An adaptive control method for turntable servo system

Abstract

The invention relates to an adaptive control method for a turntable servo system, belonging to the field of adaptive control. By introducing a funnel function into a turntable servo system in a pure feedback nonlinear system, and combining a Lyapunov function and a constraint estimation method, an asymptotic tracking given tracking curve is finally output, and a nonlinear system with high relativity and time-varying uncertainty can be processed. At the same time, the globally specified transient performance is guaranteed, so that the performance indicators in terms of stabilization time and tracking accuracy can be pre-allocated offline according to task requirements, without relying on initial conditions and any design parameters. At the same time, asymptotic output tracking is realized, and it is not necessary to understand the high-order derivatives of the reference trajectory.

Description

Technical Field

[0001] The invention relates to the technical field of adaptive control, and in particular to an adaptive control method for a turntable servo system. Background Art

[0002] The statements herein merely provide background information related to the present invention and do not necessarily constitute prior art.

[0003] Output tracking control of pure feedback nonlinear systems has been a subject of considerable research; the typical goal is to design a controller to ensure the stability and steady-state tracking performance of the closed-loop system. However, the control of many practical complex systems, such as spacecraft rendezvous and docking, missile interception, process control, etc., in addition to the necessary stability requirements, also places additional emphasis on transient performance for the purpose of mission completion or operational quality.

[0004] In existing methods, the specified performance indicators can be achieved through control design, such as the convergence speed of tracking error, settling time, etc., which are called specified performance control problems; however, in actual systems, sudden failures of actuators may occur during operation, resulting in system performance degradation or even catastrophic accidents. Therefore, adaptive fault-tolerant control is required in control design to ensure the reliability and safety of operation.

[0005] As a special form of pure feedback nonlinear system, the turntable servo system is subject to ubiquitous time-varying and interference in practice. However, the existing methods are too dependent on the original conditions and design parameters of the turntable servo system, which makes it impossible to guarantee the globally specified transient performance. At the same time, the existing methods need to consider the high-order derivatives of the trajectory, which makes the entire control method more complicated and unable to achieve accurate output tracking. Summary of the invention

[0006] The technical problem to be solved by the present invention is to provide an adaptive control method for a turntable servo system. By introducing a funnel function in the turntable servo system and combining the Lyapunov function and the constraint estimation method, the final output asymptotically tracks a given tracking curve to ensure the globally specified transient performance, so that the performance indicators in terms of stabilization time and tracking accuracy can be pre-allocated offline according to the task requirements without relying on initial conditions and any design parameters, and at the same time, there is no need to understand the high-order derivatives of the reference trajectory.

[0007] The object of the present invention is to provide an adaptive control method for a turntable servo system, comprising:

[0008] The dynamic equation of the rotational motion of the turntable servo system is constructed, and the state equation of a special pure feedback nonlinear system with mismatched inherent unknown time-varying parameters and external non-vanishing interference is obtained according to the dynamic equation.

[0009] Considering the unexpected actuator failures that may occur in the turntable servo system, the Fault function; where and is an unknown function, but bounded and piecewise continuous, and Indicates the effectiveness of the brakes. Indicates additive drive fault;

[0010] Construct a funnel constraint function to constrain the tracking error variable to eliminate the initial condition dependence restriction in the tracking control and ensure the globally specified transient performance. At the same time, the coordinate transformation of the dynamic equation is performed based on the funnel constraint function and the coordinate transformation function.

[0011] Construct Lyapunov function, virtual control law, adaptive control law and actual control input to verify the first-order derivative of the selected Lyapunov function Is it established? If holds, it proves that the designed finite-time predetermined performance adaptive control method makes the closed-loop system stable within a finite time; if If it does not hold, then reconstruct the Lyapunov function, virtual control law, adaptive control law and actual control input until Until establishment.

[0012] As a further technical solution, the turntable servo system is composed of a permanent magnet synchronous motor, a DSP and a PWM amplifier in a motor drive card.

[0013] As a further technical solution, the state equation is:

[0014] ;

[0015] in, is the time-varying parameter in the turntable servo system, They are The first derivative of and is the external disturbance, is the motor inertia, is the actual control input, , , , is the system parameter, is the friction torque, is the load torque, is the disturbance torque, is the torque constant, is the electromotive force coefficient, For resistance.

