CN107807531A - A kind of adaptive inversion tracking and controlling method for ultra-magnetic telescopic tracking platform - Google Patents
A kind of adaptive inversion tracking and controlling method for ultra-magnetic telescopic tracking platform Download PDFInfo
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Abstract
The invention discloses a kind of adaptive inversion tracking and controlling method for ultra-magnetic telescopic tracking platform, comprise the following steps：First, off-line identification obtains the left inverse model of ultra-magnetic telescopic actuator；Secondly, based on Filtered ε LMS algorithms, the left inverse model of two identical nonlinear filters duplication ultra-magnetic telescopic actuator is used；Finally, the error signal for subtracting each other to obtain using described two nonlinear filters output adaptively finds controller C, and using the weight coefficient of LMS algorithm on-line tuning wave filter, until the output of ultra-magnetic telescopic actuator and the output of reference model are identical；Wherein, two described identical nonlinear filters, the input of one of nonlinear filter export for object；The input of another nonlinear filter is the output of reference model.Sluggish part of the invention by offsetting ultra-magnetic telescopic actuator, realize the accurate tracing control to ultra-magnetic telescopic actuator.
Description
Technical Field
The invention relates to a self-adaptive inverse tracking control method for a giant magnetostrictive tracking platform, and belongs to the field of modeling and control of a dynamic hysteresis nonlinear system.
Background
Common smart materials used in modern industry are piezoelectric, giant magnetostrictive, shape memory alloys, and the like. They exhibit coupling properties of electric, thermal, magnetic, force fields, with which they can be designed as actuators or sensors. For position tracking of displacements in the micrometer range, giant magnetostrictive materials are generally used. However, the smart material has serious dynamic hysteresis nonlinear characteristics. The dynamic hysteresis non-linear characteristic not only reduces the control accuracy of the control system, but also reduces the stability of the closed-loop system and even leads to system oscillation.
The self-adaptive inverse control uses the inverse of the controlled object as a series controller to carry out open loop control on the dynamic characteristic of the system, avoids the instability problem caused by feedback, and simultaneously can separate the control of the dynamic characteristic of the system and the control of object disturbance without influencing each other, thereby having great superiority. Specifically, when the adaptive inverse is used for tracking control, the controlled object is driven by an adaptive inverse controller (the transfer function of the controller is the inverse of the controlled object), so that the output of the object follows the desired input. Generally, since the controlled object is unknown, it is necessary to adaptively adjust the parameters of the controller to approximate to the real controlled object inverse, and the mean square error is minimized by using the error signal of the output and the expected input of the controlled object and adjusting the parameters of the controller by using an adaptive algorithm.
The existing linear adaptive inverse control method mainly comprises a Filtered-X LMS algorithm and a Filtered-epsilon LMS algorithm, however, the control algorithm based on the linear adaptive filter is difficult to meet when facing a dynamic hysteresis nonlinear system. Specifically, for the Filtered-X LMS algorithm, there is a problem in that the product of the left inverse of the system and the system is not equal to the product of the right inverse of the system and the system, and thus cannot be applied to nonlinear system control; for the Filtered-epsilon LMS algorithm, the linear controlled object adaptive inverse controller approximates the reciprocal of the transfer function of the controlled object, however, for the nonlinear controlled object, the transfer function does not exist, so the Filtered-epsilon LMS algorithm cannot be directly applied to the nonlinear system control (namely, cannot be directly applied to the giant magnetostrictive tracking platform). Improvements are therefore needed.
Disclosure of Invention
The invention aims to provide an adaptive inverse tracking control method for a giant magnetostrictive tracking platform, which can effectively solve the problems in the prior art and realize accurate tracking control on a giant magnetostrictive actuator.
In order to solve the technical problems, the invention adopts the following technical scheme: an adaptive inverse tracking control method for a giant magnetostrictive tracking platform comprises the following steps: firstly, performing off-line identification to obtain a left inverse model of the giant magnetostrictive actuator; secondly, based on a Filtered-epsilon LMS algorithm, two identical nonlinear filters are used for copying a left inverse model of the giant magnetostrictive actuator; finally, the controller C is searched in a self-adaptive mode by utilizing an error signal obtained by subtracting the outputs of the two nonlinear filters, and the weight coefficient of the filter is adjusted on line by adopting an LMS algorithm until the output of the giant magnetostrictive actuator is the same as the output of the reference model; wherein, the input of one of the two identical nonlinear filters is the object output; the input of the other nonlinear filter is the output of the reference model.
Off-line finding left inverse model of giant magnetostrictive actuatorThe output of the signal generator needs to have the same dynamic and statistical properties as the controller output; the accurate dynamic characteristics of the output of the signal generator are very critical to the solving of the nonlinear inverse model.
