CN113126484B - Improved model-free sliding mode control system and method for hydraulic system - Google Patents
Improved model-free sliding mode control system and method for hydraulic system Download PDFInfo
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Abstract
The invention discloses an improved model-free sliding mode control system and method of a hydraulic system, aiming at the characteristics of strong nonlinearity, uncertainty and the like of the hydraulic system, combining the control rules of a model-free controller and a model-free terminal integral sliding mode controller, fusing human-simulated intelligent control and model-free sliding mode control, integrating control quantity information obtained by multiplying deviation and deviation change rate, enriching dynamic information of deviation processing, improving the response speed of the controller and effectively improving dynamic and steady-state performances. The method has the characteristics of small calculation amount and easy realization of on-line control of the hydraulic system.
Description
Technical Field
The invention relates to the technical field of hydraulic system control, in particular to an improved model-free sliding mode control system and method for a hydraulic system.
Background
The output of the electro-hydraulic system has the characteristics of large force/torque output, quick response time and the like, plays a very important role in industry, and is widely applied to modern airplanes, automobiles, robots, mechanical hands, machine tools, manufacturing industries, mould oscillators and suspension systems. The complexity, nonlinearity and uncertainty of electro-hydraulic systems are rooted in: nonlinear flow and pressure characteristics, bulk modulus, control valve backlash, actuator friction, fluid volume changes due to piston motion, fluid compressibility, external interference and wear and cavitation.
A large number of researchers have been working on modeling, identifying and controlling nonlinear systems using nonlinear models. In order to improve the precision of a hydraulic servo system, a sign function is replaced by a sigmoid function in a sliding mode controller, a self-correcting controller is constructed, buffeting is effectively weakened, the tracking speed is accelerated, and the robustness of the system is improved. In addition, the existing research aims at the problems of anti-interference and control precision in the position control of the branched chains of the parallel motion platform, and provides a sliding mode control algorithm based on self-adaptive inversion. However, these control algorithms require an accurate mathematical model. In order to further improve the control accuracy of the hydraulic system, a more effective control algorithm is sought, and the requirements of high accuracy, high stability and the like of the hydraulic control system are met, which is always a goal sought in engineering.
Disclosure of Invention
The invention provides an improved model-free sliding mode control system and method for a hydraulic system, which aim to improve the control precision and stability of the hydraulic control system.
In order to solve the problems, the invention is realized by the following technical scheme:
the improved model-free sliding mode control method of the hydraulic system comprises the following steps:
step 1, acquiring displacement output quantity y (k) of a hydraulic system at a current time k, displacement output quantity y (k-1) at a previous time k-1 of the current time and displacement output quantity y (k-2) at a previous two times k-2 of the current time;
Step 2, setting quantity y based on displacement of the hydraulic system at the current moment k*(k) And calculating displacement deviation amount e (k) of the hydraulic system at current time k by using displacement output amount y (k), wherein e (k) y*(k) -y (k); setting quantity y based on displacement of hydraulic system at previous moment k-1 of current moment*(k-1) and the displacement output quantity y (k-1) calculate the displacement deviation quantity e (k-1) of the hydraulic system at the previous moment k-1 of the current moment, and the e (k-1) is equal to y*(k-1) -y (k-1); and a set amount y based on the displacement of the hydraulic system at the first two times k-2 of the current time*(k-2) and the displacement output quantity y (k-2) calculate the displacement deviation quantity e (k-2) of the hydraulic system at the two previous moments k-2 of the current moment, and the e (k-2) is equal to y*(k-2)-y(k-2)；
Step 3, calculating an input control increment delta u (k) of the hydraulic system at the current time k:
where xi is a set correction coefficient and 0<ξ<1；λ1、λ2And λ3Adjustment coefficients set for 3, and 0<λ1<1，0<λ2<1，0<λ3<1；y*(k +1) is a displacement setting amount of the hydraulic system at the next moment k +1 of the current moment; y (k) is the displacement output quantity of the hydraulic system at the current moment k; e (k) is the displacement deviation amount of the hydraulic system at the current moment k; e (k-1) is the displacement deviation amount of the hydraulic system at the previous moment k-1 of the current moment; e (k-2) is the displacement deviation amount of the hydraulic system at the two previous moments k-2 of the current moment; 
The pseudo partial derivative of the hydraulic system at the current moment k is obtained;
step 4, superposing the input control increment delta u (k) of the hydraulic system at the current time k obtained in the step 3 to the input control quantity u (k) of the hydraulic system at the current time k to obtain an input control quantity u (k +1) of the hydraulic system at the next time k +1 of the current time, wherein u (k +1) is u (k) + delta u (k);
and 5, controlling the hydraulic system by using the input control quantity u (k +1) of the hydraulic system at the next moment k +1 of the current moment obtained in the step 4.
