CN110376902A - A kind of design method of Underactuated Mechanical Systems Servo Restriction tracking control unit - Google Patents
A kind of design method of Underactuated Mechanical Systems Servo Restriction tracking control unit Download PDFInfo
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Abstract
The present invention provides a kind of design methods of Underactuated Mechanical Systems Servo Restriction tracking control unit, comprising the following steps: the kinetic model of Underactuated Mechanical Systems of the building containing parameter uncertainty, and the uncertainty in the system is effectively decomposed；The tracking performance requirement that the system to be realized is considered as Servo Restriction, constructs the second order form of Servo Restriction；Kinetic model and second order Servo Restriction design adaptive law robust controller based on the building；Stability analysis is carried out to the adaptive law robust controller of building；Major parameter in the adaptive law robust controller of building is adjusted, and analysis and Control effect.The design of Underactuated Mechanical Systems constraint tracking control unit of the invention can effectively deal with the influence of system parameter uncertainty and external interference, while making system fast and stable and accurately tracking given tracking performance requirement.
Description
Technical Field
The invention relates to the field of mechanical system dynamics control, in particular to a design method of an under-actuated mechanical system servo constraint tracking controller.
Background
The under-actuated system is a nonlinear system with the number of independent control variables of the system smaller than the number of degrees of freedom of the system, and is superior to a completely-actuated system in the aspects of saving energy, reducing manufacturing cost, lightening weight, enhancing system flexibility and the like. The under-actuated system has a simple structure and is convenient for integral dynamics analysis and test. Meanwhile, due to the reasons of high nonlinearity of the system, parameter perturbation, multi-target control requirements, limited control quantity and the like, the under-actuated system is complex enough, and is convenient for researching and verifying the effectiveness of various algorithms. Bridge cranes, inverted pendulum systems, vertical take-off and landing aircraft, flexible manipulators, and the like are typical under-actuated systems.
In contrast, the difficulty of controlling an under-actuated system is much higher than that of a fully actuated system, and theoretically, the system is expected to be fully actuated, but in practice, in many cases, due to physical and economic reasons, many systems cannot achieve full actuation, and meanwhile, due to the fact that the number of control variables of the under-actuated system is small, the under-actuated system has the advantages of low cost and manufacturing cost, high flexibility, weight reduction, energy consumption reduction and the like in control, so that the under-actuated system is required to be used in many cases. In addition, some fully-actuated systems automatically switch to under-actuated systems when they fail. In a certain sense, the under-actuated system can be regarded as the fault-tolerant situation of the full-actuated system, and has application value in practical application, both from the aspect of cost and the aspect of result. Therefore, research into under-actuated systems is necessary.
For the control problem of an under-actuated mechanical system, researchers at home and abroad successively develop various control methods, and obtain certain effects, which are typically PID control, linear feedback control, LQR (linear quadratic regulator) control, robust control and the like. The system is easy to vibrate under nonlinear disturbance by PID control and linear feedback control, the robustness of LQR control is not strong, and overshoot and unnecessary control consumption are easy to generate by robust control.
Therefore, it is highly desirable to provide a control scheme with high stability and robustness.
Disclosure of Invention
Aiming at the technical problems, the invention provides a design method of an under-actuated mechanical system servo constraint tracking controller, which can effectively process the influence of uncertainty of system parameters and external interference, and simultaneously enables the system to quickly, stably and accurately control torque output.
The technical scheme adopted by the invention is as follows:
a design method of an under-actuated mechanical system servo constraint tracking controller comprises the following steps:
constructing an under-actuated mechanical system dynamics model containing parameter uncertainty, and effectively decomposing the uncertainty in the system;
the tracking performance requirement to be realized by the under-actuated mechanical system is regarded as servo constraint, and the second-order expression form of the servo constraint is obtained by derivation of the constraint;
a certain assumption requirement is put forward aiming at the characteristics of an under-actuated mechanical system and the servo constraint characteristics;
designing a self-adaptive robust constraint tracking controller based on the established dynamic model of the under-actuated system, second-order servo constraint and the provided hypothesis requirement, wherein the self-adaptive law can be adjusted in real time according to the tracking error;
performing stability analysis on the constructed adaptive robust controller;
and adjusting main parameters in the constructed adaptive robust controller, and analyzing the control effect.