Preferably, the nonlinear filter adopts a GPO nonlinear adaptive filter, so that the dynamic hysteresis characteristic of the giant magnetostrictive actuator can be described more accurately.
Preferably, the envelope function of the GPO nonlinear adaptive filter is an inverse function a tanh of a hyperbolic tangent function, so that the nonlinear characteristic of the object can be effectively offset (the hyperbolic tangent function is selected when the GPO nonlinear filter is used for identifying the object).
In the foregoing adaptive inverse tracking control method for a giant magnetostrictive tracking platform, an envelope function of a GPO is obtained by identification through the following method: applying a desired input signal to the giant magnetostrictive actuator; collecting input/output data of the giant magnetostrictive actuator, then taking the output of the giant magnetostrictive actuator as the input of a model, taking the input of the giant magnetostrictive actuator as the output of the model, and identifying by a nonlinear fitting method to obtain an envelope function of the GPO:
γl＝a1a tanh(a2u(t)+a3)+a4
γr＝b1a tanh(b2u(t)+b3)+b4
wherein, r islAnd rrRespectively, the left and right envelope functions of the non-linear filter.
By the method, the envelope function of the nonlinear filter can be quickly and accurately obtained.
The self-adaptive inverse tracking control method for the giant magnetostrictive tracking platform specifically comprises the following steps:
s1, initializing variables, and determining the order n +1, the threshold r, the convergence factor mu and the envelope function of the nonlinear filter (according to the system priori knowledge); randomly giving an initial weight coefficient W (0) of the nonlinear filter, and enabling k to be 0;
s2, obtaining a left inverse model of the giant magnetostrictive actuator through off-line identification;
s3, inputting the modeling excitation signal x (k) into the system;
s4, based on Filtered-epsilon LMS algorithm, two identical nonlinear filters are used for copying a left inverse model of the giant magnetostrictive actuator, the hysteresis characteristic of the giant magnetostrictive actuator is counteracted, an output signal y (k) and an output signal H (k) of the filter are obtained, and an estimation error between an actual controller and an ideal controller is calculated
And S5, updating the weight coefficient of the nonlinear filter: w (k +1) ═ W (k) +2 μ ∈ (k) H (k); wherein,
s6, let k be k + 1; updating the input vector x (k); and obtains a new output signal y (k) and the output signal H (k) of the filter, and the estimated error between the actual controller and the ideal controller
S7, judgmentIf yes, go to step S6; otherwise, the final controller C is obtained.
By adopting the method, the tracking control precision of the giant magnetostrictive actuator can be greatly improved.
In the foregoing adaptive inverse tracking control method for a giant magnetostrictive tracking platform, the method further includes: and the PID feedback controller is adopted to control the non-hysteresis characteristic of the giant magnetostrictive tracking platform, the input of the PID feedback controller is the difference value between an input signal and the output of an object, and the output of the PID feedback controller and the output of the controller C are summed to act on the giant magnetostrictive actuator.
By the method, the tracking control precision of the giant magnetostrictive tracking platform can be further improved.
Preferably, the control parameters of the PID feedback controller are selected by adopting an engineering setting method, and the differential parameters are set to be 0, so that the tracking control precision of the giant magnetostrictive tracking platform can be improved, and the oscillation caused by the differential link can be avoided.
Compared with the prior art, the invention copies the left inverse model of the giant magnetostrictive actuator by using two identical nonlinear filters, cancels the hysteresis part of the giant magnetostrictive actuator by using the left inverse model, and utilizes the error signal obtained by subtracting the outputs of the two nonlinear filters to adaptively find the controller C, thereby realizing the accurate tracking control of the giant magnetostrictive actuator. In addition, the invention directly controls the nonlinear system by designing the nonlinear controller C, the control is more direct, the invention identifies the nonlinear controller C on line, the requirement on the model is not high, and when the object state changes, the controller can automatically adjust the parameters to adapt to the change, thereby greatly improving the precision and the stability of the tracking control. In addition, the invention adopts a feedforward feedback PID composite controller based on Filtered-epsilon LMS nonlinear adaptive inverse, thereby further improving the tracking control precision of the giant magnetostrictive actuator.