[0016] As a further technical solution, the expression of the funnel constraint function is:

[0017] ;

[0018] in, For a given precision bound, is the convergence time, is satisfied A positive integer.

[0019] As a further technical solution, the coordinate transformation function is:

[0020] ;

[0021] in, is the output of the turntable servo system, is the expected trajectory, is a virtual control function in controller design, is the funnel constraint function.

[0022] As a further technical solution, the Lyapunov function includes:

[0023] ;

[0024] ;

[0025] in, is the adaptive rate, is the estimation error, is a constant.

[0026] As a further technical solution, the virtual control law includes:

[0027] ;

[0028] in, , is a positive time-varying function.

[0029] As a further technical solution, the adaptive control law includes:

[0030] ;

[0031] in, Represents an unknown constant The estimate, is a positive time-varying function, , , , .

[0032] As a further technical solution, the actual control input is:

[0033] ;

[0034] in, is the virtual control law, is a positive time-varying function.

[0035] Beneficial effects of one or more of the above technical solutions:

[0036] The present invention introduces a funnel function into a turntable servo system in a pure feedback nonlinear system, and combines the Lyapunov function and the constraint estimation method to finally output an asymptotic tracking given tracking curve, which can handle nonlinear systems with high relativity and time-varying uncertainty; at the same time, the globally specified transient performance is guaranteed, so that the performance indicators in terms of stabilization time and tracking accuracy can be pre-allocated offline according to task requirements without relying on initial conditions and any design parameters; at the same time, asymptotic output tracking is realized without the need to understand the high-order derivatives of the reference trajectory. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] The drawings in the specification that constitute a part of this application are used to provide further understanding of the present application. In order to facilitate understanding, the proportions between the structures of each part are adjusted. The schematic embodiments of the present application and their descriptions are used to explain the present application and do not constitute a limitation on the present application.

[0038] Figure 1 This is a diagram of a servo system driven by a permanent magnet synchronous motor in the present invention.

[0039] Figure 2 It is a trajectory diagram of the servo system output and tracking signal in the present invention.

[0040] Figure 3 FIG. 4 is an output tracking error trajectory diagram of the servo system with specified performance of the present invention.

[0041] Figure 4 It is a state trajectory diagram of the servo system of the present invention.

[0042] Figure 5 It is the input trajectory diagram of the servo system of the present invention.

[0043] Figure 6 It is the adaptive estimation trajectory diagram of the servo system of the present invention. DETAILED DESCRIPTION

[0044] The following is combined with Figure 1-6 , clearly and completely describe the technical solutions in the embodiments of the present invention.

[0045] Embodiment 1

[0046] Reference Figure 1 The turntable servo system is a special form of pure feedback nonlinear system; and the turntable servo system targeted by this embodiment is composed of a permanent magnet synchronous motor (HC-UFS 13), a DSP (TMS 3202812) and a PWM amplifier in a motor driver card (MR-J2 S-10A).

[0047] Figure 1 The permanent magnet synchronous motor is a type of turntable servo motor and is the research object of this implementation; DSP is a digital signal processor, which has a QEP circuit, a PWM amplifier and an encoder, and the PWM amplifier is consistent with the PWM amplifier in the motor driver card (MR-J2 S-10A); and the host is used to receive the operating data of the permanent magnet synchronous motor and write instructions to control the permanent magnet synchronous motor, and write the control instructions in the DSP.

[0048] The host includes a compiler and a graphical interface. The compiler is used to write, convert and transmit control instructions, while the graphical interface is used to display graphics after receiving the operating data of the permanent magnet synchronous motor. The encoder in the DSP is used to encode the received data, the QEP circuit in the DSP is used to decode, and the PWM amplifier in the DSP is used to modulate the pulse width; at the same time, the servo controller in the DSP is equivalent to the control instructions written by the host for the permanent magnet synchronous motor.

[0049] Specifically, the permanent magnet synchronous motor transmits the operating data to the DSP. The encoder in the DSP encodes the received operating data and transmits the encoded data to the host. The host writes the control instructions in the DSP (servo controller) through the compiler, and the DSP first decodes the control instructions through the QEP circuit, modulates the decoded data signal through the PWM amplifier, and finally transmits it to the permanent magnet synchronous motor, thereby completing the control of the permanent magnet synchronous motor's operation.

