A sliding mode observer spliced arc motor model predictive control method

Abstract

The application discloses a splicing arc motor model prediction control method of a sliding mode observer, obtains a current prediction equation by Euler discretization of a voltage model in a rotating coordinate system of the splicing arc motor; designs a sliding mode disturbance observer based on a novel logarithmic reaching law, obtains a parameter disturbance estimation value and substitutes the parameter disturbance estimation value into the current prediction equation; then outputs actual and expected speed errors through a super-helix sliding mode control, acquires a q-axis reference current, substitutes the q-axis reference current into the current prediction equation; substitutes voltage vectors into the prediction equation in sequence, selects an optimal prediction current through a value function, and an optimal voltage vector signal corresponding to the optimal prediction current is used for driving the splicing arc motor by an inverter. The application increases a disturbance estimation module, thereby restraining parameter uncertainty, and improves speed stability and precision through super-helix sliding mode speed control.

Description

Technical Field

[0001] This invention belongs to the field of special motor control technology, specifically relating to a predictive control method for a spliced ​​arc motor model using a sliding mode observer. Background Technology

[0002] The spliced ​​arc permanent magnet synchronous motor has advantages such as high power factor, good robustness, and low maintenance cost, and has been used in the field of astronomical instruments for azimuth axis drive of large telescopes in recent years. However, because the spliced ​​arc motor is a complex nonlinear system, traditional motor vector control is easily affected by internal and external disturbances and changes in load and speed, and can no longer meet the high precision requirements of the motor. Therefore, an advanced control theory that takes into account all aspects is needed to improve the stability and accuracy of the motor system.

[0003] Current research on vector control improvements has made some progress. Common methods include fractional-order control, fuzzy control, model predictive control, variable structure control, Hamiltonian model control, ADRC control, and a series of optimization algorithms such as particle swarm optimization, fruit fly swarm optimization, and wolf pack swarm optimization. These methods have also been combined with PID control for motor speed control, achieving some success. However, these algorithms have some disadvantages. For example, fractional-order PID control requires adjusting a large number of parameters, and the fuzzy rules of fuzzy PID control need further optimization. Therefore, achieving high-performance control of spliced ​​arc motors requires further improvements in multiple aspects.

[0004] Traditional sliding mode control struggles to suppress its inherent chattering. Current designs typically employ improved linear sliding surfaces to enhance convergence and response speed, such as fast nonsingular terminal sliding surfaces, fractional sliding surfaces, and integral sliding surfaces. Furthermore, improvements are made to the switching functions used in the reaching law to suppress chattering caused by discontinuous switching, such as using sigmoid functions, hyperbolic sine functions, and saturation functions. Additionally, fractional-order and fuzzy logic theories can be combined to improve the reaching law structure and accelerate the response of state variables. Summary of the Invention

[0005] Technical problems solved: In view of the technical problems of insufficient output accuracy, poor system robustness and chattering of phase current waveform in the spliced ​​arc motor under traditional control in the existing technology, in order to ensure the stable operation of equipment such as telescopes, this invention provides a model predictive control method for spliced ​​arc motors in sliding mode observers. It adds a disturbance estimation module to suppress parameter uncertainty and improves speed stability and accuracy through super-helical sliding mode speed control.

[0006] Technical solution:

[0007] A predictive control method for a spliced ​​arc motor model using a sliding mode observer, the method comprising the following steps:

[0008] Step 1: Obtain the speed error of the splicing arc motor based on the desired speed of the motor and the speed feedback from the encoder;

[0009] Step 2: Obtain the q-axis reference current by controlling the speed error of the splicing arc motor based on the super spiral sliding mode controller;

[0010] Step 3: Analyze the disturbances caused by parameter uncertainty to the motor control system, and design a sliding mode disturbance observer for the spliced ​​arc motor; measure the motor angular velocity through the encoder, obtain the dq axis current through current sampling, and substitute the motor angular velocity and dq axis current into the sliding mode disturbance observer to obtain the disturbance estimate and dq axis current compensation value.

[0011] Step 4: Discretize the voltage equation of the spliced ​​arc motor to obtain the current prediction model of the spliced ​​arc motor;

[0012] Step 5: Substitute the disturbance estimate and dq-axis current compensation value into the current prediction model; then apply the voltage vector to the current prediction equation to obtain the corresponding predicted current value.