By establishing a giant magnetostrictive actuator model and then performing simulation control by using the feedforward Filtered-epsilon LMS nonlinear adaptive inverse tracking control technology, GMA (giant magnetostrictive actuator) can be well controlled in a certain frequency range, so that an output signal tracks an expected input signal, and the control relative error is within 4%; in addition, the feedforward feedback PID composite controller based on Filtered-epsilon LMS nonlinear adaptive inverse is used for simulation control, the relative error of single-frequency expected input signal tracking control can be guaranteed to be within 3% in the frequency range of 1-100 Hz, and compared with the feedforward Filtered-epsilon LMS nonlinear adaptive inverse tracking control, the single-frequency input signal tracking error is obviously reduced after the PID controller is added.
When two controllers in the invention are used for carrying out real-time tracking control on a GMA (giant magnetostrictive actuator), the Filtered-epsilon LMS nonlinear adaptive inverse tracking control technology can ensure that the relative error of single-frequency expected input signal tracking control is within 7 percent and the relative error of composite-frequency expected input signal tracking control is within 10 percent in the practical application process, which shows that the control technology can be completely applied to certain engineering practice. In addition, the feedforward feedback PID composite tracking controller based on the feedforward Filtered-epsilon LMS nonlinear adaptive inverse can ensure that the relative error of single-frequency expected input signal tracking control is within 4 percent and the relative error of composite frequency expected input signal tracking control is within 9 percent in the practical application process, and compared with the feedforward filtering-epsilon LMS nonlinear adaptive inverse tracking control, after the PID controller is added, the tracking error of the single-frequency input signal is obviously reduced, and the tracking error of the composite frequency input signal is also reduced.
Drawings
FIG. 1 is a method flow diagram of one embodiment of the present invention;
FIG. 2 is a schematic diagram of Filtered- ε LMS control for a nonlinear system;
FIG. 3 is a basic flowchart of an offline identification of a left inverse model;
FIG. 4 is a block diagram of Filtered- ε LMS adaptive inverse tracking control;
FIG. 5 is a structural diagram of a Hammerstein model;
FIG. 6 shows the Filtered- ε LMS nonlinear adaptive inverse tracking control experiment results
FIG. 7 is a block diagram of a feedforward feedback PID composite control structure based on a feedforward Filtered-epsilon LMS nonlinear adaptive inverse;
FIG. 8 is a schematic diagram of a feedforward feedback PID composite control experiment result based on a feedforward Filtered-epsilon LMS nonlinear adaptive inverse;
FIG. 9 is a diagram of a Filtered- ε LMS adaptive inverse tracking control experiment structure;
FIG. 10 is a schematic diagram of the Filtered- ε LMS nonlinear adaptive inverse tracking control experiment result;
FIG. 11 is a schematic diagram of a PID feedback composite control experiment based on feedforward Filtered-epsilon LMS nonlinear adaptive inverse compensation;
FIG. 12 is a schematic diagram of the PID feedback composite control experiment result based on feedforward Filtered-epsilon LMS nonlinear adaptive inverse compensation.
The invention is further described with reference to the following figures and detailed description.
Detailed Description
Example 1 of the invention: an adaptive inverse tracking control method for a giant magnetostrictive tracking platform, as shown in fig. 1, comprises the following steps: firstly, performing off-line identification to obtain a left inverse model of the giant magnetostrictive actuator; secondly, based on a Filtered-epsilon LMS algorithm, two identical nonlinear filters are used for copying a left inverse model of the giant magnetostrictive actuator; finally, the controller C is searched in a self-adaptive mode by utilizing an error signal obtained by subtracting the outputs of the two nonlinear filters, and the weight coefficient of the filter is adjusted on line by adopting an LMS algorithm until the output of the giant magnetostrictive actuator is the same as the output of the reference model; wherein, the input of one of the two identical nonlinear filters is the object output; the input of the other nonlinear filter is the output of the reference model. The nonlinear filter can adopt a GPO nonlinear adaptive filter. The envelope function of the GPO nonlinear adaptive filter may adopt an inverse function atanh of a hyperbolic tangent function. The envelope function of the GPO can be identified by the following method: applying a desired input signal to the giant magnetostrictive actuator; collecting input/output data of the giant magnetostrictive actuator, then taking the output of the giant magnetostrictive actuator as the input of a model, taking the input of the giant magnetostrictive actuator as the output of the model, and identifying by a nonlinear fitting method to obtain an envelope function of the GPO:
γl＝a1a tanh(a2u(t)+a3)+a4
γr＝b1a tanh(b2u(t)+b3)+b4
wherein, γ islAnd gammarRespectively, the left envelope function and the right envelope function of the GPO nonlinear filter.
