CN113467243B - Hot pressing furnace temperature composite control method based on improved delay observer - Google Patents

Hot pressing furnace temperature composite control method based on improved delay observer Download PDF

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CN113467243B
CN113467243B CN202110767214.1A CN202110767214A CN113467243B CN 113467243 B CN113467243 B CN 113467243B CN 202110767214 A CN202110767214 A CN 202110767214A CN 113467243 B CN113467243 B CN 113467243B
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observer
delay
sliding mode
disturbance
output
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CN113467243A (en
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常雨芳
胡宇博
严怀成
张皓
黄文聪
张惠雯
王浩源
杨子潇
朱自铭
张凤顺
朱禛浩
潘风
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Hubei University of Technology
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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
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Abstract

The invention relates to the field of hot-pressing furnace temperature control, in particular to a hot-pressing furnace temperature composite control method based on an improved delay observer.

Description

Hot pressing furnace temperature composite control method based on improved delay observer
Technical Field
The invention relates to the field of temperature control of a hot-pressing furnace, in particular to a method for compensating system disturbance by establishing a delay observer and a disturbance observer and combining the delay observer and the disturbance observer, which effectively inhibits adverse effects of time delay on a system, thereby improving the stability (disturbance resistance) of the system under disturbance and meeting the performance requirements of the hot-pressing furnace on temperature control.
Background
The temperature control system is used as an important component of intelligent equipment and is widely applied to the industrial field. With the development of industrial and intelligent manufacturing technologies, the precision requirement on a temperature control system is further improved, and whether the hot-pressing furnace equipment can be stably and accurately maintained at the required temperature is always an important aspect of research in the field of hot-pressing furnace temperature control. The accuracy and stability of the temperature control of the hot-pressing furnace can be influenced by disturbance caused by environmental condition change, large delay of a system and uncertainty of large inertia. Therefore, it is necessary to improve the response speed and the anti-interference capability of the system.
PID control systems which are controlled in proportion (P), integral (I) and derivative (D) of the deviation are nowadays more common in temperature control strategies. The conventional PID has a simple and practical structure, but the field PID parameter setting is troublesome, is easy to be interfered by the outside, and has overlong adjusting time for the process with large delay. The precise temperature is an important factor influencing the working process of the equipment, and the temperature of the equipment is required to quickly and accurately reach a set value in many times. Therefore, domestic and foreign scholars continuously improve and perfect on the basis, for example, the PID control strategy based on the neural network is utilized to optimize the system temperature control, but the method is easy to cause control parameter setting errors. In order to improve the stability and the anti-interference capability of a temperature control system of the hot pressing furnace, a sliding mode controller is selected, the sliding mode observer is few in adjusting parameters, fast in response speed, insensitive to disturbance and strong in anti-interference capability.
But the control system still has a delay problem. The time-lag system is a system with signal delay in time transmission, and the change of a controlled object lags behind disturbance due to the lag, so that the system is easy to be unstable. In order to solve the time lag problem of the temperature control system of the autoclave, a Delay Observer (Delay Observer) is designed in the system. The output before the delay time tau second is observed by the delay observer and then fed back to the input, so that the problem of system time lag is solved.
In summary, the present invention provides a composite control method for the temperature of a hot pressing furnace based on an improved delay observer, that is, the required temperature requirement is quickly and accurately met through sliding mode control, and the delay observer is used to observe the required temperature
Figure BDA0003152248740000025
The output before the second solves the problem of time delay of the control system, and simultaneously compensates the external interference on the system by combining with a disturbance observer, thereby effectively improving the disturbance resistance of the system.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the method for designing the sliding mode controller by combining the delay observer and the disturbance observer is provided, so that the accuracy and the stability of the temperature control system of the hot-pressing furnace are improved, the temperature control system has good disturbance resistance, adverse effects caused by time delay can be effectively solved, and the performance requirement of the hot-pressing furnace on temperature control is better met.
The invention solves the technical problem by adopting the specific scheme that: by adopting a sliding mode control method based on an exponential approaching law, the hot-pressing furnace system can reach the required temperature quickly and accurately, the adverse effect caused by time delay is effectively solved through the design of a delay observer, and the compensation of external disturbance is completed by utilizing a disturbance observer. The method comprises the following steps:
a hot-pressing furnace temperature compound control method based on an improved time delay observer is characterized in that a control object transfer function is defined as
Figure BDA0003152248740000021
Wherein
Figure BDA0003152248740000022
In order to be a lag link,
Figure BDA0003152248740000023