[0013] Step 6: Substitute the dq-axis reference current and the predicted current value into the minimization value function, use the minimization value function to determine the minimum current, and obtain the optimal voltage vector corresponding to the minimum current.

[0014] Furthermore, in step 2, an improved superspiral sliding mode controller is designed using a hyperbolic tangent function with a steepness factor:

[0015] ;

[0016] In the formula: Represents a state. It is the measurement output. , For design parameters, It is a power variable.

[0017] The hyperbolic tangent function containing the steepness factor is expressed as follows:

[0018] ;

[0019] In the formula: For sliding surface, This is the steepness factor.

[0020] Furthermore, in step 3, the model equations for the sliding mode disturbance observer are:

[0021] ;

[0022] In the formula: , It is the dq axis voltage. , For dq axis current, For stator resistance, For inductance, Electric angular velocity, For magnetic linkage, , This is the estimated disturbance caused by the mismatch of the dq axis parameters. , These are the estimated current values ​​for the d-axis and q-axis, respectively. , This is the sliding mode control function for the dq axis. and These are adjustable parameters for the dq axis controller.

[0023] Furthermore, in step 3, the calculation process of the sliding mode control function includes the following steps:

[0024] Based on the estimated d-q axis current and the actual current error, the sliding surfaces of the observer for the d-axis and q-axis are designed as follows: , ;

[0025] In the formula: , ;

[0026] The sliding mode logarithmic function reaching law based on the hyperbolic tangent function with steepness factor is designed as follows:

[0027] ;

[0028] In the formula, , , All are positive numbers; ; And it is an even number; These are adjustable parameters; The meaning is the same as that of a super-spiral sliding mode controller.

[0029] By combining the designed reaching law with the sliding surfaces of the d-axis and q-axis, and the model equations of the disturbance observer, the sliding control functions of the d-axis and q-axis can be calculated. , :

[0030] .

[0031] Furthermore, in step 4, the system is discretized, and the output of the sliding mode observer is... Compensation current at any time , and Time-based perturbation , Substituting into the current prediction model equation, we get Current prediction model equation at time:

[0032] ;

[0033] In the formula: Indicates the sampling time.

[0034] Furthermore, in step 6, the q-axis reference current output by the superspiral sliding mode controller is... d-axis reference current and predictions Actual current at time , Substitute into the cost function respectively : The minimum current obtained corresponds to the optimal voltage vector.

[0035] Beneficial effects:

[0036] First, the sliding mode observer model predictive control method for spliced ​​arc motors of the present invention improves the control system of spliced ​​arc motors in several aspects. Traditional motor speed loop control uses a PI controller, which requires empirical parameter tuning. The present invention uses an improved super-spiral speed controller, which effectively suppresses sliding mode chattering and ensures fast response and anti-interference capability of the sliding mode. For the current loop, traditional control using a PI controller cannot meet the accuracy requirements and robustness of the current loop. Based on model predictive control, the present invention uses an improved sliding mode observer to update and compensate model parameters in real time, effectively improving the accuracy and precision of model predictive current control.

[0037] Secondly, the splicing arc motor model predictive control method of the sliding mode observer of the present invention, which uses a speed super-spiral controller and a model prediction-based sliding mode observer, can comprehensively consider the influence of the speed loop and current loop on the motor output, and use the sliding mode observer to compensate for disturbances, effectively improving the overall performance of the system. Attached Figure Description

[0038] Figure 1 This is a block diagram illustrating the principle of the predictive control method for spliced ​​arc motor models using a sliding mode observer according to an embodiment of the present invention.

[0039] Figure 2 This is a schematic diagram of the hyperbolic tangent function with steepness factor according to an embodiment of the present invention;

[0040] Figure 3(a) is a graph showing the speed change curves under the control of changing the rotation speed and sudden load in an embodiment of the present invention.

[0041] Figure 3(b) shows the speed change curves under traditional model predictive control with changes in rotational speed and sudden load.

[0042] Figure 4(a) is a waveform diagram of a cycle current under the control of an embodiment of the present invention.

[0043] Figure 4(b) shows a one-cycle current waveform under traditional model predictive control. Detailed Implementation

[0044] The following embodiments are provided to enable those skilled in the art to more fully understand the present invention, but do not limit the invention in any way.