The self-adaptive inverse tracking control method for the giant magnetostrictive tracking platform can specifically comprise the following steps of:
s1, initializing variables, and determining the order n +1, the threshold r, the convergence factor mu and the envelope function of the nonlinear filter (according to the system priori knowledge); randomly giving an initial weight coefficient W (0) of the nonlinear filter, and enabling k to be 0;
s2, obtaining a left inverse model of the giant magnetostrictive actuator through off-line identification;
s3, inputting the modeling excitation signal x (k) into the system;
s4, based on Filtered-epsilon LMS algorithm, two identical nonlinear filters are used for copying a left inverse model of the giant magnetostrictive actuator, the hysteresis characteristic of the giant magnetostrictive actuator is counteracted, an output signal y (k) and an output signal H (k) of the filter are obtained, and an estimation error between an actual controller and an ideal controller is calculated
And S5, updating the weight coefficient of the nonlinear filter: w (k +1) ═ W (k) +2 μ ∈ (k) H (k); wherein,
s6, let k be k + 1; updating the input vector x (k); and obtains a new output signal y (k) and the output signal H (k) of the filter, and the estimated error between the actual controller and the ideal controller
S7, judgmentIf yes, go to step S6; otherwise, the final controller C is obtained.
The method can also comprise the following steps: and the PID feedback controller is adopted to control the non-hysteresis characteristic of the giant magnetostrictive tracking platform, the input of the PID feedback controller is the difference value between an input signal and the output of an object, and the output of the PID feedback controller and the output of the controller C are summed to act on the giant magnetostrictive actuator. Wherein, the control parameter of the PID feedback controller can be selected by adopting an engineering adjustment method, and the differential parameter is set to be 0.
Example 2: an adaptive inverse tracking control method for a giant magnetostrictive tracking platform, as shown in fig. 1, comprises the following steps: firstly, performing off-line identification to obtain a left inverse model of the giant magnetostrictive actuator; secondly, based on a Filtered-epsilon LMS algorithm, two identical nonlinear filters are used for copying a left inverse model of the giant magnetostrictive actuator; finally, the controller C is searched in a self-adaptive mode by utilizing an error signal obtained by subtracting the outputs of the two nonlinear filters, and the weight coefficient of the filter is adjusted on line by adopting an LMS algorithm until the output of the giant magnetostrictive actuator is the same as the output of the reference model; wherein, the input of one of the two identical nonlinear filters is the object output; the input of the other nonlinear filter is the output of the reference model.
The envelope function of the non-linear filter can be implemented by the prior art.
Example 3: an adaptive inverse tracking control method for a giant magnetostrictive tracking platform, as shown in fig. 1, comprises the following steps: firstly, performing off-line identification to obtain a left inverse model of the giant magnetostrictive actuator; secondly, based on a Filtered-epsilon LMS algorithm, two identical nonlinear filters are used for copying a left inverse model of the giant magnetostrictive actuator; finally, the controller C is searched in a self-adaptive mode by utilizing an error signal obtained by subtracting the outputs of the two nonlinear filters, and the weight coefficient of the filter is adjusted on line by adopting an LMS algorithm until the output of the giant magnetostrictive actuator is the same as the output of the reference model; wherein, the input of one of the two identical nonlinear filters is the object output; the input of the other nonlinear filter is the output of the reference model. The nonlinear filter can adopt a GPO nonlinear adaptive filter.
Example 4: an adaptive inverse tracking control method for a giant magnetostrictive tracking platform, as shown in fig. 1, comprises the following steps: firstly, performing off-line identification to obtain a left inverse model of the giant magnetostrictive actuator; secondly, based on a Filtered-epsilon LMS algorithm, two identical nonlinear filters are used for copying a left inverse model of the giant magnetostrictive actuator; finally, the controller C is searched in a self-adaptive mode by utilizing an error signal obtained by subtracting the outputs of the two nonlinear filters, and the weight coefficient of the filter is adjusted on line by adopting an LMS algorithm until the output of the giant magnetostrictive actuator is the same as the output of the reference model; wherein, the input of one of the two identical nonlinear filters is the object output; the input of the other nonlinear filter is the output of the reference model. The nonlinear filter adopts a GPO nonlinear adaptive filter. The envelope function of the GPO nonlinear adaptive filter adopts an inverse function a tanh of a hyperbolic tangent function.
