CN117784622B - Second-order observer-based electrohydraulic servo system global sliding mode control method - Google Patents
Second-order observer-based electrohydraulic servo system global sliding mode control method Download PDFInfo
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Abstract
The invention discloses a global sliding mode control method of an electrohydraulic servo system based on a second-order observer, and belongs to the technical field of electrohydraulic servo system control; for an electrohydraulic servo system, firstly, establishing a model of the system; secondly, a second-order self-adaptive extended state observer is constructed, and the observer has a simple structure and can cooperatively improve the tracking performance and the estimation performance of the system; then, an improved global sliding mode control law is provided, and the control law not only can overcome the defects of poor convergence and weak robustness of the existing method, but also can effectively improve the control precision; finally, the disturbance estimated by the second-order self-adaptive extended state observer is compensated in a global sliding mode control law to form a controller, and the limited time stability of the system is proved under the action of the controller; by adopting the control method, the invention can simplify the design of the controller of the electrohydraulic servo system, effectively improve the control precision and ensure the limited time stability of the system.
Description
Technical Field
The invention relates to the technical field of electrohydraulic servo system control, in particular to a global sliding mode control method of an electrohydraulic servo system based on a second-order observer.
Background
Typical electrohydraulic servo systems have strong nonlinear characteristics such as dead zone, time-varying parameters, internal and external disturbances, and the like. These nonlinearities present challenges to high performance tracking control of the system. In order to overcome the above problems, scholars have developed various effective electrohydraulic servo system control methods aiming at improving the control performance. In the existing method, the sliding mode control based on the extended state observer shows strong competitiveness and is widely applied to an electrohydraulic servo system, but the defects of complex structure, weak global robustness, poor disturbance estimation performance, incapability of eliminating disturbance estimation errors, sliding mode buffeting and the like exist, so that the high-performance control requirements of the electrohydraulic servo system on high response speed, high precision and no overshoot cannot be met.
Disclosure of Invention
The invention aims to provide a global sliding mode control method of an electrohydraulic servo system based on a second-order observer, which comprises the steps of firstly, establishing a model of the electrohydraulic servo system; secondly, a smooth and continuous self-adaptive strategy is designed according to a preset tracking error threshold value, and a second-order self-adaptive extended state observer is designed to realize the aim of cooperatively improving disturbance estimation performance and tracking performance; then, based on the output of the trigonometric function and the observer, a novel smooth continuous convergence function, a filter and a saturation function are designed, so that a global sliding mode control law is provided to eliminate sliding mode buffeting, improve global robustness, inhibit disturbance estimation errors and ensure limited time stability of the system; and finally, compensating disturbance estimated by the second-order self-adaptive extended state observer in a global sliding mode control law to form a controller, and proving limited time stability of the electrohydraulic servo system under the action of the controller.
In order to achieve the above purpose, the invention provides a global sliding mode control method of an electrohydraulic servo system based on a second-order observer, which comprises the following steps:
s1: establishing an electrohydraulic servo system model;
s2: designing a second-order self-adaptive extended state observer;
s3: providing an equivalent control law and a sliding mode robust control term to obtain a global sliding mode control law;
S4: combining the disturbance estimated by the observer with the global sliding mode control law in the step S3 to obtain a controller;
S5: aiming at the electrohydraulic servo system in the step S1, a limited time stability proving process of the electrohydraulic servo system is given under the action of a controller.
Preferably, in the step S1, a model of the electrohydraulic servo system is as follows:
(1)
In the above-mentioned method, the step of, Is the system state,/>And/>System control inputs and outputs, respectively,/>Is the control gain,/>Representing the lumped disturbance.
Preferably, in the step S2, a specific process of designing the second-order adaptive extended state observer is as follows:
Defining a tracking error threshold as A smooth and continuous adaptive strategy is designed, with the following formula:
(2)
In the above-mentioned method, the step of, Is tracking error,/>Is the tracking error threshold,/>Is an exponential function, when/>In the time-course of which the first and second contact surfaces,As an exponential function, when/>，/>As a linear function;
Order the And constructing a second-order self-adaptive extended state observer according to a formula (2), wherein the formula is as follows:
(3)
In the above, define Is a new state variable,/>And/>Are respectively/>And/>Estimate of/>And/>Is the gain.
