CN111240192B - Smooth switching function-based target value control method for transition process - Google Patents

Smooth switching function-based target value control method for transition process Download PDF

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CN111240192B
CN111240192B CN201811449010.8A CN201811449010A CN111240192B CN 111240192 B CN111240192 B CN 111240192B CN 201811449010 A CN201811449010 A CN 201811449010A CN 111240192 B CN111240192 B CN 111240192B
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switching function
smooth switching
transition process
target value
function
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CN111240192A (en
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姜志斌
刘铁军
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Shenyang Institute of Automation of CAS
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance

Abstract

The invention relates to a smooth switching function-based control method for a target value in a transition process, which comprises the following steps: selecting the upper limit and the lower limit of the independent variable of the smooth switching function according to the controlled object transition process adjusting time; then according to the requirements of overshoot and the adjustment time in the transition process, selecting a proper smooth switching function from three types of smooth switching functions such as power function type, polynomial type and trigonometric function type; and finally, calculating a target value or a control quantity of the controller in the transition process according to the smooth switching function. And technical guarantee is provided for realizing that the actual value can track the target value quickly, smoothly and stably in the transition process.

Description

Smooth switching function-based target value control method for transition process
Technical Field
The invention relates to the technical field of control, in particular to a transition process target value control method based on a smooth switching function.
Background
The basic requirements of a control system mainly include rapidity, accuracy and stability, and the control process of the control system is generally divided into a transition process and a steady-state process. The performance of the steady-state process is directly influenced by the quality of the adjustment of the transition process, so that the adjustment of the transition process is very important to the whole control process, and the method has practical significance and application value for improving the performance of the control system.
In the past, people pay more attention to the steady-state process, but no matter in the transition process or the steady-state process, the target value is always unchanged, so that the problems of overlarge overshoot, increased adjusting time and the like in the transition process are easily caused. If the given target value is gradually increased to the final target value along with a certain rule in the transition process, the error between the target value and the actual value is reduced, so that the system is easier to follow the target value, the overshoot of the transition process is obviously smaller, and the steady-state process is more quickly started.
Therefore, a simple and practical control method for the target value in the transition process is researched, and the practical control problem which needs to be solved urgently is solved by solving the defects that overshoot is easy to occur or the adjusting time is too long in the control process.
Disclosure of Invention
Based on the above background, the present invention provides a smooth switching function-based control method for a target value of a transition process, which can achieve a fast, smooth and small overshoot transition process of a control system, and improve the rapidity and stability of the control system.
The technical scheme adopted by the invention for realizing the purpose is as follows: a transition process target value control method based on a smooth switching function comprises the following steps:
determining the upper limit and the lower limit of the independent variable of the smooth switching function according to the adjustment time of the transition process;
selecting a smooth switching function according to the overshoot and the adjustment time in the transition process;
and calculating a target value of the transition process or a control quantity of the controller according to the smooth switching function.
The smooth switching function is any one of a power function class, a polynomial class and a trigonometric function class.
The power function class takes the form:
Figure BDA0001884055180000021
Figure BDA0001884055180000022
where x is the argument of the smooth switching function f (x), t+And t-Respectively representing the upper and lower limits of the smooth switching function, n being a positive even number not greater than 4.
The polynomial class takes the form:
Figure BDA0001884055180000023
where x is the argument of the smooth switching function f (x), t+And t-Respectively representing the upper limit and the lower limit of the smooth switching function, and n is a positive even number.
The trigonometric function class takes the form:
Figure BDA0001884055180000024
Figure BDA0001884055180000025
where x is the argument of the smooth switching function f (x), t+And t-Respectively representing the upper and lower limits of the smooth handover function.
The argument of the smooth switching function is the transition process adjustment time.
The target value of the transition process is calculated according to the smooth switching function, and the following form is adopted:
R(x)＝Rstart+(Rend-Rstart)f(x)
wherein R isstartIs a preset target value at the beginning of the transition, RendIs a preset target value at the end of the transition, r (x) is the target value for the transition, and f (x) is the smooth switching function.
The calculating the control quantity of the controller according to the smooth switching function comprises the following steps: the control amount for calculating the output for two different controllers is calculated in the following form:
u(x)＝f(x)u1(x)+(1-f(x))u2(x)
wherein u is1(x) Is the control quantity, u, of the calculation output of the known first controller2(x) Is the control quantity calculated and output by the known second controller, u (x) is the control quantity when the two controllers work together, and f (x) is a smooth switching function.
The invention has the following beneficial effects and advantages:
1. the invention provides a target value control method for three types of transition processes, such as power function type, polynomial type, trigonometric function type and the like, and provides a solution for realizing the requirement of smooth control of the transition process.
2. The invention is implemented by adjusting the upper limit t of the smooth switching function only+And a lower limit t_The control performance of the controller can be adjusted, the adjusting parameters are few, and the method can be conveniently and quickly applied to actual control engineering.
Drawings
FIG. 1 is a schematic diagram of an incremental smooth handover function of the present invention;
FIG. 2 is a schematic diagram of a decreasing smooth switching function according to the present invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples.
The invention relates to a smooth switching function-based control method for a target value in a transition process, which comprises the following steps:
the first step is as follows: according to the characteristic that the controlled object is executed fast or slow or the system state changes fast or slow, the upper limit and the lower limit of the independent variable of the smooth switching function, namely t, are selected+And t-。
As shown in fig. 1 and 2, the abscissa t+＝0.3，t-The ordinate is the value of the smooth switching function f (x) at 0.
The second step is that: according to the performance requirement of the control system and the characteristics of the smooth switching function, an appropriate smooth switching function is selected from three types of smooth switching functions such as a power function type, a polynomial type and a trigonometric function type. The control system for measuring overshoot and the adjustment time in the transition process are basically contradictory control requirements, and when the emphasis is on small overshoot and the adjustment time can be slightly longer, a smooth switching function with smaller curvature, such as y, can be selected1And y4(ii) a When the emphasis on short tuning time and slightly larger overshoot are used, a smooth switching function with larger curvature, such as y, can be selected3And y5(ii) a When the amount of emphasis on overshoot is small and the settling time is short, a smooth switching function with moderate curvature, such as y, can be selected2。
As shown in fig. 1 and 2:
Figure BDA0001884055180000041
wherein, t+0.3 and t -0 denotes the upper and lower limits of the smooth switching function, respectively, and n is 2.
Figure BDA0001884055180000042
Wherein, t+0.3 and t -0 denotes the upper and lower limits of the smooth switching function, respectively, and n is 2.
Figure BDA0001884055180000043
Wherein, t+0.3 and t -0 denotes the upper and lower limits of the smooth switching function, respectively, and n is 2.
Figure BDA0001884055180000044
Wherein, t+0.3 and t -0 denotes the upper and lower limits of the smooth handover function, respectively.
Figure BDA0001884055180000045
Wherein, t+0.3 and t -0 denotes the upper and lower limits of the smooth handover function, respectively.
The third step: for calculating the control target value and the control quantity of the controller in the transition process, the following two forms are adopted for calculation:
1) calculation of the target value:
R(x)＝Rstart+(Rend-Rstart)f(x) (1)
wherein R isstartIs a preset target value at the beginning of the transition, RendIs a preset target value at the end of the transition, r (x) is a target value calculated during the transition, and f (x) is a smooth switching function.
2) Calculation of control amount of controller:
when the control quantity calculated by two different control methods acts on the controlled object, the smooth switching function is used for obtaining the control quantity in the switching action process of the two control methods, and the following form is adopted:
u(x)＝f(x)u1(x)+(1-f(x))u2(x) (2)
wherein u is1(x) Is the control quantity, u, calculated by the first control method2(x) Is the control quantity calculated by the second control method, u (x) is the control quantity when the two control methods work together, and f (x) is the smooth switching function.