Pseudo partial derivative of hydraulic system at current moment k
Comprises the following steps:
in the formula, eta is a set step factor and 0<Eta is less than or equal to 1; mu is a set gain adjustment coefficient and 0<μ<1; y (k) is the displacement output quantity of the hydraulic system at the current moment k; y (k-1) is the displacement output quantity at the previous moment k-1 of the current moment;
is the pseudo partial derivative of the hydraulic system at a time k-1 preceding the current time; Δ u (k-1) is the input control increment of the hydraulic system at a time k-1 prior to the current time.
When k is 1, the pseudo partial derivative of the hydraulic system at the current time k
Is a randomly generated random number, and
the displacement output quantity y (k-1) of the hydraulic system at the previous moment k-1 of the current moment and the displacement output quantity y (k-2) at the previous moment k-2 of the current moment are both 0.
The improved model-free sliding mode control system of the hydraulic system comprises an industrial computer, a displacement sensor and the hydraulic system; the hydraulic system comprises an electro-hydraulic proportional valve and a hydraulic cylinder; wherein the industrial computer is embedded with an improved model-free sliding mode control module based on the method, and is provided with an A/D conversion card and a D/A conversion card; the input end of the displacement sensor is connected with the output end of the hydraulic cylinder, the output end of the displacement sensor is connected with the input end of the A/D conversion card, the output end of the A/D conversion card is connected with the input end of the improved model-free sliding mode control module, the output end of the improved model-free sliding mode control module is connected with the input end of the D/A conversion card, the output end of the D/A conversion card is connected with the input end of an electro-hydraulic proportional valve of the hydraulic system, the output end of the electro-hydraulic proportional valve of the hydraulic system is connected with the input end of the hydraulic cylinder, and the output end of the hydraulic cylinder is connected with the load.
The industrial computer is also provided with a display and/or a network card; the display and/or the network card are connected with the improved model-free sliding mode control module.
Compared with the prior art, the invention has the following characteristics:
1. a core technology of the product of the deviation and the deviation change rate of the humanoid intelligent control is integrated into sliding mode control, a brand new sliding mode function is designed, and the humanoid sliding mode control method is invented.
2. The human-simulated sliding mode control method is combined with a model-free controller, and an improved model-free sliding mode controller is designed.
3. The control method has small calculation amount and is convenient for forming an embedded hydraulic control system.
Drawings
FIG. 1 is a schematic block diagram of an improved modeless sliding mode control system for a hydraulic system.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to specific examples.
The invention introduces the core idea of humanoid intelligent control, designs a new sliding mode function, forms an improved model-free sliding mode control module, adds new information, namely control quantity information obtained by multiplying deviation variation and deviation, improves the response speed of hydraulic system control, reduces overshoot and steady-state error, and achieves the purpose of improving the control precision and stability of the hydraulic control system.