Preferably, in the step S3, the process of obtaining the global sliding mode control law is as follows:
based on the output of the second-order adaptive extended state observer, a first-order low-pass filter is designed as follows:
(4)
In the above-mentioned method, the step of, Is the gain factor,/>Is the output of the filter; /(I)Is a virtual control law, and is specifically designed as follows:
(5)
defining a new tracking error The formula is as follows:
(6)
Bonding of Design ideal slip form face/>The formula is as follows:
(7)
Based on the cosine function, a smooth and continuous convergence function is designed as follows:
(8)
In the above-mentioned method, the step of, Is convergence time,/>，/>Is the gain factor, according to equations (7) and (8), the global slip plane is designed as follows:
(9)
According to Lyapunov theory, the design equivalent control law is as follows:
(10)
In the above-mentioned method, the step of, Is an equivalent control law;
based on the sign and sine functions, a smooth and continuous saturation function is designed, with the following formula:
(11)
In the above-mentioned method, the step of, Is the gain factor,/>Represents the thickness of the boundary layer;
The sliding mode robust control term is designed as follows in combination with the formula (11):
(12)
In the above-mentioned method, the step of, ，/>，/>And/>Are all odd numbers and satisfy/>；
Combining the formula (10) and the formula (12), constructing a global sliding mode control law as follows:
(13)
In the above-mentioned method, the step of, Representing a global sliding mode control law.
Preferably, in the step S4, the process of obtaining the controller is as follows:
The disturbance estimated by the observer formula (3) is compensated in the global sliding mode control law formula (13), and a controller formula of the electrohydraulic servo system is obtained:
(14)
In the above-mentioned method, the step of, Is the controller formula.
Preferably, in the step S5, the proving process is as follows:
for a control system, if its Lyapunov function satisfies the formula:
(15)
In the above, when Is the gain factor,/>Is the gain factor,/>Is a positive number,/>Is a Lyapunov function,/>Is/>The system is stable for a finite time, and the convergence time is formulated as follows:
(16)
Under the proposed controller formula (14), the electrohydraulic servo system model formula (1) has limited time stability, and the convergence time is as follows:
(17)
In connection with equation (3), the derivative of equation (9) is calculated as follows:
(18)
the following lyapunov function was selected:
(19)
taking the derivative of equation (19) and taking equations (14) and (17) into it yields the equation:
(20)
According to formula (20), the electro-hydraulic servo system has limited time stability under the action of the controller formula (14), and the convergence time is formula (17).
Therefore, the electrohydraulic servo system global sliding mode control method based on the second-order observer has the following advantages:
(1) In the present invention, a second order adaptive extended state observer is provided. Specifically, by analyzing the internal relation between the estimated performance of the extended state observer and the tracking performance of the system, an adaptive strategy based on a tracking error threshold and an exponential function is constructed, and a second-order adaptive extended state observer is designed. The proposed extended state observer can respond to tracking dynamics in real time with a simple structure, and realize the cooperative improvement of the tracking performance of an electrohydraulic servo system and the estimation performance of a second-order self-adaptive extended state observer;
(2) In the invention, based on cosine function and extended state observer output, a convergence strategy and a first order filter are designed to construct a global sliding mode surface, and an equivalent control law is designed. Then, a smooth continuous saturation function is designed based on the cosine function, and a robust control term is constructed. On the basis, a global sliding mode control law is provided to improve global robustness, inhibit estimation errors and ensure limited time control.
The technical scheme of the invention is further described in detail through the drawings and the embodiments.
Drawings
FIG. 1 is a flow chart of a global sliding mode control method of an electrohydraulic servo system based on a second-order observer;
FIG. 2 is a diagram of reference signals in a global sliding mode control method of an electrohydraulic servo system based on a second-order observer;
FIG. 3 is a graph of the tracking response of the system in the global sliding mode control method of the electrohydraulic servo system based on the second-order observer;
FIG. 4 is a graph of tracking error in a global sliding mode control method of an electrohydraulic servo system based on a second-order observer;
FIG. 5 is a control input diagram of a system in an electrohydraulic servo system global sliding mode control method based on a second-order observer.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. The components of the embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations. The specific model specification needs to be determined by selecting the model according to the actual specification and the like of the device, and the specific model selection calculation method adopts the prior art in the field, so detailed description is omitted.
Examples
As shown in fig. 1, the invention provides a global sliding mode control method of an electrohydraulic servo system based on a second-order observer, which comprises the following steps:
S1: an electrohydraulic servo system model is established, and the formula is as follows:
(1)
In the above-mentioned method, the step of, Is the system state,/>And/>System control inputs and outputs, respectively,/>Is the control gain,/>Lumped disturbances are represented, including time-varying parameters, dead zone nonlinearities, internal and external disturbances, etc.
