RU2568386C2 - Method for self-tuning of pid control system - Google Patents

Abstract

FIELD: radio engineering, communication.

SUBSTANCE: disclosed is a method for self-tuning of a PID control system, based on transmitting a pilot signal to a control object, determining parameters of a model of the control object based on measured data of a transient process and determining control settings based on parameters of the model, wherein the control object is approximated with a first-order aperiodic link with delay, and self-tuning is performed in two steps: at the first step, transmitting step action to the control object, and at the second step, including two-position control and then determining PID control settings, which are optimal on the integral criterion of the minimum of the modulus of the control error.

EFFECT: high efficiency of self-tuning and improved quality of controlling inertial objects.

6 dwg

Description

FIELD OF THE INVENTION

The invention relates to the field of control of continuous technological processes, in particular inertial objects, using computing hardware and can be used in chemical, petrochemical and other industries.

State of the art

There is a method of self-tuning an object control system based on applying a control action to an object in the form of a non-periodic test signal, determining the parameters of the object model based on its reaction, determining custom parameters based on the transfer functions of the object models and the reference system according to the overshoot criterion with minimal system complexity (RU 2304298 C2, 10/05/2005, G05B 13/00).

The known method as applied to inertial objects does not provide the required efficiency of self-tuning and an acceptable quality of regulation, since it uses only a non-periodic test signal, it provides for a difficult-to-practical configuration scheme for matching the object model and the reference system, and the criterion used is ineffective for inertial objects.

There is also a known method of automatically adjusting the control system based on the use of on-off regulation with adjusting the values of the amplitude of self-oscillations in different auto-tuning cycles, determining the moment of completion of the transition process to achieve equality of the sum of errors at adjacent intervals and equal durations of these intervals, determining the controller settings from the measured amplitude and self-oscillation frequency (RU 2002289 C1, 07.26.89, G05B 13/00).

The known method as applied to inertial objects does not provide the required efficiency of self-tuning and an acceptable quality of regulation, since the theoretical approach used in the method to implement frequency methods for analyzing regulation systems in practice is difficult.

Closest to the technical nature of the present invention is a method of optimal automatic tuning of the control system, based on the filing on the control object (OS) of a step test signal with adjustable amplitude and polarity, determining the characteristic points of the transition process, determining using the auxiliary functions from these points settings controller with the criterion of maximum degree of stability (RU 2243584 C2, 03.24.2003, G05B 13/00) (prototype).

The disadvantage of this method is the lack of efficiency of self-tuning and low quality regulation of inertial objects due to the low accuracy of determining the parameters used in the method of characteristic points and the complexity of the formulas used, as well as inadequacy for the inertial objects of the applied structure of the model.

Disclosure of invention

The purpose of the invention is improving the efficiency of self-tuning and improving the quality of regulation of inertial objects.

This goal is achieved by the fact that, in contrast to the known technical solution, in the proposed method, the control object (OS) is approximated by an aperiodic link of the first order with delay

Self-tuning is carried out in two stages:

, по длительности последнего цикла автоколебаний и величине L определяют постоянную времени Т, а настройки определяют по интегральному критерию минимума модуля ошибки регулирования.at the first stage, a stepwise effect on the opamp is applied, the end of the transition process is determined by decreasing the derivative of the op amp output signal below a predetermined value and the gain A is determined, at the second stage they include on-off regulation, maintain two full cycles of the system’s self-oscillations, the value of the ratio is determined by the amplitude of the last self-oscillation cycle $$L=\frac{\tau }{T}$$

, according to the duration of the last cycle of self-oscillations and the value of L, the time constant T is determined, and the settings are determined by the integral criterion of the minimum modulus of the control error.

Description of drawings

The implementation and features of the proposed method are illustrated by figures.

Figure 1. Feedback control scheme.

Figure 2. Acceleration curves of the object and model.

Figure 3. Self-tuning cycle.

Figure 4. Dependences of the amplitude of self-oscillations

Figure 5. Dependences of the duration of a cycle of self-oscillations.

6. Dependencies of optimal settings.

The implementation of the invention

The feedback control scheme considered in the proposed method is presented in figure 1.

The PID control algorithm is written as follows:

$$U=K_{\mathrm{ABOUT}}(K_{P}E+\frac{\mathrm{one}}{T_{\mathrm{AND}}}{\displaystyle \int Edt+T_D\frac{dE}{dt}})$$

where E = X ^ass -X - regulation error.