1. Humanoid intelligent control
The human-simulated intelligent control is a control algorithm designed according to human thinking mode. And in the control process, selecting a control strategy and a control mode according to the variation trend of the control deviation. The human-simulated intelligent control algorithm comprises the following steps:
Wherein u is the controller output, KpIs a proportionality coefficient, k is a suppression coefficient, e is a deviation of a set value from a controlled variable,
as rate of change of deviation, emaxiIs the peak of the ith deviation.
Is the core idea of the humanoid intelligent control, and the control quantity of the humanoid intelligent control is based on
And obtaining a corresponding control strategy.
2. Modeless sliding mode control
Control law of model-free adaptive control (MFAC):
wherein u (k) and u (k-1) are input control amounts at a current time k and a time k-1 immediately before the current time, respectively, and y*(k +1) is the set output quantity of the hydraulic system at the next moment k +1 of the current moment, y (k) is the actual output quantity at the current moment k, 0<λ<1 is the adjustment factor, 0<ρ<1 is a gain factor.
The mathematical expression of the pseudo partial derivative of the hydraulic system at the current moment k is as follows:
wherein, 0<h≤1 is a step factor, 0<μ<1 is a sufficiently small gain adjustment factor.
And
is the pseudo-partial derivative of the current time k and the time k-1 preceding the current time.
Is that
The initial value of (a) is,
is a random number randomly generated in the range of 0-1. Δ u (k-1) is an input control increment of the hydraulic system at a time k-1 before the current time, and Δ u (k-1) ═ u (k-1) -u (k), u (k-1) is an input control quantity at the time k-1 before the current time, and u (k) is an input control quantity at the current time k. Δ y (k) is a displacement output increment of the hydraulic system at the current time k, Δ y (k) is y (k) -y (k-1), y (k) is a displacement output quantity at the current time k, and y (k-1) is a displacement output quantity at the previous time k-1.
Combining discrete sliding mode control with a model-free controller, and integrating the discrete sliding mode control into sliding mode control on the basis of the model-free adaptive sliding mode control to obtain model-free sliding mode control (MFA-SMC). Taking a sliding mode function s (k):
s(k)＝λ1e(k)+λ2E(k-1) (4)
where e (k) is the displacement deviation amount of the hydraulic system at the current time k, and e (k) y*(k)-y(k)，y*(k) And y (k) is the displacement output quantity at the current moment k. Lambda1And λ2For two adjustment factors, 1>λ1>0，1>λ2>The integral term E (k) is E (k-1) + E (k), and the initial value E (1) is E (1).
After the sliding mode control and the model-free control are fused, the model-free sliding mode control u is as follows:
where 0< ξ <1 is the correction factor.
3. Model-free sliding mode control integrating human-simulated intelligent control and sliding mode control
Considering that the sliding mode control and the humanoid intelligent control are developed on a phase plane, the humanoid intelligent control idea is that the deviation is multiplied by the deviation derivative, and the humanoid intelligent control idea is integrated into the sliding mode controller to obtain the modeless sliding mode control which is integrated by the humanoid intelligent control and the sliding mode control, namely the improved modeless sliding mode control.
Defining a deviation:
e(k)＝y*(k)-y(k) (6)
wherein, y*(k) And y (k) are the desired displacement output amount (i.e., displacement set amount) and the actual displacement output amount (i.e., displacement output amount) at time k, respectively.