[0050] Through the above control method of permanent magnet synchronous motor, the design of adaptive control method of permanent magnet synchronous motor is completed; at the same time, data transmission between host and DSP is carried out through TCP / IP protocol. Figure 1 The two “encoders” shown in refer to the encoders in the DSP, and the “PWM amplifier” and “amplifier” shown refer to the PWM amplifier in the DSP.

[0051] The dynamic equation of the rotational motion of the turntable servo system is described as:

[0052] (1)

[0053] in, is the angular position, is the angular velocity, is the angular acceleration, is the motor inertia, For unknown resonances and modeling uncertainties, is the friction torque, is the load torque, is the disturbance torque, is the input voltage, is the torque constant, is the electromotive force coefficient, is the inductor, is the current, For resistance.

[0054] Meanwhile, in this embodiment, represent The first derivative of ; represent The transpose of Refers to each function or parameter in this application.

[0055] All system parameters in the turntable servo system are considered to be time-varying and unknown to the control design; therefore, , that is, the angular position and angular velocity are the state variables of the system.

[0056] However, unexpected actuator failures may occur in the turntable servo system, and actuator failures and external interference need to be considered; therefore, the fault representation function is defined as:

[0057] (2)

[0058] in, and is an unknown function, but bounded and fragment-continuous, Indicates the effectiveness of the brakes. Indicates an additive drive fault. is the actual control input.

[0059] Therefore, based on formula (2), formula (1) can be rewritten as the state equation shown below:

[0060] (3)

[0061] in, , , , is the system parameter, and For external disturbance.

[0062] In order to facilitate the design of the control system, it is necessary to introduce corresponding assumptions and lemmas first; as shown below:

[0063] Assumption 1: Expected Trajectory and the first-order derivative are all bounded and cannot be used for feedback.

[0064] Assumption 2: and The signs are known, and there are positive constants and satisfy .

[0065] Assumption 3: There are some unknown constants and , so that .

[0066] Lemma 1: For any scalar positive function and any variable , the following inequality holds .

[0067] Among them, in this embodiment, Representative ratio A large normal number, Representative ratio A small positive constant; and here The same refers to each function or parameter in this application.

[0068] In order to achieve the predetermined performance goal, the present invention introduces the following funnel constraint function:

[0069] First, the funnel constraint function is defined as: for a given precision bound and convergence time , a time-varying function , defined in , and is abbreviated as or .

[0070] And the funnel constraint function meets the following conditions:

[0071] Condition 1: ,and In all established on.

[0072] Condition 2: belong ,in represents a class of bounded functions whose derivatives are bounded.

[0073] Condition 3: There is a moment in time , so that In all Established at that time.

[0074] Based on the above conditions, the performance funnel is defined as:

[0075] (4)

[0076] In the present invention, the expression of the funnel constraint function is:

[0077] (5)

[0078] in, For a given precision bound, is the convergence time, is satisfied A positive integer.

[0079] At the same time, coordinate transformation is performed on the control design to ensure tracking error within the funnel constraint function and converges asymptotically.

[0080] The coordinate transformation function is:

[0081] (6)

[0082] in, is a virtual control function in controller design, is the output of the turntable servo system.

[0083] In the following design, Represents an unknown constant The estimation error is ; At the same time, a series of positive time-varying functions and To assign a value, choose , , , , ,in , , and is a positive constant. In addition, the positive scalar , will be used to design the parameters, and is the control gain used to adjust the error convergence rate, Indicates the adaptation rate.

[0084] Then the controller design is performed for the second-order system:

[0085] According to formulas (3) and (6), we can solve The time derivative of ; and is expressed as follows:

[0086] (7)

[0087] And the selected Lyapunov function is as follows:

[0088] (8)

[0089] According to formulas (7) and (8), it can be verified that The time derivative of satisfies:

[0090] (9)

[0091] in, , and used for controller design. The second condition is that there is a constant , so that At the same time, in order to deal with bounded time-varying uncertainty, we define ;in, The definition is as follows:

[0092] (10)

[0093] In addition,

[0094] (11)

[0095] (12)

[0096] Then, by Lemma 1 we can get:

[0097] (13)

[0098] (14)

[0099] in, , .