Example 5: an adaptive inverse tracking control method for a giant magnetostrictive tracking platform, as shown in fig. 1, comprises the following steps: firstly, performing off-line identification to obtain a left inverse model of the giant magnetostrictive actuator; secondly, based on a Filtered-epsilon LMS algorithm, two identical nonlinear filters are used for copying a left inverse model of the giant magnetostrictive actuator; finally, the controller C is searched in a self-adaptive mode by utilizing an error signal obtained by subtracting the outputs of the two nonlinear filters, and the weight coefficient of the filter is adjusted on line by adopting an LMS algorithm until the output of the giant magnetostrictive actuator is the same as the output of the reference model; wherein, the input of one of the two identical nonlinear filters is the object output; the input of the other nonlinear filter is the output of the reference model. The nonlinear filter adopts a GPO nonlinear adaptive filter (so that the dynamic hysteresis characteristic of the giant magnetostrictive actuator can be described more accurately). Identifying and obtaining an envelope function of the GPO by the following method: applying a desired input signal to the giant magnetostrictive actuator; collecting input/output data of the giant magnetostrictive actuator, then taking the output of the giant magnetostrictive actuator as the input of a model, taking the input of the giant magnetostrictive actuator as the output of the model, and identifying by a nonlinear fitting method to obtain an envelope function of the GPO:
γl＝a1a tanh(a2u(t)+a3)+a4
γr＝b1a tanh(b2u(t)+b3)+b4
wherein, γ islAnd gammarRespectively, the left envelope function and the right envelope function of the GPO nonlinear filter.
Example 6: an adaptive inverse tracking control method for a giant magnetostrictive tracking platform, as shown in fig. 1, comprises the following steps: firstly, performing off-line identification to obtain a left inverse model of the giant magnetostrictive actuator; secondly, based on a Filtered-epsilon LMS algorithm, two identical nonlinear filters are used for copying a left inverse model of the giant magnetostrictive actuator; finally, the controller C is searched in a self-adaptive mode by utilizing an error signal obtained by subtracting the outputs of the two nonlinear filters, and the weight coefficient of the filter is adjusted on line by adopting an LMS algorithm until the output of the giant magnetostrictive actuator is the same as the output of the reference model; wherein, the input of one of the two identical nonlinear filters is the object output; the input of the other nonlinear filter is the output of the reference model. The nonlinear filter adopts a GPO nonlinear adaptive filter.
The invention specifically comprises the following steps:
s1, initializing variables, and determining the order n +1, the threshold r, the convergence factor mu and the envelope function of the nonlinear filter (according to the system priori knowledge); randomly giving an initial weight coefficient W (0) of the nonlinear filter, and enabling k to be 0;
s2, obtaining a left inverse model of the giant magnetostrictive actuator through off-line identification;
s3, inputting the modeling excitation signal x (k) into the system;
s4, based on Filtered-epsilon LMS algorithm, two identical nonlinear filters are used for copying a left inverse model of the giant magnetostrictive actuator, the hysteresis characteristic of the giant magnetostrictive actuator is counteracted, an output signal y (k) and an output signal H (k) of the filter are obtained, and an estimation error between an actual controller and an ideal controller is calculated
And S5, updating the weight coefficient of the nonlinear filter: w (k +1) ═ W (k) +2 μ ∈ (k) H (k); wherein,
s6, let k be k + 1; updating the input vector x (k); and obtains a new output signal y (k) and the output signal H (k) of the filter, and the estimated error between the actual controller and the ideal controller
S7, judgmentIf yes, go to step S6; otherwise, the final controller C is obtained.
Example 7: an adaptive inverse tracking control method for a giant magnetostrictive tracking platform, as shown in fig. 1, comprises the following steps: firstly, performing off-line identification to obtain a left inverse model of the giant magnetostrictive actuator; secondly, based on a Filtered-epsilon LMS algorithm, two identical nonlinear filters are used for copying a left inverse model of the giant magnetostrictive actuator; finally, the controller C is searched in a self-adaptive mode by utilizing an error signal obtained by subtracting the outputs of the two nonlinear filters, and the weight coefficient of the filter is adjusted on line by adopting an LMS algorithm until the output of the giant magnetostrictive actuator is the same as the output of the reference model; wherein, the input of one of the two identical nonlinear filters is the object output; the input of the other nonlinear filter is the output of the reference model.
Further comprising: and the PID feedback controller is adopted to control the non-hysteresis characteristic of the giant magnetostrictive tracking platform, the input of the PID feedback controller is the difference value between an input signal and the output of an object, and the output of the PID feedback controller and the output of the controller C are summed to act on the giant magnetostrictive actuator. The control parameters of the PID feedback controller can be selected by adopting an engineering tuning method, and the differential parameters are set to be 0.
The working principle of one embodiment of the invention is as follows:
and for the linear controlled object, the adaptive inverse controller approximates the inverse of the controlled object transfer function. However, for a nonlinear controlled object, the transfer function is not existed. For the control of the nonlinear object, a nonlinear filter may be used to apply the output of the nonlinear filter as a control signal to the controlled object.