for lag parameters, a, b and k are all system parameters, and the transfer function is converted into a time domain expression as
Figure BDA0003152248740000024
Where y (t) is the system temperature output and u (t) is the control input, including:
selecting a disturbance observer to predict the external disturbance of the system, and feedforward compensating the disturbance estimated value to a forward channel behind the controller,estimating a system by a delay observer
Figure BDA0003152248740000031
Output before second
Figure BDA0003152248740000032
And state
Figure BDA0003152248740000033
And fed back to the input end of the sliding mode controller, and the sliding mode controller receives
Figure BDA0003152248740000034
And state
Figure BDA0003152248740000035
And according to the set sliding mode surface and the control rate, the system moves according to the set state track through the sliding mode controller.
In the above method for compositely controlling the temperature of the hot-pressing furnace based on the improved delay observer, the disturbance observer is defined based on the following:
Figure BDA0003152248740000036
wherein Q(s) is a second order low pass filter, Y(s) is a system output, U(s) is a control input,
Figure BDA0003152248740000037
is the inverse of the minimum phase part of the transfer function of the system
Figure BDA0003152248740000038
Time of flight
Figure BDA0003152248740000039
In the above composite control method for the temperature of the hot pressing furnace based on the improved delay observer, the delay observer is defined based on the following:
get
Figure BDA00031522487400000310
Then
Figure BDA00031522487400000311
Is shown as
Figure BDA00031522487400000312
Wherein
Figure BDA00031522487400000313
Is a matrix of systematic coefficients, H ═ 0, k]TA matrix is input to the system. The system has hysteresis and the system is a single-input single-output system, so that the output signal is defined to have delay,
Figure BDA00031522487400000314
for the time delay of the output to be,
Figure BDA00031522487400000315
wherein, C ═ 10]. At this time
Figure BDA00031522487400000316
Aiming at the delay system
Figure BDA00031522487400000317
Taking the observed value
Figure BDA00031522487400000318
The delay observer is then:
Figure BDA00031522487400000319
wherein the content of the first and second substances,
Figure BDA00031522487400000320
is that
Figure BDA00031522487400000321
N is an error gain matrix.
In the above composite control method for the temperature of the hot pressing furnace based on the improved delay observer, the sliding mode controller is defined based on the following:
definition error
Figure BDA0003152248740000041
Sliding mode function of sliding mode controller
Figure BDA0003152248740000042
Wherein c > 0, [ c 1 ]]Is a sliding mode surface parameter matrix. By means of a time-delay observer
Figure BDA0003152248740000043
And
Figure BDA0003152248740000044
the control law of the sliding mode controller designed based on the exponential approaching law is as follows:
Figure BDA0003152248740000045
wherein epsilon and m are approach law parameters, epsilon is more than 0, m is more than 0, and in order to avoid larger system buffeting, a saturation function sat(s) is adopted in the controller to replace a sign function sat(s), namely
Figure BDA0003152248740000046
Where Δ is the boundary layer.
Compared with the prior art, the invention has the following advantages:
(1) the sliding mode controller is used for controlling the temperature of the hot pressing furnace, so that the speed of the system reaching the set temperature is effectively increased, and the response speed of the system is accelerated.
(2) In order to solve the inherent time lag problem of a control system, a time delay observer is designed. The output of the observer and the actual input form a linear system without time lag through the time delay observer, the influence of the time lag is eliminated, and the design of the sliding mode controller is simplified.
(3) Compared with the conventional method of performing PI feedback, the disturbance observer can estimate disturbance in advance and actively perform disturbance compensation, and the method has the advantages of having the advance and effectively improving the disturbance resistance of the system.
Drawings
FIG. 1 is a block diagram of a hot-pressing furnace temperature compound control system based on an improved delay observer.
FIG. 2 is a graph comparing the output of the present invention with a conventional PID.
Detailed Description
The following detailed description of embodiments of the invention refers to the accompanying drawings.
The invention solves the technical problem by adopting the specific scheme that: by adopting a sliding mode control method, the hot pressing furnace system can reach the required temperature quickly and accurately, the adverse effect caused by time delay is effectively solved through the design of the delay observer, and the compensation of system disturbance is completed by utilizing the disturbance observer.
Fig. 1 is a block diagram of a hot-pressing furnace temperature composite control system based on an improved delay observer, wherein SMC is a sliding-mode controller; d(s) is the system disturbance; the virtual frame 1 is a disturbance observer; the virtual frame 2 is a delay observer; gp(s) is the actual controlled object;
Figure BDA0003152248740000051
and
Figure BDA0003152248740000052
respectively, a disturbance observation value, an output observation value before time lag and a state.
Forcing the system to move according to a set state trajectory by a sliding mode controller, Gp(s) is an actual controlled object, a disturbance Observer is selected to predict external disturbance possibly suffered by the system, a disturbance estimation value is feedforward compensated to a forward channel, a Delay Observer is used as a Delay Observer, and the system is estimated through the Delay Observer
Figure BDA0003152248740000053
Output before second
Figure BDA0003152248740000054
And state
Figure BDA0003152248740000055
And fed back to the input of the sliding mode controller.
FIG. 2 is a graph showing the temperature control output of PID-based control of the furnace temperature and the temperature control output of the modified time-delay observer-based furnace temperature combination. Wherein, the solid curve is a set temperature value; the SMC + D-DOV dotted line is an output curve of the invention; the dashed PID line is the output curve for conventional PID-based temperature control.