[0100] Substituting formula (13) and (14) into formula (9), we can obtain:

[0101] (15)

[0102] in, .

[0103] Will Add and subtract on the right side of formula (15), where , we can get:

[0104] (16)

[0105] Design of virtual control law and the first adaptive control law ; and as follows:

[0106] (17)

[0107] (18)

[0108] Among them, the introduction The purpose of this term is to prevent parameter estimation from drifting.

[0109] According to formula (17), from assumption 2 and Lemma 1, we can get:

[0110] (19)

[0111] Then using the perfect square formula, we get:

[0112] (20)

[0113] And through formulas (17), (18), (19) and (20), we can get:

[0114] (twenty one)

[0115] Notice yes is a smooth function, so we can get and is defined as:

[0116] (twenty two)

[0117] in,

[0118] (twenty three)

[0119] in, They are The transpose of They are The transpose of .

[0120] at this time, The time derivative of can be expressed as:

[0121] (twenty four)

[0122] in, .

[0123] From Assumptions 2 and 3, we can conclude that there is a constant Make .

[0124] At this time, the Lyapunov function can be expressed as:

[0125] (25)

[0126] So The derivative of satisfies:

[0127] (26)

[0128] because , and exist is bounded, so we define , , . Then, by Lemma 1, we can get:

[0129] (27)

[0130] in, .

[0131] Substitute formula (27) into (26) and follow the similar derivation process of formulas (16)-(21) to convert the actual control input into Select as:

[0132] (28)

[0133] in, ,and The update conditions are:

[0134] (29)

[0135] And finally got

[0136] (30)

[0137] At the same time, in the simulation, it is assumed that the system parameters , , , , , , and ; External disturbance , The actuator fault parameters are set to , .

[0138] The turntable servo system is a special form of pure feedback nonlinear system, so the proposed control can be directly used to achieve tracking control. The control goal is to make the system output Asymptotically tracking the desired trajectory , while ensuring that the desired transient tracking accuracy can be achieved within the specified time of 1.5s .

[0139] Based on the above design procedure, we choose a funnel constraint function with a specified time As the form of equation (2), where the parameters are set as , , The controller parameters are selected as , , , , , The estimated initial value is set to , , and the initial value .

[0140] The simulation results are as follows Figure 2-6 As shown, Figure 2 and 3 The output tracking performance is demonstrated, showing that the controller designed by the present invention can achieve output tracking within 1.5 and is within the predetermined performance. Figure 4 and 5 Describes the status and control input The trajectory of Figure 6 The estimates of the unknown parameters are shown. It is clear from these results that all closed-loop signals are bounded. Figure 2 and Figure 3 It can be seen that under different initial conditions, the output Can track the expected trajectory , and the tracking error always satisfies the predetermined constraints and eventually converges to zero, which is consistent with the theoretical results.

[0141] Therefore, based on the description of the above process, a new prescribed performance fault-tolerant control scheme is proposed by introducing a special funnel function and integrating the barrier Lyapunov function technology and adaptive estimation method. Compared with the existing results, this scheme has the following attractive features: (1) It can handle nonlinear systems with high relative and time-varying uncertainties; (2) It can guarantee the globally prescribed transient performance, so that the performance indicators in terms of stabilization time and tracking accuracy can be pre-allocated offline according to the task requirements, without relying on the initial conditions and any design parameters; (3) At the same time, asymptotic output tracking can be achieved without knowing the high-order derivatives of the reference trajectory.

[0142] Embodiment 2

[0143] The above embodiment 1 takes the pure feedback nonlinear system transfer table servo system as an example to demonstrate the feasibility of the technical solution. When it comes to other pure feedback nonlinear systems, the technical solution is as follows:

[0144] Step 1: The expression of the nonlinear system with pure feedback form is:

[0145] (31)

[0146] in, is the state vector, and They are control input and output; and is an unknown time-varying bounded parameter vector, and is an unknown smooth function; and is a known continuous function, The external disturbance satisfies , Unknown, but .

[0147] Likewise, in this embodiment, represent The first-order derivative of represent The transposition of Representative ratio A large normal number, Representative ratio A small normal number; and here Refers to each function or parameter in this application.