FIG. 2 is a schematic diagram of the Filtered- ε LMS control of the nonlinear system of the present invention, when there is a filtering error ε and the inverse model of the controlled objectIt works well when the input signal has the same statistical properties and dynamic range as the controlled object output. In order to obtain the error signal epsilon, in the system shown in fig. 2, two identical non-linear filter replicas are usedTheir outputs are subtracted to obtain an error signal for use in an adaptive search controller
The desired input to the system is denoted I in fig. 2. Ignoring the interference experienced by the object, the output of the object can be recorded as
Equation (1) shows that the input signal first acts onThen theIs applied to the object P, the output of the object P is Z. In FIG. 2 the ideal controller is denoted C*. Controller C*Are assumed. Assuming input I acts on C*And allow C*Drives the object P, when the output of the object P is equal to the output of the reference model, denoted as M.
PC*I＝MI (2)
Comparing the output of the real controller with the output of the ideal controller, the controller output error ε can be expressed as:
in FIG. 2, the error signalIs used to design the controllerNeglecting interference, the error signal can be represented by the signal flow diagram of fig. 2 as:
bringing formula (1) into formula (4) to obtain:
the adaptation process of (2) is shown in figure 2. As can be taken from fig. 2, when the adaptation process error is sufficiently small,andthe series of (c) will be approximately equal to unity gain. Returning again to equation (5), assumeClose enough to P to useReplacing P:
handleReplacing with unity gain:
thus, when adaptingMake itIs used, the mean square error of epsilon is minimized at the same time, i.e. a controller is selected that is as close as possible to an ideal controller.
Selecting a GPO nonlinear adaptive filter in the selection of the filter; the identification method of the envelope function parameter of the GPO nonlinear adaptive filter comprises the following steps: applying an expected input signal to the giant magnetostrictive actuator, collecting input/output data of the giant magnetostrictive actuator, taking the output of an object as the input of a model, and identifying the input of the object as the output of the model by a nonlinear fitting method to obtain an envelope function of the GPO:
γl＝a1a tanh(a2u(t)+a3)+a4
γr＝b1a tanh(b2u(t)+b3)+b4
the parameters of the controller are adjusted on line, the controller is connected with the controlled object in series, and the obtained error signal is usedThe LMS algorithm is used to adjust the filter's weight coefficients on-line until the output of the object is the same as the output of the reference model.
Because there is a difficulty in identifying the weight coefficients of multiple adaptive filters on line at the same time in the experimental process, the left inverse of the object is obtained by using the system shown in fig. 3 for off-line identification, and then the weight coefficients of the controller are adjusted on line as shown in the schematic diagram shown in fig. 4.
To verify the effect of the present invention, the inventors also performed the following simulation test:
filtered-epsilon LMS nonlinear adaptive inverse tracking control
Since the controller designed by the present invention is directed to a nonlinear system with rate dependent hysteresis over a range of frequencies, the control system shown in FIG. 4In the system, a rate-dependent Hammerstein model (equivalent to the aforementioned one) of a giant magnetostrictive actuator is established based on a least squares support vector machine model). The Hammerstein model is composed of a static hysteresis nonlinear element NL and a dynamic linear element G (z) in series, and is shown in FIG. 5.
The static hysteresis nonlinear part of the Hammerstein model is obtained by identifying input/output data under the action of a 1Hz single-frequency input signal through a least square support vector machine model, and then generating a special input signal containing 1-100 Hz frequency characteristics by adopting an input signal function idinput of a Matlab system identification toolbox:
V＝idinput(10000,'SINE',[0,0.02],[-0.5,0.5],[20,10])
the actuators are activated and the corresponding input/output signals are used to identify the latter dynamic linear portion. The Hammerstein linear dynamic model which can be identified by an ARX function is as follows:
a Hammerstein model in the frequency range of 1-100 Hz of GMA is obtained through modeling to replace the object in the graph 4, simulation is carried out according to the graph 4, and the simulation result is shown in the graph 6 and the table 4. As can be seen from FIG. 6 and Table 4, the feedforward Filtered-epsilon LMS nonlinear adaptive inverse tracking control of the present invention can well control GMA (i.e. giant magnetostrictive actuator) in a certain frequency range, so that the output signal tracks the expected input signal, and the control relative error is within 4%.