Taking a sliding mode function ss (k):
ss(k)＝λ1e(k)+λ2E(k-1)+λ3e(k-1)Δe(k-1) (7)
wherein ss (k) is a sliding mode function of the current time k, 1>λ1>0,1>λ2>0,1>λ3>0 is three adjustment coefficients. The integral term E (k) ═ E (k-1) + E (k). And delta e (k-1) ═ e (k-1) -e (k-2) is the displacement deviation increment of the hydraulic system at the previous moment k-1 of the current moment. e (k) is the displacement deviation of the hydraulic system at the current time k, and e (k) is y*(k) -y (k). e (k-1) is the displacement deviation of the hydraulic system at the previous moment k-1, and e (k-1) is equal to y*(k-1) -y (k-1), e (k-2) is the displacement deviation amount of the hydraulic system at the two previous moments k-2 of the current moment, and e (k-2) ═ y*(k-2)-y(k-2)。
After the humanoid intelligent control and the sliding mode control are integrated, the improved model-free sliding mode control law of the invention is as follows:
where xi is a set correction coefficient and 0<ξ<1；λ1、λ2And λ3Adjustment coefficients set for 3, and 0<λ1<1，0<λ2<1，0<λ3<1；y*(k +1) is a displacement setting amount of the hydraulic system at the next moment k +1 of the current moment; y (k) is the displacement output quantity of the hydraulic system at the current moment k; e (k) is the displacement deviation amount of the hydraulic system at the current moment k; e (k-1) is the displacement deviation amount of the hydraulic system at the previous moment k-1 of the current moment; e (k-2) is the displacement deviation amount of the hydraulic system at the two previous moments k-2 of the current moment;
is the pseudo-partial derivative of the hydraulic system at the current instant k. The initial value e (1) is 0. The invention relates to a method for preparing e (k-1) [ e (k-1) -e (k-2) ]And e (k) -e (k-1)]Two items of new information are introduced, and the deviation multiplication characteristic quantity is added for describing the extreme value state information of the deviation, so that the improvement of the system in the aspects of response speed, steady-state error and the like is facilitated.
Based on the above analysis, the improved model-free sliding mode control method for the hydraulic system, which is designed by the invention, comprises the following steps:
initialization: let k equal to 1;
pseudo partial derivative of hydraulic system at current moment k
Is a randomly generated random number, and
y(0)＝y(-1)＝0。
step 1, acquiring displacement output quantity y (k) of a hydraulic system at a current time k, displacement output quantity y (k-1) at a previous time k-1 of the current time and displacement output quantity y (k-2) at a previous two times k-2 of the current time;
step 2, setting amount y based on displacement of the hydraulic system at current time k*(k) And the displacement output quantity y (k) is used for calculating the displacement deviation quantity e (k) of the hydraulic system at the current time k, and e (k) is equal to y*(k) -y (k); based on the displacement set value y of the hydraulic system at the previous moment k-1 of the current moment*(k-1) and the displacement output quantity y (k-1) calculate the displacement deviation quantity e (k-1) of the hydraulic system at the previous moment k-1 of the current moment, and the e (k-1) is equal to y*(k-1) -y (k-1); and a set amount y based on the displacement of the hydraulic system at the first two times k-2 of the current time *(k-2) and the displacement output quantity y (k-2) calculate the displacement deviation quantity e (k-2) of the hydraulic system at the previous two times k-2 of the current time, and e (k-2) is equal to y*(k-2)-y(k-2)；
Step 3, calculating an input control increment delta u (k) of the hydraulic system at the current time k:
in the formula, xi is a set correction coefficient and 0<ξ<1，λ1、λ2And λ3Adjustment coefficients set for 3, and 0<λ1<1，0<λ2<1，0<λ3<1，y*(k +1) is a displacement set quantity of the hydraulic system at the next moment k +1 of the current moment, y (k) is a displacement output quantity of the hydraulic system at the current moment k, e (k) is a displacement deviation quantity of the hydraulic system at the current moment k, e (k-1) is a displacement deviation quantity of the hydraulic system at the previous moment k-1 of the current moment, e (k-2) is a displacement deviation quantity of the hydraulic system at the previous two moments k-2 of the current moment,
the pseudo-partial derivative of the hydraulic system at the present instant k,
h is a set step factor and 0<h is less than or equal to 1, mu is a set gain adjustment coefficient and is 0<μ<1, y (k-1) isThe displacement output quantity at the previous time k-1 to the current time,
the method comprises the steps that a pseudo partial derivative of a hydraulic system at a previous moment k-1 of a current moment is adopted, and an input control increment of the hydraulic system at the previous moment k-1 of the current moment is adopted;
step 4, superposing the input control increment delta u (k) of the hydraulic system at the current time k obtained in the step 3 to the input control quantity u (k) of the hydraulic system at the current time k to obtain an input control quantity u (k +1) of the hydraulic system at the next time k +1 of the current time, wherein u (k +1) is u (k) + delta u (k);
And 5, controlling the hydraulic system by using the input control quantity u (k +1) of the hydraulic system at the next moment k +1 of the current moment obtained in the step 4.