[0148] Step 2: Assumptions are differentiable, and their partial derivatives are continuous For the nonlinear system (31), define According to the mean value theorem, there exists ,thereby We further assume ;in is the unknown time-varying bounded parameter vector is an unknown smooth function; therefore, the nonlinear system formula (31) can be transformed into the following form:

[0149] (32)

[0150] in, is an unknown time-varying bounded parameter vector, is an unknown smooth function.

[0151] Step 3: Simulated unexpected actuator failures will occur in the nonlinear system; the fault representation function is as follows:

[0152] (33)

[0153] in, and are unknown functions, but are bounded and piecewise continuous, identifying brake effectiveness and additive drive faults, respectively.

[0154] Step 4: In order to facilitate the design of the control system, the following assumptions and lemmas need to be made first.

[0155] Assumption 1: Expected Trajectory and the first-order derivative are all bounded and cannot be used for feedback.

[0156] Assumption 2: and The signs are known, and there are positive constants and satisfy .

[0157] Assumption 3: There are some unknown constants and , so that .

[0158] Lemma 1: For any scalar positive function and any variable , the following inequality holds:

[0159] (34)

[0160] Step 5: In order to achieve the predetermined performance target, a funnel constraint function is introduced.

[0161] The funnel constraint function is defined as: for a given precision bound and convergence time , a time-varying function , defined in , and is abbreviated as or .

[0162] And the funnel constraint function meets the following conditions:

[0163] Condition 1: ,and In all established on.

[0164] Condition 2: belong ,in represents a class of bounded functions whose derivatives are bounded.

[0165] Condition 3: There is a moment in time , so that In all Established at that time.

[0166] Based on the above conditions, the performance funnel is defined as:

[0167] (35)

[0168] In the present invention, the expression of the funnel constraint function is:

[0169] (36)

[0170] in, is satisfied A positive integer.

[0171] Step 6: Perform coordinate transformation on the control design to ensure Within the funnel constraint function, it converges asymptotically. The coordinate transformation function is:

[0172] (37)

[0173] (38)

[0174] in, It is a virtual control function in controller design.

[0175] In the following design, Represents an unknown constant The estimate will be step is specified, and the estimated error is ; At the same time, a series of positive time-varying functions and To assign a value, choose , , , , ,in , , and is a positive constant. In addition, the positive scalar , will be used to design the parameters, and is the control gain used to adjust the error convergence rate, Indicates the adaptation rate.

[0176] Step 7: Calculate using formulas (32) and (37) The time derivative of ; is as follows:

[0177] (39)

[0178] At the same time, the selected Lyapunov function is as follows:

[0179] (40)

[0180] And through formulas (39) and (40) it can be verified that The time derivative of satisfies the following formula:

[0181] (41)

[0182] in, , and used for controller design. The existence of constant , so that At the same time, in order to deal with bounded time-varying uncertainty, we define ;in, The definition is as follows:

[0183] (42)

[0184] In addition,

[0185] (43)

[0186] (44)

[0187] Then, by Lemma 1 we can get:

[0188] (45)

[0189] (46)

[0190] in, , .

[0191] Step 8: Substituting formula (45) and (46) into formula (41), we can obtain:

[0192] (47)

[0193] in, .

[0194] Step 9: Add and subtract on the right side of formula (47), where , we can get:

[0195] (48)

[0196] Step 10: Design virtual control law and the first adaptive control law ; and as follows:

[0197] (49)

[0198] (50)

[0199] Among them, the introduction The purpose of this term is to prevent parameter estimation from drifting.

[0200] According to formula (49), from assumption 2 and Lemma 1, we can get:

[0201] (51)

[0202] Then using the perfect square formula, we get:

[0203] (52)

[0204] And through formulas (49), (50), (51) and (52), we can get:

[0205] (53)

[0206] Step 11: Referring to formulas (49) and (50), the virtual control law and adaptive control law Design as follows:

[0207] (54)

[0208] (55)

[0209] in, ,and ,and is a vector of known smooth functions that can be calculated.

[0210] According to formulas (32) and (38), it can be verified that the time derivative Satisfies the following formula:

[0211] (56)

[0212] in, ,for When , the last term on the right side of formula (56) is zero.