[0045] like Figure 1 As shown, the improved sliding mode observer of the present invention for predictive control of spliced ​​arc motor models includes:

[0046] Establish a mathematical model of the permanent magnet synchronous motor in a rotating coordinate system:

[0047] (1);

[0048] In the formula: , It is the dq axis voltage. , For dq axis current, For stator resistance, For inductance, Electric angular velocity, It is a magnetic flux.

[0049] Traditional PI speed controllers cannot effectively control errors and output q-axis reference current. Super spiral sliding mode is used to control speed errors. Super spiral sliding mode is a type of second-order sliding mode. Compared with traditional first-order sliding mode, super spiral sliding mode does not have high-frequency switching, so the system has better chatter suppression effect.

[0050] In sliding mode control, the system state needs to be constantly switched. The key is the smoothness of the switching function. The common switching function is the Sign function, but this function is not smooth enough during state transitions. Therefore, this invention adopts an extended hyperbolic tangent function. The traditional hyperbolic tangent function expression is:

[0051] (2);

[0052] Inject steepness factor into variable s The new expression is:

[0053] (3).

[0054] Figure 2This is a schematic diagram of the hyperbolic tangent function with steepness factor described in this article. When the steepness factor... The larger the value of , the closer its curve is to the Sign function, while still ensuring the smoothness of the curve.

[0055] Therefore, the superspiral sliding mode controller is designed as follows:

[0056] (4);

[0057] In the formula: , For design parameters, It is a sliding surface.

[0058] Based on the forward Euler discrete equations, the prediction equations for the dq-axis current model at the next moment are written as follows:

[0059] (5).

[0060] In the control of splicing arc motors, changes in motor parameters have a significant impact on the performance of the control system; the more accurate the parameters, the smaller the disturbance to the motor.

[0061] Rewrite the dq-axis voltage equation of the spliced ​​arc motor, considering the effects of parameter disturbances:

[0062] (6);

[0063] In the formula: , The disturbance caused by the mismatch of dq axis parameters.

[0064] (7);

[0065] In the formula: , and These represent the differences between the actual resistance, inductance, and flux linkage of the motor and the desired resistance, inductance, and flux linkage.

[0066] The following section begins the design of a sliding mode perturbation observer based on parameter mismatch:

[0067] (8);

[0068] In the formula: and These are the sliding mode control functions for the dq axes, respectively. and Do not use adjustable parameters for the controller.

[0069] First, define the dq axis current error and disturbance error as follows:

[0070] , (9);

[0071] In the formula: , This is the estimated value of the dq-axis current. , The perturbation estimated for the dq axis.

[0072] Based on equations (8) and (6), the error can be obtained as follows:

[0073] (10);

[0074] (11);

[0075] Then define the sliding surface as:

[0076] , (12).

[0077] Common reaching laws typically use a switching function as the sliding mode switching function. Considering the smoothness of the logarithmic function and the hyperbolic tangent function, we design a sliding mode reaching law based on the hyperbolic tangent function:

[0078] (13);

[0079] In the formula, , , All are positive numbers; ; And it is an even number; These are adjustable parameters; The meaning is the same as that of a super-spiral sliding mode controller.

[0080] Combining the error equation and the sliding mode reaching law, we can obtain:

[0081] (14);

[0082] Calculated and :

[0083] (15);

[0084] The above sliding mode observer satisfies the Lyapunov stability condition:

[0085] (16);

[0086] Will and Substituting into equation (5), we obtain the final form of the sliding mode disturbance observer:

[0087] (17);

[0088] In the formula: .

[0089] Therefore, the sliding mode observer outputs the dq axis to estimate the compensation current. , and estimated disturbance , Substituting these output quantities into the dq-axis current prediction model equation, the current prediction model equation for the next time step is updated as follows:

[0090] (18).

[0091] At this point, the sliding mode observer is equivalent to performing a one-beat delay compensation, and the impact of hardware calculation delays and other factors no longer needs to be considered. Substituting the eight voltage vectors generated by the inverter into the updated current model equation yields the predicted dq-axis current. and .

[0092] The cost function to be minimized is: ;

[0093] Predict Actual current at time , Substitute into the cost function respectively The minimum value is calculated and selected as the optimal predicted current. The optimal predicted current corresponds to the optimal voltage vector, which is then converted into a switching signal. , , The inverter drives the motor.

