CN114489010A - ADRC extended observer state observation error real-time prediction method and system - Google Patents
ADRC extended observer state observation error real-time prediction method and system Download PDFInfo
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Abstract
A real-time prediction method and a real-time prediction system for state observation errors of an ADRC extended observer comprise the following steps: step S1: before the robot enters the motion of the t +1 moment, obtaining error values of three states from the initial moment to the t moment; step S2: judging whether the current time t meets the requirement of a cycle threshold, if so, executing a step S3, and if not, executing a step S4; step S3: fitting the error values of the three states by a least square method of a linear regression equation to obtain a fitted linear equation, and executing the step S4; step S4: substituting the error values of the three states at the time t into a prediction function to respectively obtain predicted values of the state error values at the time t +1 of the three states; step S5: the predicted value of the state error value at the time of t +1 is input into the parameter updater, and the state error value at the time of t +1 is predicted so that the number of the whole updating iteration is reduced, thus the number of the iteration updating can be reduced by using a more accurate error value, and the convergence speed requirement is accelerated.
Description
Technical Field
The invention relates to the technical field of ADRC extended observers, in particular to a method and a system for predicting state observation errors of an ADRC extended observer in real time.
Background
The Active Disturbance Rejection Controller (ADRC) is composed of a Tracking Differentiator (TD), an Extended State Observer (ESO) and a nonlinear feedback control rate (NLSEF). The ADRC has the main idea that all interference and uncertainty in a control system are regarded as total disturbance, and the total disturbance is packed into an extended observer to be uniformly estimated and compensated, so that the control performance is improved. The function of the extended state observer is to estimate the state of a research object in real time and to use the extended state to carry out unified estimation on the total disturbance of the system.
The selection of the parameters of the extended state observer directly influences the accuracy of the observed state and determines the error of the observed state, thereby influencing the tracking error of the ADRC control system. In order to reduce the influence of errors, the prior art adopts an iterative optimization method to update the parameters of the extended state observer, which is usually an off-line optimization method, that is, the errors of the last operation trajectory are saved, and the saved errors are used to optimize the parameters at this moment in the process of the operation trajectory. Further, the optimization index used in the optimization method generally includes a requirement for convergence of the trajectory error and a requirement for smooth change of the controlled variable.
But this method has a disadvantage in that it cannot sufficiently use real-time error information. The off-line optimization method utilizes the error information of the last running track and does not utilize the error information of the current running track, so that the parameter convergence speed is greatly reduced. Even though some techniques refer to using the error information of the current operation track, only the error generated at the last moment is used, and all the error information generated by the current operation track is not fully used, which greatly reduces the parameter convergence speed. The prior art needs more than 20 times of iteration to be possible to converge to the desired value, and the convergence speed of the method does not meet the requirements of the current engineering application.
Disclosure of Invention
In view of the above-mentioned drawbacks, the present invention provides a method and a system for predicting state observation errors of an ADRC extended observer in real time, which can fully use real-time error information to achieve fast convergence of parameters.
In order to achieve the purpose, the invention adopts the following technical scheme: a real-time prediction method for state observation errors of an ADRC extended observer comprises the following steps:
step S1: before the robot enters the motion of the t +1 moment, obtaining error values of three states from the initial moment to the t moment;
step S2: judging whether the current time t meets the requirement of the cycle threshold, if so, executing a step S3, and if not, executing a step S4;
step S3: fitting the error values of the three states by a least square method of a linear regression equation to obtain a fitted linear equation, and executing the step S4;
step S4: substituting the error values of the three states at the time t into a prediction function to respectively obtain predicted values of the state error values at the time t +1 of the three states;
step S5: and inputting the predicted values of the state error values at the three states at the moment of t +1 into a parameter updater to optimize the parameters of the extended observer in real time.
Preferably, the step S4 includes the following specific steps:
and if the previous time t meets the requirement of the cycle threshold, predicting to obtain a predicted value of the state error value at the time t +1 by fitting a linear equation, and if the previous time t does not meet the requirement of the cycle threshold, taking the state error value at the current time t as the predicted value of the state error value at the time t + 1.
Preferably, the method further comprises the following specific steps before step S5:
and judging the input of the predicted value of the state error value at the time t +1, and if the input of the predicted value of the state error value at the time t +1 is predicted by a fitted linear equation, correcting the predicted value of the state error value at the time t +1 by using the acceleration of the motion track of the robot.