Optionally, the constructing a dynamic model of the under-actuated system with parameter uncertainty includes:
constructing a dynamic model of the under-actuated mechanical system shown in the following equation (1):
wherein t is time, q is the generalized coordinates of the system,in order to be a broad-sense speed of the system,the method comprises the following steps of taking generalized acceleration of a system, delta as an uncertainty parameter of the system, M as an inertia matrix of the system, C as a centrifugal force/Coriolis force matrix of the system, G as a gravity term matrix of the system, tau as control input of the system, and B as a control input matrix of the system;
decomposing an uncertainty matrix in the constructed dynamics model of the under-actuated system according to the following equations (2) to (5):
wherein,the deterministic portions of the inertia matrix, the Coriolis force/centrifugal force matrix, the gravity matrix and the control input matrix of the under-actuated system are Delta M (q, delta, t),Δ G (q, δ, t), Δ B (q, δ, t) are the uncertainty parts of the inertia matrix, coriolis force/centrifugal force matrix, gravity matrix, control input matrix of the under-actuated system.
Order to Then
Δχ(q,δ,t)＝χ(q,t)Φ(q,δ,t) (6)
Based on matrixWe decompose Φ into two parts:
whereinAndthe matrices can be selected as:
for the same reason, based on matricesWe decompose the matrices Δ C, Δ G, Δ B into two parts:
whereinAndandandthe matrices can be selected as:
optionally, regarding the tracking performance requirement to be achieved by the under-actuated mechanical system as a servo constraint, deriving the constraint to obtain a second-order expression form of the servo constraint:
the target performance requirement of the under-actuated system is written in the form shown in equation (19) below:
the following equations (20) and (21) are obtained by suitably sorting and deriving equation (19):
wherein A is a constraint matrix; c is a first order constraint vector; b is a second order constraint vector.
Optionally, a certain assumption requirement is proposed for the under-actuated mechanical system characteristic and the servo constraint characteristic, and specifically includes:
1) the servo constraint equation is solvable: equation ofAre consistent.
2) Controllability of the under-actuated system: equation ofIs in agreement, wherein
3) Matrix arrayIs reversible.
4) Order toThen there is a constant pΨ>-1 such that:
5) for a given constant positive definite matrix Q, there are constantsλ>0 is such that
6) There is a vector η sum functionSo that
Simultaneous functionCan be linearly decomposed into:
optionally, designing an adaptive robust constraint tracking controller based on the constructed under-actuated system dynamic model and second-order servo constraint and the proposed hypothesis requirement, wherein adaptive parameters can be adjusted in real time according to tracking errors;
constructing a controller shown in the following equation (26) based on the constructed dynamic model and the second-order constraint form:
wherein,
wherein,
p3is used for solving the problem that the system has uncertainty, the theta function is the upper bound of the uncertainty of the system,and e is a control precision adjusting parameter for the adaptive parameter.
The adaptive parameterThe adaptation law is determined as shown by equation (30) below:
therein, ζ0,ζ1,ζ2Parameters are adjusted for the adaptive law.
Optionally, the performing the stability analysis on the constructed adaptive robust controller includes:
the final stable bound of the constructed adaptive robust controller is analyzed using the lyapunov function as shown in equation (31) below:
where Q is a positive definite matrix, ρΨIs an arbitrary constant greater than-1, and η is an upper bound parameter of uncertainty for an under-actuated mechanical system.