[0094] Figures 3(a) and 3(b) show the speed change curves of the spliced ​​arc motor under the current model predictive control of the present invention and the conventional current model, respectively, when the speed and load are changed. It can be seen that the overshoot of the motor is relatively small and the response time is short under the strategy of the present invention.

[0095] Figure 4(a) and Figure 4(b) show the phase current waveforms of the spliced ​​arc motor under the load change cycle of the strategy of the present invention and the conventional current model predictive control, respectively. It can be seen that the current under the strategy of the present invention has smaller jitter changes when the load changes.

[0096] As can be seen from the above analysis, in the control strategy provided by the present invention, the sliding mode observer can effectively eliminate the disturbance factors predicted by the traditional model and improve the robustness of the system. At the same time, the improved sliding mode speed controller is used to replace PI control, which effectively suppresses the chattering of the sliding mode.

[0097] The above are merely preferred embodiments of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should be considered within the scope of protection of the present invention.

Claims

1. A predictive control method for a spliced ​​arc motor model using a sliding mode observer, characterized in that, The predictive control method for the spliced ​​arc motor model includes the following steps: Step 1: Obtain the speed error of the splicing arc motor based on the desired speed of the motor and the speed feedback from the encoder; Step 2: Obtain the q-axis reference current by controlling the speed error of the splicing arc motor based on the super spiral sliding mode controller; In step 2, an improved superspiral sliding mode controller is designed using a hyperbolic tangent function with a steepness factor: ； In the formula: Represents a state. It is the measurement output. , For design parameters, It is a power variable; The hyperbolic tangent function containing the steepness factor is expressed as follows: ； In the formula: For sliding surface, Steepness factor; Step 3: Analyze the disturbances caused by parameter uncertainty to the motor control system, and design a sliding mode disturbance observer for the spliced ​​arc motor; measure the motor angular velocity through the encoder, obtain the dq axis current through current sampling, and substitute the motor angular velocity and dq axis current into the sliding mode disturbance observer to obtain the disturbance estimate and dq axis current compensation value. In step 3, the model equations for the sliding mode disturbance observer are: ； In the formula: , It is the dq axis voltage. , For dq axis current, For stator resistance, For inductance, Electric angular velocity, For magnetic linkage, , This is the estimated disturbance caused by the mismatch of the dq axis parameters. , These are the estimated current values ​​for the d-axis and q-axis, respectively. , This is the sliding mode control function for the dq axis. and Adjustable parameters for the dq axis controller; Step 4: Discretize the voltage equation of the spliced ​​arc motor to obtain the current prediction model of the spliced ​​arc motor; Step 5: Substitute the disturbance estimate and dq-axis current compensation value into the current prediction model; then apply the voltage vector to the current prediction equation to obtain the corresponding predicted current value. Step 6: Substitute the dq-axis reference current and the predicted current value into the minimization value function, use the minimization value function to determine the minimum current, and obtain the optimal voltage vector corresponding to the minimum current.

2. The predictive control method for spliced ​​arc motor models using a sliding mode observer according to claim 1, characterized in that, Step 3, the calculation process of the sliding mode control function includes the following steps: Based on the estimated d-q axis current and the actual current error, the sliding surfaces of the observer for the d-axis and q-axis are designed as follows: , ; In the formula: , ; The sliding mode logarithmic function reaching law based on the hyperbolic tangent function with steepness factor is designed as follows: ； In the formula, , , All are positive numbers; ; And it is an even number; These are adjustable parameters; This is the expression for the hyperbolic tangent function containing a steepness factor; By combining the designed reaching law with the sliding surfaces of the d-axis and q-axis, and the model equations of the disturbance observer, the sliding control functions of the d-axis and q-axis can be calculated. , : 。 3. The predictive control method for spliced ​​arc motor models using a sliding mode observer according to claim 1, characterized in that, In step 4, the system is discretized, and the output of the sliding mode observer is... Compensation current at any time , and Time-based perturbation , Substituting into the current prediction model equation, we get Current prediction model equation at time: ； In the formula: Indicates the sampling time.

4. The predictive control method for spliced ​​arc motor models using a sliding mode observer according to claim 1, characterized in that, In step 6, the cost function is designed based on the least squares current error. The q-axis reference current output by the superspiral sliding mode controller d-axis reference current and predictions Actual current at time , Substitute into the cost function respectively : ； The minimum current obtained corresponds to the optimal voltage vector.

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