CN109739248B - Ship-borne three-degree-of-freedom parallel stable platform stability control method based on ADRC - Google Patents
Ship-borne three-degree-of-freedom parallel stable platform stability control method based on ADRC Download PDFInfo
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Abstract
The invention discloses a stability control method of a ship-borne three-degree-of-freedom parallel stable platform based on ADRC, which has the advantage of not depending on an accurate mathematical model of the ship-borne three-degree-of-freedom parallel stable platform, effectively solves the problem of uncertain disturbance of the platform caused by ship shaking motion due to uncertain dynamic and frequently-changed stormy waves of the ship-borne three-degree-of-freedom parallel stable platform, and is simple in design of a control scheme and easy for engineering realization. The method uses the extended state observer to well estimate the dynamic uncertainty and the disturbance uncertainty of the ship-borne three-degree-of-freedom parallel stable platform, is used for inhibiting the disturbance, and particularly has good control effect on a large-load object with unpredictable marine environment disturbance, such as the ship-borne three-degree-of-freedom parallel stable platform. The good estimation precision of the extended state observer not only effectively improves the stability control precision of the shipborne three-degree-of-freedom parallel stable platform, but also can save sensors and reduce the cost of a control system.
Description
Technical Field
The invention relates to the field of ship and ocean engineering, in particular to a ship-borne three-degree-of-freedom (rolling, pitching and heaving) parallel stable platform stability control method based on ADRC (active disturbance rejection control technology).
Background
The marine vessel is disturbed by the marine environment to generate swaying motion (rolling, yawing, pitching and heaving), which affects the normal operation of the equipment on the vessel. Usually, the motions of three degrees of freedom of the ship, such as yawing, surging and surging, can be compensated through a dynamic positioning system of the ship, and the motions of yawing, surging and surging need to be compensated through an auxiliary system. The ship-borne three-degree-of-freedom (rolling, pitching and heaving) parallel stable platform can isolate the influence of the motion and the attitude of a ship, so that the upper supporting surface of the ship-borne three-degree-of-freedom parallel stable platform keeps relatively stable relative to an inertial space under the influence of disturbance of an ocean environment, and the normal and stable operation of ship equipment on the supporting surface is ensured just like on the land. The shipborne three-degree-of-freedom parallel stable platform is widely applied to the fields of modern military and civil use and plays an increasingly important role.
The marine environment is complex and changeable, the problem that disturbance uncertainty is caused to the ship-mounted platform by ship swaying motion caused by uncertain dynamic and frequently-changing stormy waves obviously exists in the ship-mounted parallel platform, and the stable control method with anti-interference capability and robustness is necessary. A master thesis of Li Avenu of Jiangsu science and technology university, namely 'research on parallel ship-borne stable platforms' (2013), designs a three-degree-of-freedom ship-borne three-degree-of-freedom parallel stable platform stable controller by using a classical PID control method, and carries out simulation verification; a fuzzy adaptive PID control method is used for designing a three-degree-of-freedom shipborne three-degree-of-freedom parallel stable platform stability controller to improve the control precision in 'parallel three-degree-of-freedom wave compensation stable platform key technology research' (2013) of a Master thesis Wang Jiangsu science and technology university; the master thesis of Sushie of Yanshan university "parallel connection four-degree-of-freedom ship-borne stable platform characteristics and control research" (2014) designs a feedforward PID stable controller aiming at a four-degree-of-freedom ship-borne three-degree-of-freedom parallel connection stable platform, and verifies the effectiveness of the controller under the condition of middle sea through simulink simulation; a paper published by Wang Aijun of the fertilizer industry university in the journal of engineering design, namely MATLAB-based 3-RPS parallel mechanism control system simulation (2016, 23 (02): 172-plus 180), aims at a parallel three-free stable platform, designs a sliding mode variable structure stable controller (SMC), and carries out simulation comparison with a PID (proportion integration differentiation) controller, and the result shows that the SMC controller has the advantages of high tracking precision, response speed, small steady-state error and the like. However, none of the above documents comprehensively considers the uncertainty of the dynamics of the onboard three-degree-of-freedom parallel stable platform and the uncertainty of the disturbance of the onboard platform caused by the ship swaying motion caused by the constantly changing wind and wave.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a stability control method of a ship-borne three-degree-of-freedom parallel stable platform based on ADRC, which can solve the problem of uncertain disturbance of the platform caused by ship shaking motion due to uncertain dynamic and frequently-changing stormy waves of the ship-borne three-degree-of-freedom parallel stable platform, improve the anti-interference capability and enhance the system robustness.