Optionally, the analyzing the final stable boundary of the constructed adaptive law robust controller by using the lyapunov function shown in equation (31) specifically includes:
calculation of equation (31) yields the following formula (32):
wherein,
and obtaining a balance parameter R of the final consistent and stable limit of the under-actuated mechanical system based on the formula (32), as shown in the following formula (33):
and (3) obtaining the final consistent stable limit of the active anti-roll system based on the formula (32), as shown in the following formula (34):
wherein,da lower limit value representing the size of the final stable limit of the under-actuated mechanical system, λmin(Q) represents the minimum eigenvalue, λ, of the positive definite matrix Qmax(Q) represents the maximum eigenvalue of the positive definite matrix Q;
according to the lyapunov stability theory, the time for the active anti-roll system to reach the final stable limit can be obtained, as shown in the following formula (35):
wherein T represents the time for the under-actuated mechanical system to reach the final consistent stable limit, r represents the initial state of the system,is arbitrarily greater thandPositive number of (c).
Optionally, the adjusting main parameters in the constructed adaptive robust controller, and analyzing the control effect includes:
adjusting initial condition incompatible compensation parameters, adaptive law adjustment parameters and control precision adjustment parameters in the constructed adaptive law robust controller;
and analyzing whether the constraint tracking error of the system meets the preset error requirement or not based on the adjusted parameters.
The invention has the beneficial effects that:
the design method of the servo constraint tracking controller of the under-actuated mechanical system comprises the following steps of firstly constructing a dynamic model of the under-actuated mechanical system with parameter uncertainty, and effectively decomposing the uncertainty in the system; secondly, regarding the tracking performance requirement to be realized by the system as servo constraint, and constructing a second-order form of the servo constraint; then, designing an adaptive robust controller based on the constructed dynamic model and second-order servo constraint; finally, performing stability analysis on the constructed adaptive robust controller; and adjusting main parameters in the constructed adaptive robust controller, and analyzing the control effect. The design of the under-actuated mechanical system constraint tracking controller can effectively process the influence of uncertainty of system parameters and external interference, and simultaneously, the system can quickly and stably track the given tracking performance requirement accurately.
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Fig. 1 is a schematic flow chart of a design method of an under-actuated mechanical system servo constraint tracking controller according to an embodiment of the present invention;
fig. 2 is a schematic overall structure diagram of a controller according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of the overall structure of a trolley-swing link system provided in the embodiment of the present invention;
fig. 4 is a schematic diagram illustrating a simulation of the stability of the trolley-swing link system according to the embodiment of the present invention.
Detailed Description
In order to make the technical problems, technical solutions and advantages of the present invention more apparent, the following detailed description is given with reference to the accompanying drawings and specific embodiments.
Fig. 1 is a schematic flow chart of a design method of an under-actuated mechanical system servo constraint tracking controller according to an embodiment of the present invention. As shown in fig. 1, a method for designing an under-actuated mechanical system servo constraint tracking controller according to an embodiment of the present invention includes the following steps:
s101, constructing a dynamic model of the under-actuated mechanical system with parameter uncertainty;
s102, analyzing uncertainty parameters in the system and performing effective decomposition;
s103, providing a target performance constraint requirement of the under-actuated system, and constructing a second-order constraint form of the servo constraint;
s104, aiming at the system characteristics and the servo constraint characteristics, providing certain assumption requirements;
s105, designing a self-adaptive robust controller based on the constructed dynamic model and the second-order constraint form, wherein self-adaptive parameters can be adjusted in real time according to tracking errors;
s106, performing stability analysis on the constructed adaptive robust controller;
and S107, adjusting main parameters in the constructed adaptive robust controller, and analyzing the control effect.
In the present invention, the dynamic model constructed in step S101 is the basis for the model-based adaptive robust controller design in step S105; step S102, analyzing and effectively decomposing uncertainty parameters in the system, namely step S105, designing a model-based adaptive robust controller to process a benchmark of uncertainty; the second-order form of the performance constraint constructed in step S103 is the final control target for the model-based adaptive robust controller design in step S105; step S104 is to make a certain request for the mechanical system characteristics and the servo constraint characteristics involved in step S101, step S102 and step S103; s106, analyzing the stability of the designed adaptive robust controller to ensure that the controller can realize the final stability of the system; step S107 is to analyze the influence of the main parameters in the adaptive robust controller designed in step S105 on the control effect.