The improved model-free sliding mode control system of the hydraulic system for realizing the method comprises an industrial computer (IPC machine), a displacement sensor and the hydraulic system, as shown in figure 1. The hydraulic system comprises an electro-hydraulic proportional valve and a hydraulic cylinder. The industrial computer is embedded with an improved model-free sliding mode control module based on the method of claim 1 and is provided with an A/D conversion card, a D/A conversion card, a display and a network card.
The input end of the displacement sensor is connected with the output end of the hydraulic cylinder, the output end of the displacement sensor is connected with the input end of the A/D conversion card, the output end of the A/D conversion card is connected with the input end of the improved model-free sliding mode control module, the output end of the improved model-free sliding mode control module is connected with the input end of the D/A conversion card, the output end of the D/A conversion card is connected with the input end of an electro-hydraulic proportional valve of the hydraulic system, the output end of the electro-hydraulic proportional valve of the hydraulic system is connected with the input end of the hydraulic cylinder, and the output end of the hydraulic cylinder is connected with the load. The display and the network card are connected with the improved model-free sliding mode control module.
The displacement sensor detects the displacement of the hydraulic cylinder. And the A/D conversion card performs analog-to-digital conversion on the displacement sent by the displacement sensor and then sends the displacement to the improved model-free sliding mode algorithm module. The control quantity output by the improved model-free sliding mode algorithm module is sent to an electro-hydraulic proportional valve in a hydraulic system after being subjected to digital-to-analog conversion by a D/A conversion card. The electro-hydraulic proportional valve converts the control signal into a hydraulic power information signal to drive the hydraulic cylinder, and the hydraulic cylinder is driven to push the load to move. And displaying the received displacement signal and the control signal, and displaying the dynamic control process. The network card communicates with the outside, can transmit and output the control information, can also connect the external displacement reference command. The control system realizes high-precision displacement control of the hydraulic system through displacement closed-loop control.
Aiming at the characteristics of strong nonlinearity, uncertainty and the like of a hydraulic system, the invention combines the control rules of a model-free controller and a model-free terminal integral sliding mode controller, integrates the humanoid intelligent control and the model-free sliding mode control, integrates the control quantity information of multiplying the deviation and the deviation change rate, enriches the dynamic information of error deviation processing, improves the response speed of the controller, and effectively improves the dynamic and steady-state performances. The method has small calculation amount and is easy to realize the online control of the hydraulic system.
It should be noted that, although the above-mentioned embodiments of the present invention are illustrative, the present invention is not limited thereto, and therefore, the present invention is not limited to the above-mentioned specific embodiments. Other embodiments, which can be devised by those skilled in the art in light of the teachings of the present invention, are considered to be within the scope of the present invention without departing from its principles.