Preferably, the specific formula for correcting the predicted value of the state error value at the time t +1 is as follows:
wherein the content of the first and second substances,
the corrected value of the predicted value of the state error value at the moment t +1 of the ith state is the range of (1, 2, 3),
the predicted value of the state error value at the t +1 moment of the ith state is a, the acceleration of the motion trail of the robot is a, and f (t) is the value of a fitted linear equation at the t moment.
Preferably, the cycle threshold in step S2 is 5 cycles.
A real-time prediction system for state observation errors of an ADRC extended observer uses the real-time prediction method and the real-time prediction system for the state observation errors of the ADRC extended observer, and comprises the following steps: the system comprises a current error value acquisition module, a period threshold value judgment module, an equation fitting module, a prediction module and an input module;
the error value acquisition module is used for acquiring error values of three states from an initial moment to a t moment before the robot enters the movement of the t +1 moment;
the period threshold judging module is used for judging whether the current time t meets the period threshold requirement;
the equation fitting module is used for fitting the error values of the three states by a least square method of a linear regression equation to obtain a fitted linear equation;
the prediction module is used for substituting the error values of the three states at the time t into a prediction function to respectively obtain the predicted values of the state error values at the time t +1 of the three states;
the input module is used for inputting the predicted values of the state error values at the three states at the moment of t +1 into the parameter updater to optimize the parameters of the extended observer in real time.
Preferably, the cycle threshold value judging module further comprises a selecting module;
the selection module is used for judging whether the previous time t meets the requirement of a cycle threshold, if so, the predicted value of the state error value at the time t +1 is obtained through the prediction of a fitted linear equation, and if not, the state error value at the current time t is used as the predicted value of the state error value at the time t + 1.
Preferably, the robot further comprises a correction module, the correction module is configured to determine input of a predicted value of the state error value at the time t +1, and if the input of the predicted value of the state error value at the time t +1 is predicted by fitting a linear equation, correct the predicted value of the state error value at the time t +1 by using the acceleration of the robot motion trajectory.
One of the above technical solutions has the following advantages or beneficial effects: the state error value at time t +1 is predicted so that the number of overall update iterations becomes smaller, so that the overall parameter can converge quickly to the desired value. If no prediction is made, the error value used is the error value at the previous time, and the predicted real-time error value is used to reduce the number of iterations, and the predicted real-time error value will actually be closer to the desired error value, thus reducing the number of iteration updates with a more accurate error value and speeding up the convergence speed requirement.
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FIG. 1 is a schematic flow diagram of one embodiment of the method of the present invention;
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of the present invention, "a plurality" means two or more unless otherwise specified.
In the description of the present invention, it should be noted that, unless otherwise explicitly specified or limited, the terms "mounted," "connected," and "connected" are to be construed broadly, e.g., as meaning either a fixed connection, a removable connection, or an integral connection; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.
As shown in fig. 1, a method and a system for real-time prediction of state observation errors of an ADRC extended observer include the following steps:
step S1: before the robot enters the motion of the t +1 moment, obtaining error values of three states from the initial moment to the t moment;
step S2: judging whether the current time t meets the requirement of a cycle threshold, if so, executing a step S3, and if not, executing a step S4;
step S3: fitting the error values of the three states by a least square method of a linear regression equation to obtain a fitted linear equation, and executing the step S4;
step S4: substituting the error values of the three states at the time t into a prediction function to respectively obtain predicted values of the state error values at the time t +1 of the three states;
step S5: and inputting the predicted values of the state error values at the three states at the moment of t +1 into a parameter updater to optimize the parameters of the extended observer in real time.