Specifically, in step S101, a dynamic model of the under-actuated mechanical system shown in the following equation (1) is constructed:
wherein t is time, q is the generalized coordinates of the system,in order to be a broad-sense speed of the system,the generalized acceleration of the system is shown, delta is an uncertainty parameter of the system, M is an inertia matrix of the system, C is a centrifugal force/Coriolis force matrix of the system, G is a gravity term matrix of the system, tau is a control input of the system, and B is a control input matrix of the system.
Further, step S102 decomposes the uncertainty matrix in the constructed dynamics model of the under-actuated system according to the following equations (2) to (5):
wherein,inertia matrix, Coriolis force/centrifugal force matrix, gravitational moment for under-actuated systemsDeterministic portions of the matrix, control input matrix, Δ M (q, δ, t),Δ G (q, δ, t), Δ B (q, δ, t) are the uncertainty parts of the inertia matrix, coriolis force/centrifugal force matrix, gravity matrix, control input matrix of the under-actuated system.
Order to Then
Δχ(q,δ,t)＝χ(q,t)Φ(q,δ,t) (6)
Based on matrixWe decompose Φ into two parts:
whereinAndthe matrices can be selected as:
for the same reason, based on matricesWe decompose the matrices Δ C, Δ G, Δ B into two parts:
whereinAndandandthe matrices can be selected as:
further, in step S103, the tracking performance requirement to be achieved by the under-actuated mechanical system is regarded as a servo constraint, and the constraint is derived to obtain a second-order expression form of the servo constraint:
the target performance requirement of the under-actuated system is written in the form shown in equation (19) below:
the following equations (20) and (21) are obtained by suitably sorting and deriving equation (19):
wherein A is a constraint matrix; c is a first order constraint vector; b is a second order constraint vector.
Further, in step S104, a certain assumption requirement is proposed for the under-actuated mechanical system characteristic and the servo constraint characteristic, specifically including:
1) the servo constraint equation is solvable: equation ofAre consistent.
2) Controllability of the under-actuated system: equation ofIs in agreement, wherein
3) Matrix arrayIs reversible.
4) Order toThen there is a constant pΨ>-1 such that:
5) for a given constant positive definite matrix Q, there are constantsλ>0 is such that
6) There is a vector η sum functionSo that
Simultaneous functionCan be linearly decomposed into:
further, in step S105, based on the constructed under-actuated system dynamic model and second-order servo constraint and the proposed assumption requirement, a self-adaptive robust constraint tracking controller is designed, wherein self-adaptive parameters can be adjusted in real time according to tracking errors;
constructing a controller shown in the following equation (26) based on the constructed dynamic model and the second-order constraint form:
wherein,
wherein,
p3is used for solving the problem that the system has uncertainty, the theta function is the upper bound of the uncertainty of the system,and e is a control precision adjusting parameter for the adaptive parameter.
The adaptive parameterThe adaptation law is determined as shown by equation (30) below:
therein, ζ0,ζ1,ζ2Parameters are adjusted for the adaptive law.
Further, the performing the stability analysis on the constructed adaptive robust controller in step S106 includes:
the final stable bound of the constructed adaptive robust controller is analyzed using the lyapunov function as shown in equation (31) below:
where Q is a positive definite matrix, ρΨIs an arbitrary constant greater than-1, and η is an upper bound parameter of uncertainty for an under-actuated mechanical system.
Calculation of equation (31) yields the following formula (32):
wherein,
and obtaining a balance parameter R of the final consistent and stable limit of the under-actuated mechanical system based on the formula (32), as shown in the following formula (33):
and (3) obtaining the final consistent stable limit of the active anti-roll system based on the formula (32), as shown in the following formula (34):
wherein,da lower limit value representing the size of the final stable limit of the under-actuated mechanical system, λmin(Q) represents the minimum eigenvalue of the positive definite matrix Q,λmax(Q) represents the maximum eigenvalue of the positive definite matrix Q;
according to the lyapunov stability theory, the time for the active anti-roll system to reach the final stable limit can be obtained, as shown in the following formula (35):
wherein T represents the time for the under-actuated mechanical system to reach the final consistent stable limit, r represents the initial state of the system,is arbitrarily greater thandPositive number of (c).