According to a mathematical model of temperature control, a sliding mode controller is constructed in Matlab/Simulink, so that the control process of the whole temperature control system is constructed, meanwhile, a common PID control temperature control system is also constructed, and the output contrast diagram is obtained after operation. The set temperature was 250 ℃, the black dashed line is the PID output curve, and the blue dashed line is the output curve based on the invention. According to the graph in the figure, the hot pressing furnace temperature control system based on the invention can reach the preset temperature value more quickly, has smaller overshoot and is stabilized at the set value more quickly. When disturbance exists in the system, the temperature control system based on the invention is more quickly stabilized at a preset value, and the robustness of the system is improved. The method comprises the following specific steps:
and the temperature of the hot-pressing furnace is controlled by using a sliding mode controller. The sliding mode controller can force the system to move according to a state track of a preset sliding mode according to the current state of the system in a dynamic process. The method is characterized in that the sliding mode can be designed and is independent of object parameters and disturbance. The method specifically comprises the following steps:
1. definition error
Figure BDA0003152248740000061
Designing sliding mode function
Figure BDA0003152248740000062
Wherein c is more than 0, and the sliding mode control rate is as follows:
Figure BDA0003152248740000063
wherein epsilon and m are approximate law parameters, epsilon is more than 0, m is more than 0, and the temperature of the hot-pressing furnace can quickly reach the target temperature yd(s)。
2. Because of time lag of the system, in order to eliminate the influence of the time lag on the stability of the systemAnd designing a delay observer. System by time delay observer
Figure BDA0003152248740000064
The output and state before the second are observed and fed back, so that the output of the observer and the actual input form a linear system without time lag. The feedback control of the delay observer not only eliminates the influence of time lag, but also simplifies the design of the sliding mode controller.
3. The lumped disturbance of the system is observed by a disturbance observer and feed-forward compensated to the forward channel.
4. By designing the sliding mode controller and utilizing the combination of the delay observer and the disturbance observer, the temperature of the hot-pressing furnace is accurately controlled, the disturbance resistance of the system is effectively improved, and the influence caused by the time lag problem of the system is solved. The method specifically comprises the following steps:
(1) considering objects
Figure BDA0003152248740000065
Establishing
Figure BDA0003152248740000066
Time domain mathematical model, where is the system temperature output and u (t) is the control input.
(2) Get
Figure BDA0003152248740000067
Then the above formula
Figure BDA0003152248740000068
Can be expressed as
Figure BDA0003152248740000071
Wherein
Figure BDA0003152248740000072
Is a matrix of systematic coefficients, H ═ 0, k]TA matrix is input to the system. Because the system is a single-input single-output system, I can see that the output signal has delay,
Figure BDA0003152248740000073
for the time delay of the output to be,
Figure BDA0003152248740000074
wherein, C ═ 10]. At this time
Figure BDA0003152248740000075
Aiming at the delay system
Figure BDA0003152248740000076
Taking the observed value
Figure BDA0003152248740000077
Designing a time delay observer:
Figure BDA0003152248740000078
wherein the content of the first and second substances,
Figure BDA0003152248740000079
is that
Figure BDA00031522487400000710
N is an error gain matrix.
Is provided with
Figure BDA00031522487400000711
Leading: for linear delay systems
Figure BDA00031522487400000712
The stability condition is sigma I-A-Be-AσThe real part of the feature root is negative, and the delay system is exponentially stable. Thus, can obtain
Figure BDA00031522487400000713
Then according to the lemma, the stability condition of the delay observer is: selecting proper K to make the designed delay observer
Figure BDA00031522487400000714
Is negative, the delay systemThe exponent δ (t) converges to 0 for exponential stability, i.e., t → ∞.
(3) Considering object model formula
Figure BDA00031522487400000715
Definition error
Figure BDA00031522487400000716
Designing sliding mode functions for sliding mode controllers
Figure BDA00031522487400000717
Wherein c > 0, [ c 1 ]]Is a sliding mode surface parameter matrix. Observing by using the time-delay observer in (2)
Figure BDA00031522487400000718
And
Figure BDA00031522487400000719
the control law of the sliding mode controller designed based on the exponential approaching law is as follows:
Figure BDA00031522487400000720
wherein epsilon and m are approach law parameters, epsilon is more than 0, m is more than 0, and in order to avoid larger system buffeting, a saturation function sat(s) is adopted in the controller to replace a sign function sgn(s), namely
Figure BDA0003152248740000081
Where Δ is the boundary layer.
(4) Mathematical model formula considering objects
Figure BDA0003152248740000082
Inverse of minimum phase according to transfer function of controlled system
Figure BDA0003152248740000083
Designing a disturbance observer:
Figure BDA0003152248740000084
wherein Q(s) is a second order low pass filter, Y(s) is a system output, U(s) is a control input,
Figure BDA0003152248740000085
is the inverse of the minimum phase part of the transfer function of the system
Figure BDA0003152248740000086
Time of flight
Figure BDA0003152248740000087
The specific embodiments described herein are merely illustrative of the spirit of the invention. Various modifications or additions may be made to the described embodiments or alternatives may be employed by those skilled in the art without departing from the spirit or ambit of the invention as defined in the appended claims.