Claims (2)

1. A transition process target value control method based on a smooth switching function is characterized by comprising the following steps:
determining the upper limit and the lower limit of the independent variable of the smooth switching function according to the adjustment time of the transition process;
selecting a smooth switching function according to the overshoot and the adjustment time in the transition process;
calculating a target value of the transition process or a control quantity of the controller according to the smooth switching function;
the smooth switching function is any one of a power function class, a polynomial class and a trigonometric function class;
the power function class takes the form:
Figure FDA0003412817190000011
or
Figure FDA0003412817190000012
Figure FDA0003412817190000013
Or
Figure FDA0003412817190000014
Where x is the argument of the smooth switching function f (x), t+And t-Respectively representing the upper limit and the lower limit of the smooth switching function, and taking a positive even number not greater than 4 as n;
the polynomial class takes the form:
Figure FDA0003412817190000015
or
Figure FDA0003412817190000016
Where x is the argument of the smooth switching function f (x), t+And t-Respectively representing the upper limit and the lower limit of the smooth switching function, wherein n is a positive even number;
the trigonometric function class takes the form:
Figure FDA0003412817190000021
or
Figure FDA0003412817190000022
Figure FDA0003412817190000023
Or
Figure FDA0003412817190000024
Where x is the argument of the smooth switching function f (x), t+And t-Respectively representing the upper limit and the lower limit of the smooth switching function;
the target value of the transition process is calculated according to the smooth switching function, and the following form is adopted:
R(x)＝Rstart+(Rend-Rstart)f(x) (1)
wherein R isstartIs a preset target value at the beginning of the transition, RendIs a preset target value at the end of the transition process, r (x) is the target value of the transition process, f (x) is the smooth handover function;
the calculating the control quantity of the controller according to the smooth switching function comprises the following steps: the control amount for calculating the output for two different controllers is calculated in the following form:
u(x)＝f(x)u1(x)+(1-f(x))u2(x) (2)
wherein u is1(x) Is the control quantity, u, of the calculation output of the known first controller2(x) Is the control quantity calculated and output by the known second controller, u (x) is the control quantity when the two controllers work together, and f (x) is a smooth switching function.
2. A smooth switching function based transient target value control method as claimed in any one of claim 1, wherein the argument of said smooth switching function is the transient adjustment time.
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