[0213] The definition of time-varying uncertainty is:

[0214] (57)

[0215] (58)

[0216] in, They are The transpose of They are The transpose of .

[0217] Therefore, formula (56) can be expressed as:

[0218] (59)

[0219] Step 12: The selected Lyapunov function is as follows:

[0220] (60)

[0221] According to formula (59), It can be expressed as follows:

[0222] (61)

[0223] Among them, when When , the third term on the right side of formula (61) is For boundary estimation, it is:

[0224] (62)

[0225] (63)

[0226] Among them, for In all is bounded.

[0227] definition . By Lemma 1, we can get:

[0228] (64)

[0229] in, .

[0230] Step 13: Substitute formula (64) into formula (61) and add and subtract on the right side of formula (61) , and define , and we can get:

[0231] (65)

[0232] in, At the same time, let the virtual control law and adaptive control law To design:

[0233] (66)

[0234] (67)

[0235] Similar to formula (51), Lemma 1 can be used to obtain Therefore, combined with formula (67), we can get:

[0236] (68)

[0237] Step 14: Notice yes The smooth function of , considering formulas (32), (33) and (38) and referring to formula (57) and Similar definitions, The time derivative of can be expressed as:

[0238] (69)

[0239] in, From Assumptions 2 and 3, we can conclude that there is a constant Make .

[0240] At this time, the Lyapunov function can be expressed as:

[0241] (70)

[0242] So The derivative of satisfies:

[0243] (71)

[0244] Step 15: Due to , and exist is bounded, so we define , , . Then, by Lemma 1, we can get:

[0245] (72)

[0246] in, .

[0247] Substitute formula (72) into (71) and follow the similar derivation process of formulas (48)-(53) to convert the actual control input into Select as:

[0248] (73)

[0249] in, ,and The update conditions are:

[0250] (74)

[0251] And finally got

[0252] (75)

[0253] Consider a closed-loop system consisting of a pure feedback nonlinear system (32) with unknown actuator fault (33), an adaptive controller (73)–(74), and virtual adaptive control laws (49)–(50) and (66)–(67).

[0254] If the above assumptions 1-3 are satisfied and the function is appropriately chosen If Definition 1 is satisfied, then for any bounded initial condition, the following statement holds:

[0255] (1) All closed-loop signals are globally uniformly bounded.

[0256] (2) Achieve asymptotic tracking, that is .

[0257] (3) To a certain extent, the specified transient performance is guaranteed, that is, within the specified limited time Within the specified accuracy range, the tracking error can be guided to a predetermined ,in and All are user assignable.

[0258] prove:

[0259] (1) First, we prove that the closed-loop system under consideration is The existence and uniqueness of the maximum solution is proved, and then all closed-loop signals are proved to be globally uniformly bounded.

[0260] Note that the entire closed-loop dynamics can be expressed using the error variable and To represent. is the closed-loop system error vector. , and By using equations (37) and (38), we can conclude that:

[0261] (76)

[0262] (77)

[0263] (78)

[0264] in, and is a smooth function.

[0265] Based on equations (39), (49), (56), (66), (69) and (73), the closed-loop dynamic equation can be expressed as follows:

[0266] (79)

[0267] definition , which is non-empty and open. Also, because is always true, so Originally located at within, that is In addition, due to The piecewise continuity and boundedness of the system, as well as the smoothness of the nonlinearity and adaptive control law, exist The above is segmented and continuous. exist Upper local Lipschitz, which ensures that the interval Maximum solution The existence of uniqueness makes , .

[0268] Next, prove , for formula (75) Integrating both sides gives:

[0269] (80)

[0270] in, is a constant.

[0271] Inequality (80) means that , and exist is bounded above. The definition of exist is bounded. Always holds, we can infer that Strictly keep in collection In, therefore , is bounded.

[0272] according to By definition, we know that if and only if hour, .because is bounded, and for , is non-zero and bounded, so according to Definition, exist is also bounded. This leads to , is bounded because . Note and It contains bounded signals is a smooth function, so we can directly get , is bounded. This further gives exist Boundedness on .

[0273] Similarly, we can get and the subsequent exist It can also be deduced that Therefore, we conclude that all signals of the closed-loop system are in The upper constant is bounded, and Not relevant.