TABLE 4Filtered- ε LMS nonlinear adaptive inverse tracking control simulation error
Second, feedforward feedback PID composite control based on Filtered-epsilon LMS nonlinear adaptive inverse
A PID (Proportional integral derivative) controller in the continuous time domain can be written as:
wherein KpThe coefficient of the proportional link is the coefficient of the proportional link,is an integral element coefficient, KpTdIs a differential element coefficient. For the convenience of implementation in a computer, equation (9) is discretized. If the sampling period T is small, the inverse and integral of the error signal e (kT) at time kT can be approximately equal to:
substituting equations (10) and (11) into equation (9) can result in a discrete form of PID controller:
the invention adopts an engineering tuning method to select proper PID control parameters. Since the differential link is easy to cause oscillation and a feedforward adaptive inverse compensation controller is already provided, the differential parameter is set to be 0 in the invention.
Feedforward feedback PID composite controller design based on Filtered-epsilon LMS nonlinear adaptive inverse
The intelligent material has complex dynamic hysteresis nonlinear characteristics, so that the intelligent material is different from a common nonlinear link in the field of control engineering. The basic idea of the design of the hysteresis nonlinear system controller is to construct an inverse compensator of the system so that it can counteract the hysteresis nonlinearity in the control system. However, in an actual control system, linear terms such as disturbance and kinematics inevitably exist, so that a simple adaptive inverse hysteresis compensator may not meet the requirement of control accuracy due to the nature of an open loop. In order to improve the control precision, the invention further adopts a composite control scheme of combining the feedforward adaptive inverse compensation with a PID feedback controller, wherein the PID feedback controller is used for controlling a non-hysteresis part in the system. On the design of the composite controller, a PID feedback controller is added on the basis of a feed-forward Filtered-epsilon LMS nonlinear adaptive inverse tracking control method, and a control block diagram of the composite controller is shown in FIG. 7.
Control simulation
A simulation block diagram is built according to FIG. 7, and the expected input signal is set as a sinusoidal signal with the amplitude of 12 within the frequency range of 1-100 Hz. First identified by FIG. 3And then initializing a proper initial value for the feedforward Filtered-epsilon LMS nonlinear adaptive inverse filter. According to the engineering setting method, the parameters of the PID controller are selected to be Kp-0.01, Ki-5 and Kd-0. The simulation results are shown in fig. 8 and table 5.
TABLE 5 PID feedback composite control simulation error based on feedforward Filtered-epsilon LMS nonlinear adaptive inverse compensation
As can be seen from the results of FIG. 8 and Table 5, the feedforward feedback PID composite controller based on Filtered-epsilon LMS nonlinear adaptive inversion can ensure that the relative error of single-frequency expected input signal tracking control is within 3% in the frequency range of 1-100 Hz, and compared with the feedforward Filtered-epsilon LMS nonlinear adaptive inversion tracking control, the single-frequency input signal tracking error is obviously reduced after the PID controller is added.
Three, using the two controllers in the invention to carry out real-time tracking control experimental research on GMA (giant magnetostrictive actuator)
Results and analysis of the experiments
In order to further verify the effectiveness of a feedforward Filtered-epsilon LMS adaptive inverse controller of a dynamic hysteresis nonlinear system designed by the invention and a feedforward feedback PID composite controller based on the feedforward Filtered-epsilon LMS nonlinear adaptive inverse, the invention uses two controllers to carry out real-time tracking control experimental research on GMA (giant magnetostrictive actuator). The controller is realized in a dSPACE semi-physical simulation system, and the sampling frequency in the experiment is 10 KHz.
(1) Feedforward Filtered-epsilon LMS nonlinear adaptive inverse tracking control experiment result
An experimental control block diagram is designed based on the control structure shown in fig. 4, as shown in fig. 9. Fig. 10 shows the tracking results under the action of several sets of single-frequency and composite-frequency reference input signals, and table 6 shows the tracking control error results under different single-frequency and composite-frequency inputs. As can be seen from the results of fig. 10 and table 6, the Filtered-epsilon LMS nonlinear adaptive inverse tracking control of the present invention can ensure that the relative error of the single-frequency desired input signal tracking control is within 7% and the relative error of the composite-frequency desired input signal tracking control is within 10% in the practical application process, and such results indicate that the control algorithm can be completely applied to some engineering practice.
TABLE 6Filtered- ε LMS nonlinear adaptive inverse tracking control experiment error
(2) Feedforward-feedback PID composite control experiment result based on Filtered-epsilon LMS nonlinear adaptive inverse
The experimental control block diagram of the feedforward feedback PID composite control system based on the filtering-epsilon LMS nonlinear adaptive inverse is designed according to the control structure of FIG. 7, as shown in FIG. 11. The initial value of the parameter of the PID controller in fig. 11 is designed in the control simulation, and then is adjusted on line, and the adjustment basis is that the initial value is adjusted according to the tracking effect of the sine scanning input signal with the tracking frequency range of 1-100 Hz, so that the adjusted PID parameter can ensure that various single-frequency and composite-frequency input signals within the frequency range of 1-100 Hz can obtain good tracking effect. Fig. 12 shows the tracking control results of the reference input signal for single and complex frequencies, and table 7 shows the tracking control error results for different single and complex frequencies.