S2: the process of designing the second-order adaptive extended state observer is as follows:
the time-varying characteristic of lumped disturbance presents challenges for high-performance control, the existing extended state observer based on state estimation error ignores the inherent correlation between the estimated performance of the observer and the tracking performance of the system, the estimation process of the extended state observer cannot be adjusted in real time according to the control requirement, and the two performances are difficult to cooperatively improve, so that the tracking error threshold is defined as A smooth and continuous adaptive strategy is designed, with the following formula:
(2)
In the above-mentioned method, the step of, Is tracking error,/>Is the tracking error threshold,/>Is an exponential function, when/>When it is shown that the system has good estimation performance,/>Designed as an exponential function, when/>Indicating that the system may be in a transient state due to time-varying disturbances,/>Designed as a linear function to ensure improved tracking performance by enhancing the estimation capability of the observer;
Order the And according to formula (2), constructing a second-order adaptive extended state observer as follows:
(3)
In the above, define Is a new state variable,/>And/>Are respectively/>And/>Estimate of/>And/>Is gain;
S3: designing equivalent control law and sliding mode robust control items, and providing a global sliding mode control law, wherein the specific process is as follows:
Based on the output of the second-order adaptive extended state observer, the following first-order low-pass filter is designed.
(4)
In the above-mentioned method, the step of,Is the gain factor,/>Is the output of the filter; /(I)Is a virtual control law, and is specifically designed as follows:
(5)
defining a new tracking error The formula is as follows: 0
(6)
Bonding ofDesign ideal slip form face/>The formula is as follows:
(7)
based on the cosine function, a smooth and continuous convergence function is designed:
(8)
In the above-mentioned method, the step of, Is convergence time,/>，/>Is the gain factor, according to equations (7) and (8), the global slip plane is designed as follows:
(9)
According to Lyapunov theory, the design equivalent control law is as follows:
(10)
In the above-mentioned method, the step of, Is an equivalent control law;
based on the sign and sine functions, a smooth and continuous saturation function is designed, with the following formula:
(11)
In the above-mentioned method, the step of, Is the gain factor,/>Represents the thickness of the boundary layer;
The sliding mode robust control term is designed as follows in combination with the formula (11):
(12)
In the above-mentioned method, the step of, ，/>，/>And/>Are all odd numbers and satisfy/>；
Combining the formula (10) and the formula (12), constructing a global sliding mode control law as follows:
(13)
In the above-mentioned method, the step of, Representing a global sliding mode control law.
S4: combining the disturbance estimated in the step S2 with the global sliding mode control law in the step S3 to obtain a controller, wherein the process of obtaining the controller is as follows:
The disturbance estimated by the observer formula (3) is compensated in the global sliding mode control law formula (13), and a controller formula of the electrohydraulic servo system is obtained:
(14)
In the above-mentioned method, the step of, Is the controller formula.
S5: and (2) for the electrohydraulic servo system in the step S1, under the action of a controller, proving the limited time stability of the electrohydraulic servo system, wherein the specific proving process is as follows:
for a control system, when its Lyapunov function satisfies the formula:
(15)
In the above, when Is the gain factor,/>Is the gain factor,/>Is a positive number,/>Is a Lyapunov function,/>Is/>Then the system is stable over a finite time, the convergence time is formulated as follows:
(16)
Under the proposed controller formula (14), the electrohydraulic servo system model formula (1) has limited time stability, and the convergence time is as follows:
(17)
In connection with equation (3), the derivative of equation (9) is calculated as follows:
(18)
the following lyapunov function was selected:
(19)
taking the derivative of equation (19) and taking equations (14) and (17) into it yields the equation:
(20)
according to the formula (20), the electrohydraulic servo system has limited time stability under the action of the controller formula (14), and the convergence time is shown as the formula (17).
The specific experimental process is as follows: the electrohydraulic servo system is specifically selected as a hydraulic jumbolter system, and the effectiveness of the method is verified by performing experiments;
reference signals of the system as shown in fig. 2, the control parameters are set as follows: sampling time ，/>，，/>，/>，/>，/>，/>，/>，/>。
The tracking response of the system is shown in figure 3. Accordingly, fig. 4 shows the response trajectory of the tracking error, and fig. 5 shows the control input of the system. The above results verify that the proposed control method can achieve accurate tracking performance with lower control input, thereby verifying the effectiveness of the proposed method;
finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention and not for limiting it, and although the present invention has been described in detail with reference to the preferred embodiments, it will be understood by those skilled in the art that: the technical scheme of the invention can be modified or replaced by the same, and the modified technical scheme cannot deviate from the spirit and scope of the technical scheme of the invention.