Because of the relation between the state observation error and the track characteristic, the correlation between the state observation error and the track speed is high. The method is based on the least square fitting of the linear regression equation, and the predicted value is adjusted according to the track acceleration characteristic, so that the purpose of predicting the state observation error more accurately is achieved. In consideration of the fact that real-time prediction is needed in actual engineering, the method for predicting the state is implemented by adopting the existing simple algorithm, and the calculation speed can be increased. Therefore, before the robot enters the motion at the time t +1, error values of three states at the time t are obtained, and the obtaining of the error values is a common technology of the conventional ADRC, so that the details are not repeated in the present application. And then performing least square fitting on the error values of the three states by using a linear regression equation to obtain the value of a linear equation. The number of fitting points (i.e., period) of the linear regression equation needs to be considered, and if the number of fitting points of the regression equation is too small, the fitting effect is affected, so that the value of the linear equation is deviated. In this case, the effect of not performing fitting is better than the effect after fitting. Therefore, the error values of the three states are directly substituted into the prediction function to be used as the final prediction value of the state error value at the time t +1 when the current time t does not meet the requirement of the cycle threshold. After the current time t meets the requirement of a cycle threshold, fitting error values of three states by a least square method of a linear regression equation to obtain a fitted linear equation value, predicting the fitted linear equation value to obtain a predicted value of the state error value at the time t +1, training the predicted value by using the existing prediction model, and substituting the fitted linear equation value into the prediction model to obtain the predicted value of the state error value at the time t + 1. And then substituting the predicted value of the state error value at the time of t +1 into a parameter updater to optimize the extended observer in real time. In the process, the real-time error value at the next time (t +1) can be returned to the prediction model, and the prediction model is corrected. The accuracy of the prediction model is guaranteed, and therefore the accuracy of real-time optimization of the extended observer is guaranteed. The state error value at time t +1 is predicted so that the number of overall update iterations becomes small, allowing the overall parameter to converge quickly to the desired value. If no prediction is made, the error value used is the error value at the previous time, and the predicted real-time error value is used to reduce the number of iterations, and the predicted real-time error value will actually be closer to the desired error value, thus reducing the number of iteration updates with a more accurate error value and speeding up the convergence speed requirement.
Preferably, the step S4 includes the following specific steps:
and if the previous time t meets the requirement of the cycle threshold, predicting to obtain a predicted value of the state error value at the time t +1 by fitting a linear equation, and if the previous time t does not meet the requirement of the cycle threshold, taking the state error value at the current time t as the predicted value of the state error value at the time t + 1.
The linear regression equation is f (t) ═ zx + y, z and y are coefficients, x is the error value of three states at time t, and z and y are obtained by the least square method. The three states are respectively the observation of the position, the speed and the acceleration.
Preferably, the method further comprises the following specific steps before step S5:
and judging the input of the predicted value of the state error value at the time t +1, and if the input of the predicted value of the state error value at the time t +1 is predicted by a fitted linear equation, correcting the predicted value of the state error value at the time t +1 by using the acceleration of the motion track of the robot.
Because the robot can possess certain acceleration when moving after the robot motion satisfies the cycle demand, can effectively improve the precision of predicted value through accelerateing to revise the predicted value of the state error value at t +1 moment. When the motion of the robot does not meet the periodic requirement, the robot is represented to be at the beginning of the motion, and the acceleration value is quite small and can be ignored. Therefore, when the robot motion does not meet the cycle requirement, the predicted value of the state error value at the time t +1 does not need to be corrected.
Preferably, the specific formula for correcting the predicted value of the state error value at the time t +1 is as follows:
wherein the content of the first and second substances,
the corrected value of the predicted value of the state error value at the moment t +1 of the ith state is the range of (1, 2, 3),
the predicted value of the state error value at the t +1 moment of the ith state is a, the acceleration of the motion trail of the robot is a, and f (t) is the value of a fitted linear equation at the t moment.
Preferably, the cycle threshold in step S2 is 5 cycles.
A real-time prediction system for state observation errors of an ADRC extended observer uses the real-time prediction method and the real-time prediction system for the state observation errors of the ADRC extended observer, and comprises the following steps: the system comprises a current error value acquisition module, a period threshold value judgment module, an equation fitting module, a prediction module and an input module;
the error value acquisition module is used for acquiring error values of three states from an initial moment to a t moment before the robot enters the movement of the t +1 moment;
the period threshold judging module is used for judging whether the current time t meets the period threshold requirement;
the equation fitting module is used for fitting the error values of the three states by a least square method of a linear regression equation to obtain a fitted linear equation;
the prediction module is used for substituting the error values of the three states at the time t into a prediction function to respectively obtain the predicted values of the state error values at the time t +1 of the three states;
the input module is used for inputting the predicted values of the state error values at the three states at the moment of t +1 into the parameter updater to optimize the parameters of the extended observer in real time.
Preferably, the cycle threshold value judging module further comprises a selecting module;
the selection module is used for judging whether the previous time t meets the requirement of the period threshold, if so, the predicted value of the state error value at the time t +1 is obtained through the prediction of a fitted linear equation, and if not, the state error value at the current time t is used as the predicted value of the state error value at the time t + 1.
