controllers for time-delay systems, such as the singular frequency-based stable domain solution method proposed by Norbert H. (All stabilizing PID controllers for time delay systems, Automatica, 2009, 45( 11):2678-2684), but so far it is limited to the controlled object with a single time delay, and cannot be applied to the complex controlled object with multiple time delays

Therefore, the stability analysis and design of the controlled object with multiple time delays is very difficult

Generally, when performing model identification, such complex controlled objects are identified as a linear model with a single time delay, resulting in a large model error

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