In the proposed method as an approximating model of OS

a first-order aperiodic link with delay is used, having the following transfer function:

where A is the gain;

T is the time constant;

τ is the time of “pure” delay.

Such an approximation allows us to describe a wide range of inertial objects when the delay τ is not actual, but equivalent.

Figure 2 shows the transient process on the stepwise input impact for a complex inertial object (line 1) and its approximating model (line 2).

The equivalent delay, which significantly complicates the operation of the regulation system of such an object, provides equivalent characteristics of a closed system. The method is based on the results of a study based on digital modeling and optimization, since analytical solutions for systems with delay are extremely difficult. In the proposed method of self-tuning, complex use is made of both a stepwise test action on an object and the implementation of a self-oscillation mode.

At the 1st stage of self-tuning, a stepwise action is applied to the control channel U with an open control system (see Fig. 3).

The transition end time t _lane is determined by the fulfillment of condition (3) (achievement of the derivative of the OA output signal of the specified minimum value D _min ):

At the 1st stage of self-tuning, only the gain A is determined:

Next, the transition to the 2nd stage of self-tuning. At time t _{lane, a} closed two-position control circuit is switched on according to the following algorithm:

The system goes into self-oscillation mode (figure 3). The calculations and simulations showed that the steady state mode of self-oscillations in this formulation is achieved very quickly, therefore, two complete cycles of self-oscillations are sufficient to determine the model parameters.

. Амплитуда установившихся автоколебаний пропорциональна величине L (фиг.4).For an object with a transfer function (2), the main characteristics are determined depending on the ratio $$L=\frac{\tau }{T}$$

. The amplitude of steady-state self-oscillations is proportional to the value of L (Fig. 4).

Given this dependence, the value of L is determined from the measured amplitude b _{c of the} last (second) cycle of self-oscillations (with averaging of the amplitudes of the positive and negative half-waves to take into account possible non-linearities of the OS):

и ранее определенному значению L. Эквивалентное запаздывание легко определяется как τ=LT.The duration of the self-oscillation cycle is proportional to the value of L and also proportional to the value of the time constant T (Fig. 5). Given this dependence, the value of T is determined from the measured cycle time $$t\frac{c}{}$$$$\frac{}{2}$$

and the previously determined value of L. Equivalent delay is easily determined as τ = LT.

Thus, the parameters of the approximating equivalent OS model are determined: A, τ, T. Using these parameters, you can determine the PID control settings that are optimal by the criterion of the minimum module of the digital control error:

where h is the discreteness of regulation;

n, N - are selected in proportion to m;

α> 0.

.The dependencies by which the optimal settings K _p , T _and T _{d of the} controller (1) are determined by the criterion (7) are shown in FIG. 6. The gain of the controller K _about is defined as $$K_o=\frac{\mathrm{one}}{A}$$

.

Criterion (6) provides a sufficiently high speed with a small overshoot. The surface of this criterion in the coordinate system of the proportional, integral, and differential components of the PID control (K _p , T _and T _d ) is quite shallow in the optimum region, which facilitates the adjustment of the controller. In addition, the proposed method of self-tuning is quite simple to implement.

To implement the method, for example, the BAZIS-21.2PP control controller or another from the BASIS ^® series manufactured by Ecoresource CJSC can be used. Implementation of the proposed method in commercially available controllers of the BASIS ^® series is scheduled for 2014.

Claims (1)

The method of self-tuning the PID control system based on the supply of a test signal to the control object (OS), determining the parameters of the OS model based on the measured transient data and determining the control settings from the model parameters, characterized in that in order to increase the efficiency of self-tuning and improve the quality of regulation inertial objects, op amps are approximated by an aperiodic link of the first order with delay

Self-tuning is carried out in two stages:
at the first stage, a stepwise effect on the opamp is applied, the end of the transition process is determined by decreasing the derivative of the op amp output signal below a predetermined value and the gain A is determined, at the second stage they include on-off regulation, maintain two full cycles of the system’s self-oscillations, the value of the ratio is determined by the amplitude of the last self-oscillation cycle

the duration of the last cycle of self-oscillations and the value of L determine the time constant T, the delay time is determined as τ = LT, then using A is the gain, τ is the delay time and T is the time constant determine the PID control settings that are optimal by the integral criterion of the minimum error modulus regulation.

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