Claims (3)

1. A hot-pressing furnace temperature compound control method based on an improved time delay observer is characterized in that a control object transfer function is defined as
Figure FDA0003504544910000011
Wherein e-τsFor a lag link, tau is a lag parameter, a, b and k are system parameters, and a transfer function is converted into a time domain expression
Figure FDA0003504544910000012
Where y (t) is the system temperature output and u (t) is the control input, including:
selecting a disturbance observer to predict external disturbance on the system, feeding back and compensating a disturbance estimation value to a forward channel behind the controller, and estimating the output of the system before tau seconds by using a delay observer
Figure FDA0003504544910000013
And state
Figure FDA0003504544910000014
And fed back to sliding mode controlInput of the controller, reception of the sliding mode controller
Figure FDA0003504544910000015
And
Figure FDA0003504544910000016
enabling the system to move according to a set state track through a sliding mode controller according to a set sliding mode surface and a set control rate;
the sliding mode controller is based on the following definitions:
definition error
Figure FDA0003504544910000017
Sliding mode function of sliding mode controller
Figure FDA0003504544910000018
Wherein c > 0, [ c 1 ]]Observing the parameter matrix of the sliding mode surface by using a delay observer model
Figure FDA0003504544910000019
And
Figure FDA00035045449100000110
the control law of the sliding mode controller designed based on the exponential approaching law is as follows:
Figure FDA00035045449100000111
wherein epsilon and m are approach law parameters, epsilon is more than 0, m is more than 0, and in order to avoid larger system buffeting, a saturation function sat(s) is adopted in the controller to replace a sign function sgn(s), namely
Figure FDA00035045449100000112
Where Δ is the boundary layer.
2. The hot-pressing furnace temperature compound control method based on the improved delay observer is characterized in that the disturbance observer is defined according to the following steps:
Figure FDA0003504544910000021
wherein Q(s) is a second order low pass filter, Y(s) is a system output, U(s) is a control input,
Figure FDA0003504544910000022
is the inverse of the minimum phase part of the transfer function of the system
Figure FDA0003504544910000023
Time of flight
Figure FDA0003504544910000024
3. The hot-pressing furnace temperature compound control method based on the improved delay observer is characterized in that the delay observer is defined according to the following steps:
get
Figure FDA0003504544910000025
Then
Figure FDA0003504544910000026
Is shown as
Figure FDA0003504544910000027
Wherein
Figure FDA0003504544910000028
Is a matrix of systematic coefficients, H ═ 0, k]TFor the system input matrix, the system has hysteresis and the system is a single input single output system, so that the output signal is defined to have a delay, τ is the time delay of the output,
Figure FDA0003504544910000029
wherein, C ═ 10]At this time
Figure FDA00035045449100000210
Aiming at the delay system
Figure FDA00035045449100000211
Taking the observed value
Figure FDA00035045449100000212
The delay observer is then:
Figure FDA00035045449100000213
wherein the content of the first and second substances,
Figure FDA00035045449100000214
is that
Figure FDA00035045449100000215
N is an error gain matrix.
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