Further, the step S107 adjusts main parameters in the constructed adaptive robust controller, and analyzing the control effect includes:
an initial condition incompatibility compensation parameter kappa and an adaptive law adjustment parameter zeta in the constructed adaptive law robust controller0、ζ1、ζ2Carrying out adjustment; and analyzing whether the constraint tracking error of the system meets the preset error requirement or not based on the adjusted parameters. Specifically, Matlab software can be used for performing performance simulation of the control system, whether the constrained tracking error of the system meets the preset error requirement is analyzed, if the constrained tracking error of the system meets the preset error requirement, the process is ended, and if the constrained tracking error of the system does not meet the preset error requirement, the parameters are continuously adjusted until the preset error requirement is met.
In the embodiment of the invention, the parameter kappa is related to the incompatibility problem of the compensation initial conditions, and the larger the value of kappa is, the better the effect is and the larger the corresponding control cost is; parameter ζ0、ζ1、ζ2In relation to the compensation uncertainty, the influence of the adjustment of these three parameters on the control performance of the system and the influence of the control cost are a comprehensive adjustment process. Namely, the larger the value of the initial condition incompatible compensation parameter is, the better the control effect is, and the larger the corresponding control cost is; adaptive control parameter ζ0、ζ1、ζ2The value of (A) is a comprehensive consideration, and needs to be combined with control effectThe fruit and control costs require comprehensive regulation. The specific values of the parameters can be determined by a designer according to the actual control precision of the system. In one exemplary embodiment (trolley-swing-lever system), the better control parameter values may be: k 5, ζ0＝1,ζ1＝1,ζ2＝1。
Fig. 2 shows the overall structure of the controller of the present invention. As shown in FIG. 2, first, the nominal controller p of the system is written from the kinetic equations, target constraints, and assumptions requirements1Then, a controller p is proposed to compensate the initial condition incompatibility problem according to the error of the system2And then a controller p for compensating the uncertainty of the system is provided according to a self-adaptive law designed3。
Fig. 3 shows a trolley swing link system provided by the embodiment of the invention. As shown in fig. 3, the swing link with length l is mounted on the trolley, and the trolley moves along the direction of the horizontal plane x under the action of the external force F.
FIG. 4 shows a graph at p1、p2And p3Under the cooperative control of the three-dimensional space-based control system, the position of the swing rod follows a simulation structure schematic diagram of an expected required track. The figure shows that the force output by the controller can make the position of the swing link quickly and stably follow the expected track under the condition of uncertainty of the system. Through simulation results, the method of the invention can be found to be accurate and smooth, and the effectiveness and superiority of the design method of the invention are proved.
The above-mentioned embodiments are only specific embodiments of the present invention, which are used for illustrating the technical solutions of the present invention and not for limiting the same, and the protection scope of the present invention is not limited thereto, although the present invention is described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: any person skilled in the art can modify or easily conceive the technical solutions described in the foregoing embodiments or equivalent substitutes for some technical features within the technical scope of the present disclosure; such modifications, changes or substitutions do not depart from the spirit and scope of the embodiments of the present invention, and they should be construed as being included therein. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (8)
1. A design method of an under-actuated mechanical system servo constraint tracking controller is characterized by comprising the following steps:
constructing an under-actuated mechanical system dynamics model containing parameter uncertainty, and effectively decomposing the uncertainty in the system;
the tracking performance requirement to be realized by the under-actuated mechanical system is regarded as servo constraint, and the second-order expression form of the servo constraint is obtained by derivation of the constraint;
a certain assumption requirement is put forward aiming at the characteristics of an under-actuated mechanical system and the servo constraint characteristics;
designing a self-adaptive robust constraint tracking controller based on the established dynamic model and second-order servo constraint of the under-actuated system and the provided hypothesis requirement, wherein self-adaptive parameters can be adjusted in real time according to tracking errors;
performing stability analysis on the constructed adaptive robust controller;
and adjusting main parameters in the constructed adaptive robust controller, and analyzing the control effect.