TABLE 7 PID feedback composite control experiment error based on feedforward Filtered-epsilon LMS nonlinear adaptive inverse
As can be seen from the results of fig. 12 and table 7, the feedforward feedback PID complex tracking controller based on the feedforward Filtered-epsilon LMS nonlinear adaptive inverse of the present invention can ensure that the relative error of the single-frequency desired input signal tracking control is within 4% and the relative error of the complex frequency desired input signal tracking control is within 9% in the practical application process, and compared with the feedforward filtering-epsilon LMS nonlinear adaptive inverse tracking control, the single-frequency input signal tracking error is significantly reduced and the complex frequency input signal tracking error is also reduced after the PID controller is added.
Claims (7)
1. An adaptive inverse tracking control method for a giant magnetostrictive tracking platform is characterized by comprising the following steps: firstly, performing off-line identification to obtain a left inverse model of the giant magnetostrictive actuator; secondly, based on a Filtered-epsilon LMS algorithm, two identical nonlinear filters are used for copying a left inverse model of the giant magnetostrictive actuator; finally, the controller C is searched in a self-adaptive mode by utilizing an error signal obtained by subtracting the outputs of the two nonlinear filters, and the weight coefficient of the filter is adjusted on line by adopting an LMS algorithm until the output of the giant magnetostrictive actuator is the same as the output of the reference model; wherein, the input of one of the two identical nonlinear filters is the object output; the input of the other nonlinear filter is the output of the reference model.
2. The adaptive inverse tracking control method for giant magnetostrictive tracking platforms according to claim 1, wherein the nonlinear filter is a GPO nonlinear adaptive filter.
3. The adaptive inverse tracking control method for the giant magnetostrictive tracking platform according to claim 2, wherein the envelope function of the GPO nonlinear adaptive filter adopts an inverse function atanh of a hyperbolic tangent function.
4. The adaptive inverse tracking control method for the giant magnetostrictive tracking platform according to claim 2, wherein the envelope function of the GPO is identified by the following method: applying a desired input signal to the giant magnetostrictive actuator; collecting input/output data of the giant magnetostrictive actuator, then taking the output of the giant magnetostrictive actuator as the input of a model, taking the input of the giant magnetostrictive actuator as the output of the model, and identifying by a nonlinear fitting method to obtain an envelope function of the GPO:
γl＝a1a tanh(a2u(t)+a3)+a4
γr＝b1a tanh(b2u(t)+b3)+b4
wherein, r islAnd rrRespectively, the left and right envelope functions of the non-linear filter.
5. The adaptive inverse tracking control method for the giant magnetostrictive tracking platform according to claim 1, characterized by comprising the following steps:
s1, initializing variables, and determining the order n +1, the threshold r, the convergence factor mu and the envelope function of the nonlinear filter; randomly giving an initial weight coefficient W (0) of the nonlinear filter, and enabling k to be 0;
s2, obtaining a left inverse model of the giant magnetostrictive actuator through off-line identification;
s3, inputting the modeling excitation signal x (k) into the system;
s4, based on Filtered-epsilon LMS algorithm, two identical nonlinear filters are used for copying a left inverse model of the giant magnetostrictive actuator, the hysteresis characteristic of the giant magnetostrictive actuator is counteracted, an output signal y (k) and an output signal H (k) of the filter are obtained, and an estimation error between an actual controller and an ideal controller is calculated
And S5, updating the weight coefficient of the nonlinear filter: w (k +1) ═ W (k) +2 μ ∈ (k) H (k); wherein,
s6, let k be k + 1; updating the input vector x (k); and obtains a new output signal y (k) and the output signal H (k) of the filter, and the estimated error between the actual controller and the ideal controller
S7, judgmentIs there a If yes, go to step S6; otherwise, the final controller C is obtained.
6. The adaptive inverse tracking control method for the giant magnetostrictive tracking platform according to any one of claims 1 to 5, further comprising: and the PID feedback controller is adopted to control the non-hysteresis characteristic of the giant magnetostrictive tracking platform, the input of the PID feedback controller is the difference value between an input signal and the output of an object, and the output of the PID feedback controller and the output of the controller C are summed to act on the giant magnetostrictive actuator.
7. The adaptive inverse tracking control method for giant magnetostrictive tracking platforms according to claim 6, characterized in that the control parameters of the PID feedback controller are selected by engineering regularization, and the differential parameter is set to 0.
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