In order to achieve the purpose, the technical scheme of the invention is as follows: a ship-borne three-degree-of-freedom parallel stable platform stability control method based on ADRC is characterized in that a dynamic model of the ship-borne three-degree-of-freedom parallel stable platform is described by the following state space expression:
in the formula, x1The three-dimensional pose signal vector of the ship-borne three-degree-of-freedom parallel stable platform consists of a roll angle alpha, a pitch angle beta and a heave displacement z; x is the number of2Is a three-dimensional velocity signal vector of a ship-borne three-degree-of-freedom parallel stable platform, which is determined by the roll angular velocity
Pitch angular velocity
And heave displacement velocity
Composition is carried out; u is a three-dimensional control input vector, and the driving force tau is generated by three hydraulic cylinders of the ship-borne three-degree-of-freedom parallel stable platform1、τ2、τ3Composition is carried out; y is x1The three-dimensional output vector is the actual pose vector of the shipborne three-degree-of-freedom parallel stable platform; g (x) is a 3 x 3 dimensional control gain matrix comprising a reversible nominal gain matrix
And an uncertainty gain matrix Δ g (x), i.e.
(x) is a three-dimensional vector function which represents the dynamic state of the ship-borne three-degree-of-freedom parallel stable platform and comprises the nominal dynamic state of the ship-borne three-degree-of-freedom parallel stable platform
And uncertain dynamics Δ f (x), i.e.
Considering that a ship in the sea is influenced by disturbance of the marine environment to generate ship swaying motion, and a three-dimensional vector ζ (t) represents uncertain disturbance of the ship swaying motion on the ship-mounted three-degree-of-freedom parallel stable platform, a dynamic model (1) of the ship-mounted three-degree-of-freedom parallel stable platform is further represented as follows:
the method comprises the following steps:
A. regarding uncertain items delta f (x), delta g (x), u and zeta (t) existing in a dynamic model (2) of the shipborne three-degree-of-freedom parallel stable platform as a total disturbance vector d (x), namely d (x) delta f (x) + delta g (x) u + zeta (t), and expanding the total disturbance vector into a new three-dimensional state vector x of the shipborne three-degree-of-freedom parallel stable platform3Is recorded as x3D (x), and
w (t) represents the rate of change of the total perturbation vector, and is an unknown, bounded vector function. Then the dynamic model (2) of the shipborne three-degree-of-freedom parallel stable platform is expanded into:
B. the extended state observer is designed as follows:
wherein e is z1-y；z1、z2Respectively, a ship-borne three-degree-of-freedom parallel stable platform state vector x1、x2(ii) an estimate of (d); z is a radical of3Is the total disturbance vector x3(ii) an estimate of (d); beta is a01、β02、β03Is a design parameter of the extended state observer;
the extended state observer obtains an estimation z of a state vector of the shipborne three-degree-of-freedom parallel stable platform by utilizing a control input vector u and an actual pose output vector y of the shipborne three-degree-of-freedom parallel stable platform1、z2And estimate z of the total disturbance vector3。
Design parameter beta01、β02、β03The selection is divided into three steps:
b1, the extended state observer is designed to be a Lorberg-like nonlinear extended state observer, so first assume g in the extended state observer (4)i(e) The extended state observer (4) becomes the following form:
expanding the parameter beta of the state observer by adopting a pole allocation method01、β02、β03The initial design of (1). Subtracting the formula (3) from the formula (5) to obtain an error dynamic equation of the extended state observer:
in the formula:
z＝[z1 z2 z3]T
x＝[x1 x2 x3]T
A*＝A-LC
C＝[1 0 0]
b2, setting the control matrix A in the error dynamic equation (6) of the extended state observer*Is p1、p2、p3Then, the following formula:
determining extended state observer design parameter beta01、β02、β03The value of (c):
b3 at the determined design parameter beta01、β02、β03Carrying out simulation test on the extended state observer, and if the simulation result shows that z is zero1、z2、z3Has accurately estimatedState vector x of three-freedom parallel stable platform carried by ship1、x2And expanded state vector x3Design parameter β01、β02、β03Selected as the determined value; otherwise, returning to step B2, resetting the control matrix A*To re-determine the design parameter beta01、β02、β03Until the extended state observer accurately estimates the state vector x of the shipborne three-degree-of-freedom parallel stable platform1、x2And total disturbance vector x3Until now.