2. The design method of the servo constraint tracking controller of the under-actuated mechanical system according to claim 1, wherein the constructing the dynamic model of the under-actuated system with parameter uncertainty comprises:
constructing a dynamic model of the under-actuated mechanical system shown in the following equation (1):
wherein t is time, q is the generalized coordinates of the system,in order to be a broad-sense speed of the system,the method comprises the following steps of taking generalized acceleration of a system, delta as an uncertainty parameter of the system, M as an inertia matrix of the system, C as a centrifugal force/Coriolis force matrix of the system, G as a gravity term matrix of the system, tau as control input of the system, and B as a control input matrix of the system;
decomposing an uncertainty matrix in the constructed dynamics model of the under-actuated system according to the following equations (2) to (5):
wherein,the deterministic portions of the inertia matrix, the Coriolis force/centrifugal force matrix, the gravity matrix and the control input matrix of the under-actuated system are Delta M (q, delta, t),Δ G (q, δ, t), Δ B (q, δ, t) are the uncertainty parts of the inertia matrix, coriolis force/centrifugal force matrix, gravity matrix, control input matrix of the under-actuated system;
order to Then
Δχ(q,δ,t)＝χ(q,t)Φ(q,δ,t) (6)
Based on matrixWe decompose Φ into two parts:
whereinAndthe matrices can be selected as:
for the same reason, based on matricesWe decompose the matrices Δ C, Δ G, Δ B into two parts:
whereinAndandandthe matrices can be selected as:
3. the design method of the servo constraint tracking controller of the under-actuated mechanical system according to claim 2, wherein the tracking performance requirement to be realized by the under-actuated mechanical system is regarded as a servo constraint, and the constraint is derived to obtain a second-order expression form of the servo constraint:
the target performance requirement of the under-actuated system is written in the form shown in equation (19) below:
the following equations (20) and (21) are obtained by suitably sorting and deriving equation (19):
wherein A is a constraint matrix; c is a first order constraint vector; b is a second order constraint vector.
4. The design method of the servo constraint tracking controller of the under-actuated mechanical system according to claim 3, wherein the proposing certain assumption requirements for the characteristics of the under-actuated mechanical system and the servo constraint characteristics specifically comprises:
1) the servo constraint equation is solvable: equation ofAre consistent;
2) controllability of the under-actuated system: equation ofIs in agreement, wherein
3) Matrix arrayIs reversible;
4) order toThen there is a constant pΨ>-1 such that:
5) for a given constant positive definite matrix Q, there are constantsλ>0 is such that
6) There is a vector η sum functionSo that
Simultaneous functionCan be linearly decomposed into:
5. the design method of the servo constraint tracking controller of the under-actuated mechanical system according to claim 4, wherein an adaptive robust constraint tracking controller is designed based on the dynamic model and the second-order servo constraint of the constructed under-actuated system and the proposed hypothesis requirement, wherein the adaptive law can be adjusted in real time according to the tracking error;
constructing a controller shown in the following equation (26) based on the constructed dynamic model and the second-order constraint form:
wherein,
wherein,
p3is used for solving the problem that the system has uncertainty, the theta function is the upper bound of the uncertainty of the system,is a self-adaptive parameter, and belongs to a control precision adjusting parameter;
the adaptive parameterThe adaptation law is determined as shown by equation (30) below:
therein, ζ0,ζ1,ζ2Parameters are adjusted for the adaptive law.
6. The design method of the servo constraint tracking controller of the under-actuated mechanical system according to claim 5, wherein the stability analysis of the constructed adaptive robust controller comprises:
the final stable bound of the constructed adaptive robust controller is analyzed using the lyapunov function as shown in equation (31) below:
where Q is a positive definite matrix, ρΨIs an arbitrary constant greater than-1, and η is an upper bound parameter of uncertainty for an under-actuated mechanical system.