[0274] (2) From formula (31), we can see that are ultimately bounded. Due to the boundedness of all involved signals, it can be concluded from (39) that and are all bounded. ,but , you can build On the other hand, we can also get from (80):

[0275] (81)

[0276] This means Therefore, according to the corollary of Barbalat's lemma, we can conclude that , . Further Note and for , we have . That is, asymptotic tracking is achieved.

[0277] (3) It remains to be demonstrated that the specified transient performance is guaranteed. We have already determined in (31) that Always keep in the collection That is, the output tracking error Always evolving within the defined performance funnel (35). The third property of the level is that we know Therefore, the tracking error Can be directed to a predetermined precision area , within a specified limited time In which and , are pre-assigned to the required level based on task requirements.

[0278] The proof is complete.

[0279] In the traditional control method for achieving the predetermined performance of a pure feedback system, some systems only consider unknown constant parameters, and do not consider nonlinear systems with time-varying uncertain parameters and unknown disturbances. The method used to deal with the predetermined performance control problem is to stipulate performance constraint control, and the result of the predetermined performance control is limited by the initial conditions. In the coordinate transformation (31) of the present invention, the funnel function is cleverly introduced to solve the problem that the result of the predetermined performance control is limited by the initial conditions. The final result of the present invention can achieve asymptotic tracking, rather than only guaranteeing bounded error tracking performance, thereby improving tracking accuracy.

[0280] Although the above describes the specific implementation mode of the present invention in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art on the basis of the technical solution of the present invention without creative work are still within the scope of protection of the present invention.

Claims

1. An adaptive control method for a turntable servo system, characterized in that: include: The dynamic equation of the rotational motion of the turntable servo system is constructed, and the state equation of a pure feedback nonlinear system with mismatched inherent unknown time-varying parameters and external non-vanishing interference is obtained according to the dynamic equation. Considering the unexpected actuator failures that may occur in the turntable servo system, the Fault function; where and is an unknown function, but bounded and piecewise continuous, and Indicates the effectiveness of the brakes. Indicates additive drive fault; Construct a funnel constraint function to constrain the tracking error variable, thereby eliminating the initial condition dependence restriction in the tracking control and ensuring the globally specified transient performance. At the same time, the coordinate transformation of the dynamic equation is performed based on the funnel constraint function and the coordinate transformation function. Construct Lyapunov function, virtual control law, adaptive control law and actual control input to verify the first-order derivative of the selected Lyapunov function Is it established? If holds, it proves that the designed finite-time predetermined performance adaptive control method makes the closed-loop system stable within a finite time; if If it does not hold, then reconstruct the Lyapunov function, virtual control law, adaptive control law and actual control input until Until establishment; The expression of the funnel constraint function is: ； in, For a given precision bound, is the convergence time, is satisfied A positive integer of ; The coordinate transformation function is: ； in, is the time-varying parameter in the turntable servo system; in, is the output of the turntable servo system, is the expected trajectory, is a virtual control function in controller design, is the funnel constraint function; The actual control input is: ； in, is a positive time-varying function; in, ,and The update conditions are: in, ; is an unknown constant, is the adaptive rate; For controller parameters.

2. The adaptive control method for a turntable servo system according to claim 1, characterized in that: The turntable servo system is composed of a permanent magnet synchronous motor, a DSP and a PWM amplifier in a motor drive card.

3. The adaptive control method for a turntable servo system according to claim 1, characterized in that: The dynamic equation of the turntable servo system is: ； in, is the time-varying parameter in the turntable servo system, They are The first derivative of and is the external disturbance, is the motor inertia, is the actual control input, , , , is the system parameter, is the friction torque, is the load torque, is the disturbance torque, is the torque constant, is the electromotive force coefficient, For resistance.

4. The adaptive control method for a turntable servo system according to claim 1, characterized in that: The Lyapunov function includes: ； ； in, is the adaptive rate, is the estimation error, is a constant.

5. The adaptive control method for a turntable servo system according to claim 1, characterized in that: The virtual control law includes: ； in, , is a positive time-varying function.

6. The adaptive control method for a turntable servo system according to claim 5, characterized in that: The adaptive control law includes: ； in, Represents an unknown constant The estimate, is a positive time-varying function, , , , .

Images