C. The nonlinear state error feedback control law is designed as follows:
in the formula, e1＝yd-z1，e2＝-z2；ydThe expected pose signal vector of the shipborne three-degree-of-freedom parallel stable platform is obtained; beta is a1Is the proportional gain, beta2Is the differential gain; fal (-) is a nonlinear function:
wherein, δ, a1、a2Parameters are designed for positive controllers.
The nonlinear state error feedback control law is designed to be a nonlinear combination (5) of pose error vector signals and speed vector signal estimation of the ship-borne three-degree-of-freedom parallel stable platform, and errors between the actual pose and the expected pose of the ship-borne three-degree-of-freedom parallel stable platform can be effectively eliminated.
δ、a1、a2Taking an empirical value: δ 0.01, a1＝0.5，a20.25. Parameter beta1、β2The method has a relatively clear physical meaning, and the setting process is as follows:
c1, first, taking differential gain beta2When being equal to 0, i.e. goBy eliminating differential action, proportional gain beta1Taking the smaller value as the value, and then carrying out simulation test on the stability control of the shipborne three-degree-of-freedom stable platform; and gradually increasing the proportional gain beta1Until the simulation curve reaches the constant amplitude oscillation state.
C2 recording proportional gain beta under the equal amplitude oscillation state1And the oscillation period T of the response curvemTaking beta2＝0.125Tm. If the simulation result shows that the error between the actual pose and the expected pose of the shipborne three-degree-of-freedom parallel stable platform is controlled within the allowable range, the beta is finished1、β2Setting; otherwise, returning to the step C1, and re-setting the parameters until the error between the actual pose and the expected pose of the shipborne three-degree-of-freedom parallel stable platform reaches the allowable range.
D. Designing a disturbance compensation control law:
the disturbance compensation control law adopts a feedforward mode and utilizes the total disturbance estimation z of the extended state observer3The dynamic uncertainty of the ship-borne three-degree-of-freedom parallel stable platform and the disturbance uncertainty of the platform caused by the ship shaking motion caused by wind and waves are compensated in real time.
E. Comprehensive nonlinear state error feedback control law u0And the disturbance compensation control law u1Obtaining a stability control input u of the shipborne three-degree-of-freedom parallel stable platform:
and the control input u enables the attitude of the shipborne three-degree-of-freedom parallel stable platform to keep a relatively stable state in an inertial space.
Compared with the prior art, the invention has the following beneficial effects:
1. the ADRC control technology is adopted, so that the method has the advantage of being independent of a precise mathematical model of the shipborne three-degree-of-freedom parallel stable platform, effectively solves the problem that the ship shaking motion caused by uncertain dynamics and frequently-changed stormy waves of the shipborne three-degree-of-freedom parallel stable platform causes uncertain disturbance to the platform, and has excellent anti-interference capability and strong robustness, so that the shipborne three-degree-of-freedom parallel stable platform still has a good control effect under the condition of medium and high sea; and the method has simple controller design and is easy for engineering realization.
2. The method uses the extended state observer to well estimate the dynamic uncertainty and the disturbance uncertainty of the ship-borne three-degree-of-freedom parallel stable platform, is used for inhibiting the disturbance, and particularly has good control effect on a large-load object with unpredictable marine environment disturbance, such as the ship-borne three-degree-of-freedom parallel stable platform. The good estimation precision of the extended state observer not only effectively improves the stability control precision of the shipborne three-degree-of-freedom parallel stable platform, but also saves sensors and reduces the cost of a control system by using the extended state observer.