Claims (1)
1. The method for controlling the global sliding mode of the electrohydraulic servo system based on the second-order observer is characterized by comprising the following steps of: the method comprises the following steps:
s1: establishing an electrohydraulic servo system model;
The model of the electrohydraulic servo system is as follows:
(1)
In the above-mentioned method, the step of, Is the system state,/>And/>System control inputs and outputs, respectively,/>It is the control gain that is used to control the gain,Representing the lumped disturbance;
S2: the second-order self-adaptive extended state observer is designed, and the specific process is as follows:
Defining a tracking error threshold as A smooth and continuous adaptive strategy is designed, with the following formula:
(2)
In the above-mentioned method, the step of, Is tracking error,/>Is the tracking error threshold,/>Is an exponential function, when/>In the time-course of which the first and second contact surfaces,As an exponential function, when/>，/>As a linear function;
Order the And constructing a second-order self-adaptive extended state observer according to a formula (2), wherein the formula is as follows:
(3)
In the above, define Is a new state variable,/>And/>Are respectively/>And/>Estimate of/>And/>Is gain;
s3: providing an equivalent control law and a sliding mode robust control term to obtain a global sliding mode control law;
The process of obtaining the global sliding mode control law is as follows:
based on the output of the second-order adaptive extended state observer, a first-order low-pass filter is designed as follows:
(4)
In the above-mentioned method, the step of, Is the gain factor,/>Is the output of the filter; /(I)Is a virtual control law, and is specifically designed as follows:
(5)
defining a new tracking error The formula is as follows:
(6)
Bonding of Design ideal slip form face/>The formula is as follows:
(7)
Based on the cosine function, a smooth and continuous convergence function is designed as follows:
(8)
In the above-mentioned method, the step of, Is convergence time,/>，/>Is the gain factor, according to equations (7) and (8), the global slip plane is designed as follows:
(9)
According to Lyapunov theory, the design equivalent control law is as follows:
(10)
In the above-mentioned method, the step of, Is an equivalent control law;
based on the sign and sine functions, a smooth and continuous saturation function is designed, with the following formula:
(11)
In the above-mentioned method, the step of, Is the gain factor,/>Represents the thickness of the boundary layer;
The sliding mode robust control term is designed as follows in combination with the formula (11):
(12)
In the above-mentioned method, the step of, ，/>，/>And/>Are all odd numbers and satisfy/>；
Combining the formula (10) and the formula (12), constructing a global sliding mode control law as follows:
(13)
In the above-mentioned method, the step of, Representing a global sliding mode control law;
S4: combining the disturbance estimated by the observer with the global sliding mode control law in the step S3 to obtain a controller;
The process of obtaining the controller is as follows:
The disturbance estimated by the observer formula (3) is compensated in the global sliding mode control law formula (13), and a controller formula of the electrohydraulic servo system is obtained:
(14)
In the above-mentioned method, the step of, Is a controller formula;
S5: aiming at the electrohydraulic servo system in the step S1, a limited time stability proving process of the electrohydraulic servo system is given under the action of a controller;
The proving process is as follows:
for a control system, if its Lyapunov function satisfies the formula:
(15)
In the above, when Is the gain factor,/>Is the gain factor,/>Is a positive number,/>Is a Lyapunov function,/>Is/>The system is stable for a finite time, and the convergence time is formulated as follows:
(16)
Under the proposed controller formula (14), the electrohydraulic servo system model formula (1) has limited time stability, and the convergence time is as follows:
(17)
In connection with equation (3), the derivative of equation (9) is calculated as follows:
(18)
the following lyapunov function was selected:
(19)
taking the derivative of equation (19) and taking equations (14) and (17) into it yields the equation:
(20)
According to formula (20), the electro-hydraulic servo system has limited time stability under the action of the controller formula (14), and the convergence time is formula (17).
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| CN111338209A (en) * | 2020-03-03 | 2020-06-26 | 南京理工大学 | Electro-hydraulic servo system self-adaptive control method based on extended disturbance observer |
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| CN114692429A (en) * | 2022-04-22 | 2022-07-01 | 山东科技大学 | Control method, equipment and medium of electro-hydraulic servo system |
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| CN110572093A (en) * | 2019-08-29 | 2019-12-13 | 南京理工大学 | ARC control method based on motor position servo system expected track and interference compensation |
| CN110716506A (en) * | 2019-11-08 | 2020-01-21 | 电子科技大学 | Servo system position tracking control method based on mixed sliding mode control |
| CN111338209A (en) * | 2020-03-03 | 2020-06-26 | 南京理工大学 | Electro-hydraulic servo system self-adaptive control method based on extended disturbance observer |
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