Claims (5)
1. The improved model-free sliding mode control method of the hydraulic system is characterized by comprising the following steps of:
step 1, acquiring displacement output quantity y (k) of a hydraulic system at a current time k, displacement output quantity y (k-1) at a previous time k-1 of the current time and displacement output quantity y (k-2) at a previous two times k-2 of the current time;
step 2, setting amount y based on displacement of the hydraulic system at current time k*(k) And the displacement output quantity y (k) is used for calculating the displacement deviation quantity e (k) of the hydraulic system at the current time k, and e (k) is equal to y*(k) -y (k); based on the displacement set value y of the hydraulic system at the previous moment k-1 of the current moment*(k-1) and the displacement output quantity y (k-1) calculate the displacement deviation quantity of the hydraulic system at the previous moment k-1 of the current momente(k-1)，e(k-1)＝y*(k-1) -y (k-1); and a set amount y based on the displacement of the hydraulic system at the first two times k-2 of the current time *(k-2) and the displacement output quantity y (k-2) calculate the displacement deviation quantity e (k-2) of the hydraulic system at the previous two times k-2 of the current time, and e (k-2) is equal to y*(k-2)-y(k-2)；
Step 3, calculating an input control increment delta u (k) of the hydraulic system at the current time k:
where xi is a set correction coefficient and 0<ξ<1；λ1、λ2And λ3Adjustment coefficients set for 3, and 0<λ1<1，0<λ2<1，0<λ3<1；y*(k +1) is a displacement setting amount of the hydraulic system at the next moment k +1 of the current moment; y (k) is the displacement output quantity of the hydraulic system at the current moment k; e (k) is the displacement deviation amount of the hydraulic system at the current moment k; e (k-1) is the displacement deviation amount of the hydraulic system at the previous moment k-1 of the current moment; e (k-2) is the displacement deviation amount of the hydraulic system at the two previous moments k-2 of the current moment;
is the pseudo partial derivative of the hydraulic system at the current moment k;
step 4, superposing the input control increment delta u (k) of the hydraulic system at the current time k obtained in the step 3 to the input control quantity u (k) of the hydraulic system at the current time k to obtain an input control quantity u (k +1) of the hydraulic system at the next time k +1 of the current time, wherein u (k +1) is u (k) + delta u (k);
and 5, controlling the hydraulic system by using the input control quantity u (k +1) of the hydraulic system at the next moment k +1 of the current moment obtained in the step 4.
2. The method for improved modeless sliding mode control of a hydraulic system of claim 1, wherein the hydraulic system is configured to operate at a current timePseudo partial derivative of k
Comprises the following steps:
wherein eta is a set step factor and 0<Eta is less than or equal to 1; mu is a set gain adjustment coefficient and 0<μ<1; y (k) is the displacement output quantity of the hydraulic system at the current moment k; y (k-1) is the displacement output quantity at the previous moment k-1 of the current moment;
is the pseudo partial derivative of the hydraulic system at a time k-1 preceding the current time; Δ u (k-1) is the input control increment of the hydraulic system at a time k-1 prior to the current time.
3. The method for improved modeless sliding-mode control of a hydraulic system of claim 1 or 2, wherein the pseudo-partial derivative of the hydraulic system at the current time k is when k is 1
Is a randomly generated random number, and
the displacement output quantity y (k-1) of the hydraulic system at the previous moment k-1 of the current moment and the displacement output quantity y (k-2) at the previous moment k-2 of the current moment are both 0.
4. The improved model-free sliding mode control system of the hydraulic system is characterized by comprising an industrial computer, a displacement sensor and a hydraulic system; the hydraulic system comprises an electro-hydraulic proportional valve and a hydraulic cylinder; wherein the industrial computer is embedded with an improved model-free sliding mode control module based on the method of claim 1 and is provided with an A/D conversion card and a D/A conversion card;
The input end of the displacement sensor is connected with the output end of the hydraulic cylinder, the output end of the displacement sensor is connected with the input end of the A/D conversion card, the output end of the A/D conversion card is connected with the input end of the improved model-free sliding mode control module, the output end of the improved model-free sliding mode control module is connected with the input end of the D/A conversion card, the output end of the D/A conversion card is connected with the input end of an electro-hydraulic proportional valve of the hydraulic system, the output end of the electro-hydraulic proportional valve of the hydraulic system is connected with the input end of the hydraulic cylinder, and the output end of the hydraulic cylinder is connected with a load.
5. The improved modeless sliding-mode control system for a hydraulic system of claim 4, wherein the industrial computer further comprises a display and/or a network card; the display and/or the network card are/is connected with the improved modeless sliding mode control module.
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