Drawings
Fig. 1 is a schematic diagram of a stability control method of a ship-borne three-degree-of-freedom parallel stable platform based on ADRC.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
As shown in fig. 1, the principle of the stability control method of the onboard three-degree-of-freedom parallel stable platform based on the ADRC is as follows: the shipborne three-degree-of-freedom parallel stable platform is a controlled object, an input signal u of the shipborne three-degree-of-freedom parallel stable platform is a control input of the shipborne three-degree-of-freedom parallel stable platform, an output signal y of the shipborne three-degree-of-freedom parallel stable platform is an actual pose signal of the shipborne three-degree-of-freedom parallel stable platform and is influenced by external disturbance zeta (t), and input and output signals of the shipborne three-degree-of-freedom parallel stable platform are input to an extended state observer; the extended state observer obtains the estimated z of the pose state and the speed state of the shipborne three-degree-of-freedom parallel stable platform according to the input u and the output y of the shipborne three-degree-of-freedom parallel stable platform1、z2And estimate z of the total disturbance3(ii) a Estimation z of pose state of parallel stable platform of shipborne three-degree-of-freedom parallel stable platform1The expected pose signal y is fed back to the reference input end of the parallel stable platform of the shipborne three-degree-of-freedom parallel stable platform and is connected with the parallel stable platform of the shipborne three-degree-of-freedom parallel stable platform in paralleldComparing to form a pose deviation signal e1＝yd-z1The speed state of the ship-borne three-freedom-degree parallel stable platform is estimated and fed back, namely e2＝-z2Is input to the nonlinear state error feedback control law u0The nonlinear state error feedback control law is e1And e2The nonlinear combination of the three-degree-of-freedom parallel stable platform is used for eliminating the deviation between the actual pose and the expected pose of the ship-borne three-degree-of-freedom parallel stable platform; estimate z of total disturbance3Feedforward input to disturbance compensation control law u1The device is used for compensating the total disturbance d (x) suffered by the ship-borne three-degree-of-freedom parallel stable platform; comprehensive nonlinear state error feedback control law u0And the disturbance compensation control law u1And obtaining a final control input u, and inputting the final control input u to the shipborne three-degree-of-freedom parallel stable platform so as to enable the upper supporting surface of the shipborne three-degree-of-freedom parallel stable platform to keep a relatively stable state in an inertial space.
The present invention is not limited to the embodiment, and any equivalent idea or change within the technical scope of the present invention is to be regarded as the protection scope of the present invention.
Claims (1)
1. A ship-borne three-degree-of-freedom parallel stable platform stability control method based on ADRC is characterized in that: the dynamic model of the shipborne three-degree-of-freedom parallel stable platform is described by the following state space expression:
in the formula, x1The three-dimensional pose signal vector of the ship-borne three-degree-of-freedom parallel stable platform consists of a roll angle alpha, a pitch angle beta and a heave displacement z; x is the number of2Is a three-dimensional velocity signal vector of a ship-borne three-degree-of-freedom parallel stable platform, which is determined by the roll angular velocity
Pitch angular velocity
And heave displacement velocity
Composition is carried out; u is a three-dimensional control input vector, and the driving force tau is generated by three hydraulic cylinders of the ship-borne three-degree-of-freedom parallel stable platform1、τ2、τ3Composition is carried out; y is x1The three-dimensional output vector is the actual pose vector of the shipborne three-degree-of-freedom parallel stable platform; g (x) is a 3 x 3 dimensional control gain matrix comprising a reversible nominal gain matrix
And an uncertainty gain matrix Δ g (x), i.e.
(x) is a three-dimensional vector function which represents the dynamic state of the ship-borne three-degree-of-freedom parallel stable platform and comprises the nominal dynamic state of the ship-borne three-degree-of-freedom parallel stable platform
And uncertain dynamics Δ f (x), i.e.
Considering that a ship in the sea is influenced by disturbance of the marine environment to generate ship swaying motion, and a three-dimensional vector ζ (t) represents uncertain disturbance of the ship swaying motion on the ship-mounted three-degree-of-freedom parallel stable platform, a dynamic model (1) of the ship-mounted three-degree-of-freedom parallel stable platform is further represented as follows:
the method comprises the following steps:
A. regarding uncertain items delta f (x), delta g (x), u and zeta (t) existing in a dynamic model (2) of the shipborne three-degree-of-freedom parallel stable platform as a total disturbance vector d (x), namely d (x) delta f (x) + delta g (x) u + zeta (t), and expanding the total disturbance vector into a new three-dimensional state vector x of the shipborne three-degree-of-freedom parallel stable platform3Is recorded as x3D (x), and
w (t) represents the rate of change of the total perturbation vector, which is an unknown bounded vector function; then the dynamic model (2) of the shipborne three-degree-of-freedom parallel stable platform is expanded into:
B. the extended state observer is designed as follows:
wherein e is z1-y；z1、z2Respectively, a ship-borne three-degree-of-freedom parallel stable platform state vector x1、x2(ii) an estimate of (d); z is a radical of3Is the total disturbance vector x3(ii) an estimate of (d); beta is a01、β02、β03Is a design parameter of the extended state observer;
the extended state observer obtains the shipborne three-degree-of-freedom parallel stability by utilizing the control input vector u and the actual pose output vector y of the shipborne three-degree-of-freedom parallel stability platformEstimation of platform State vector z1、z2And estimate z of the total disturbance vector3；
Design parameter beta01、β02、β03The selection is divided into three steps:
b1, the extended state observer is designed to be a Lorberg-like nonlinear extended state observer, so first assume g in the extended state observer (4)i(e) The extended state observer (4) becomes the following form:
expanding the parameter beta of the state observer by adopting a pole allocation method01、β02、β03The initial design of (2); subtracting the formula (3) from the formula (5) to obtain an error dynamic equation of the extended state observer:
in the formula:
z＝[z1 z2 z3]T
x＝[x1 x2 x3]T
A*＝A-LC
C＝[1 0 0]
b2, setting the control matrix A in the error dynamic equation (6) of the extended state observer*Is p1、p2、p3Then, the following formula:
determining extended state observer design parameter beta01、β02、β03The value of (c):
b3 at the determined design parameter beta01、β02、β03Carrying out simulation test on the extended state observer, and if the simulation result shows that z is zero1、z2、z3Accurately estimating state vector x of shipborne three-degree-of-freedom parallel stable platform1、x2And expanded state vector x3Design parameter β01、β02、β03Selected as the determined value; otherwise, returning to step B2, resetting the control matrix A*To re-determine the design parameter beta01、β02、β03Until the extended state observer accurately estimates the state vector x of the shipborne three-degree-of-freedom parallel stable platform1、x2And total disturbance vector x3Until the end;
C. the nonlinear state error feedback control law is designed as follows:
in the formula, e1＝yd-z1，e2＝-z2；ydThe expected pose signal vector of the shipborne three-degree-of-freedom parallel stable platform is obtained; beta is a1Is the proportional gain, beta2Is the differential gain; fal (-) is a nonlinear function:
wherein, δ, a1、a2Designing parameters for a positive controller;
the nonlinear state error feedback control law is designed as a nonlinear combination (5) of pose error vector signals and speed vector signal estimation of the ship-borne three-degree-of-freedom parallel stable platform, and errors between the actual pose and the expected pose of the ship-borne three-degree-of-freedom parallel stable platform can be effectively eliminated;
δ、a1、a2taking an empirical value: δ 0.01, a1＝0.5，a20.25; parameter beta1、β2The method has a relatively clear physical meaning, and the setting process is as follows:
c1, first, taking differential gain beta2When the differential action is 0, the differential action is removed, and then a simulation test is carried out on the stability control of the shipborne three-degree-of-freedom stable platform; and gradually increasing the proportional gain beta1Until the simulation curve reaches a constant amplitude oscillation state;
c2 recording proportional gain beta under the equal amplitude oscillation state1And the oscillation period T of the response curvemTaking beta2＝0.125Tm(ii) a If the simulation result shows that the error between the actual pose and the expected pose of the shipborne three-degree-of-freedom parallel stable platform is controlled within the allowable range, the beta is finished1、β2Setting; otherwise, returning to the step C1, and re-setting the parameters until the error between the actual pose and the expected pose of the shipborne three-degree-of-freedom parallel stable platform reaches the allowable range;
D. designing a disturbance compensation control law:
the disturbance compensation control law adopts a feedforward mode and utilizes the total disturbance estimation z of the extended state observer3Compensating dynamic uncertainty of the ship-borne three-degree-of-freedom parallel stable platform and disturbance uncertainty of the platform caused by ship shaking motion caused by wind waves in real time;
E. comprehensive nonlinear state error feedback control law u0And the disturbance compensation control law u1Obtaining a stability control input u of the shipborne three-degree-of-freedom parallel stable platform:
and the control input u enables the attitude of the shipborne three-degree-of-freedom parallel stable platform to keep a stable state in an inertial space.
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| CN110687783A (en) * | 2019-09-10 | 2020-01-14 | 中国航空工业集团公司洛阳电光设备研究所 | Disturbance observation and compensation method for airborne photoelectric stable platform |
| CN112286042A (en) * | 2020-09-14 | 2021-01-29 | 西安工业大学 | Photoelectric stabilized sighting platform three-step linear control method based on extended state observer |
| CN113625546B (en) * | 2021-08-10 | 2024-03-05 | 大连海事大学 | Stabilizing control anti-saturation method for shipborne stabilized platform |
| CN113955032B (en) * | 2021-11-15 | 2024-02-02 | 上海新纪元机器人有限公司 | Force control method and system for actively reducing shaking and self-balancing device |
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