Preferably, the robot further comprises a correction module, the correction module is configured to determine an input of the predicted value of the state error value at the time t +1, and if the input of the predicted value of the state error value at the time t +1 is predicted by fitting a linear equation, correct the predicted value of the state error value at the time t +1 using the acceleration of the robot motion trajectory.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an illustrative embodiment," "an example," "a specific example," or "some examples" or the like mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
While embodiments of the invention have been shown and described, it will be understood by those of ordinary skill in the art that: various changes, modifications, substitutions and alterations can be made to the embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.
Claims (8)
1. A real-time prediction method and a real-time prediction system for an observation error of an ADRC extended observer are characterized by comprising the following steps:
step S1: before the robot enters the motion of the t +1 moment, obtaining error values of three states from the initial moment to the t moment;
step S2: judging whether the current time t meets the requirement of the cycle threshold, if so, executing a step S3, and if not, executing a step S4;
step S3: fitting the error values of the three states by a least square method of a linear regression equation to obtain a fitted linear equation, and executing the step S4;
step S4: substituting the error values of the three states at the time t into a prediction function to respectively obtain predicted values of the state error values at the time t +1 of the three states;
step S5: and inputting the predicted values of the state error values at the three states at the moment of t +1 into a parameter updater to optimize the parameters of the extended observer in real time.
2. The ADRC extended observer state observation error real-time prediction method and system according to claim 1, wherein the step S4 comprises the following steps:
and if the previous time t meets the requirement of the cycle threshold, predicting to obtain a predicted value of the state error value at the time t +1 by fitting a linear equation, and if the previous time t does not meet the requirement of the cycle threshold, taking the state error value at the current time t as the predicted value of the state error value at the time t + 1.
3. The method and system for predicting the state observation error of the ADRC extended observer in real time as claimed in claim 1, wherein the step S5 is preceded by the following steps:
and judging the input of the predicted value of the state error value at the time t +1, and if the input of the predicted value of the state error value at the time t +1 is predicted by a fitted linear equation, correcting the predicted value of the state error value at the time t +1 by using the acceleration of the motion track of the robot.
4. The method and system for predicting the state observation error of the ADRC extended observer in real time according to claim 3, wherein the specific formula for correcting the predicted value of the state error value at the time t +1 is as follows:
wherein the content of the first and second substances,
state error value at time t +1 for the ith stateI has a value range of (1, 2, 3),
the predicted value of the state error value at the t +1 moment of the ith state is a, the acceleration of the motion trail of the robot is a, and f (t) is the value of a fitted linear equation at the t moment.
5. The ADRC extended observer state observation error real-time prediction method and system as claimed in claim 1, wherein the period threshold in step S2 is 5 periods.
6. An ADRC extended observer state observation error real-time prediction system, which uses the ADRC extended observer state observation error real-time prediction method and system as claimed in any one of claims 1 to 5, characterized in that the ADRC extended observer state observation error real-time prediction method and system comprises: the system comprises a current error value acquisition module, a period threshold value judgment module, an equation fitting module, a prediction module and an input module;
the error value acquisition module is used for acquiring error values of three states from an initial moment to a t moment before the robot enters the movement of the t +1 moment;
the period threshold judging module is used for judging whether the current time t meets the period threshold requirement;
the equation fitting module is used for fitting the error values of the three states by a least square method of a linear regression equation to obtain a fitted linear equation;
the prediction module is used for substituting the error values of the three states at the time t into a prediction function to respectively obtain the predicted values of the state error values at the time t +1 of the three states;
the input module is used for inputting the predicted values of the state error values at the three states at the moment of t +1 into the parameter updater to optimize the parameters of the extended observer in real time.
7. The ADRC extended observer state observation error real-time prediction system of claim 6, wherein the period threshold determination module further comprises a selection module;
the selection module is used for judging whether the previous time t meets the requirement of the period threshold, if so, the predicted value of the state error value at the time t +1 is obtained through the prediction of a fitted linear equation, and if not, the state error value at the current time t is used as the predicted value of the state error value at the time t + 1.
8. The ADRC extended observer state observation error real-time prediction system of claim 6, further comprising a correction module, wherein the correction module is configured to determine an input of the predicted value of the state error value at the time t +1, and correct the predicted value of the state error value at the time t +1 using the acceleration of the robot motion trajectory if the input of the predicted value of the state error value at the time t +1 is predicted by fitting a linear equation.
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