7. The design method of the servo constraint tracking controller of the under-actuated mechanical system according to claim 6, wherein the analyzing the final stable bound of the constructed adaptive robust controller by using the lyapunov function shown in equation (31) specifically comprises:
calculation of equation (31) yields the following formula (32):
wherein, ζ 1＝min{2κλ(1+ρΨ),2ζ0 -1ζ2(1+ρΨ)}，ζ 2＝2ζ0 -1(1+ρΨ)(ζ1+ζ2)η，ζ 3＝2(1+ρΨ)∈；
and obtaining a balance parameter R of the final consistent and stable limit of the under-actuated mechanical system based on the formula (32), as shown in the following formula (33):
and (3) obtaining the final consistent stable limit of the active anti-roll system based on the formula (32), as shown in the following formula (34):
wherein,da lower limit value representing the size of the final stable limit of the under-actuated mechanical system, λmin(Q) represents the minimum eigenvalue, λ, of the positive definite matrix Qmax(Q) represents the maximum eigenvalue of the positive definite matrix Q;
according to the lyapunov stability theory, the time for the active anti-roll system to reach the final stable limit can be obtained, as shown in the following formula (35):
wherein T represents the time for the under-actuated mechanical system to reach the final consistent stable limit, r represents the initial state of the system,is arbitrarily greater thandPositive number of (c).
8. The design method of the servo constraint tracking controller of the under-actuated mechanical system according to claim 5, wherein the adjusting the main parameters of the constructed adaptive robust controller and the analyzing the control effect comprise:
adjusting initial condition incompatible compensation parameters, adaptive law adjustment parameters and control precision adjustment parameters in the constructed adaptive law robust controller;
and analyzing whether the constraint tracking error of the system meets the preset error requirement or not based on the adjusted parameters.
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| CN113219823A (en) * | 2021-01-22 | 2021-08-06 | 南京理工大学 | Mechanical system tracking-escape-arrival point control method based on constraint tracking |
| CN113219823B (en) * | 2021-01-22 | 2022-11-04 | 南京理工大学 | Mechanical system tracking-escape-arrival point control method based on constraint tracking |
| CN113419433A (en) * | 2021-07-23 | 2021-09-21 | 合肥中科深谷科技发展有限公司 | Design method of tracking controller of under-actuated system of self-balancing electric wheelchair |
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| CN114815627A (en) * | 2022-06-07 | 2022-07-29 | 合肥工业大学 | Robust control and optimization method of steer-by-wire system based on fuzzy parameter information |
| CN114911262A (en) * | 2022-06-07 | 2022-08-16 | 合肥工业大学 | Robust control and optimization method for yaw angle of unmanned aerial vehicle |
| CN114911262B (en) * | 2022-06-07 | 2024-10-29 | 合肥工业大学 | Robust control and optimization method for yaw angle of unmanned aerial vehicle |
| CN114815627B (en) * | 2022-06-07 | 2024-08-30 | 合肥工业大学 | Robust control and optimization method for steer-by-wire system based on fuzzy parameter information |
| CN115047769B (en) * | 2022-06-29 | 2023-10-31 | 南京理工大学 | Unmanned combat platform obstacle avoidance-arrival control method based on constraint following |
| CN115047769A (en) * | 2022-06-29 | 2022-09-13 | 南京理工大学 | Unmanned combat platform obstacle avoidance-arrival control method based on constraint following |
| CN115237164A (en) * | 2022-08-12 | 2022-10-25 | 南京理工大学 | Two-degree-of-freedom holder stability control method and system based on constraint following |
| CN115237164B (en) * | 2022-08-12 | 2024-01-23 | 南京理工大学 | Constraint following-based two-degree-of-freedom cradle head stability control method and system |
| CN116009594B (en) * | 2023-03-27 | 2023-06-02 | 合肥工业大学 | Hypersonic aircraft state constraint fault tolerance control method based on zero and game |
| CN116009594A (en) * | 2023-03-27 | 2023-04-25 | 合肥工业大学 | Hypersonic aircraft state constraint fault tolerance control method based on zero and game |
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