ADRC optimization compensation control method and system based on partial differential flatness characteristics of controlled object

Abstract

The present invention discloses an ADRC optimization compensation control method and system based on partial differential flatness characteristics of a controlled object. The method analyzes the differential flatness characteristics of the controlled object, divides the system into two parts, differential flatness and non-differential flatness, and designs a dual closed-loop control structure to achieve control. For the inner loop differential flat part, accurate trajectory planning and tracking can be achieved based on the differential flatness control technology DFC; while for the outer loop non-differential flat part, the self-disturbance rejection control ADRC is introduced to observe and compensate for disturbances, thereby enhancing the robustness of the system. Through this dual closed-loop control structure, not only the known partial characteristic information of the model is fully utilized to improve the dynamic performance of the control system, but also it does not need to rely on the model accuracy of the non-differential flat part, making the control strategy more flexible and adaptable.

Description

Technical Field

[0001] The present invention belongs to the field of complex nonlinear system control, and in particular relates to an ADRC optimization compensation control method and system based on partial differential flatness characteristics of a controlled object. Background Art

[0002] For nonlinear systems, Differential Flatness Control (DFC) and Active Disturbance Rejection Control (ADCC) are two effective control methods. The former can achieve accurate trajectory planning based on its complete description of the state trajectory of the nonlinear system, while the latter achieves system robustness by observing and compensating for disturbances. However, when the controlled object only has partial differential flatness characteristics, differential flatness control cannot completely decouple the controlled system, and there are often model uncertainties and external disturbances in actual systems, which makes it difficult to directly apply control strategies based on differential flatness. Active disturbance rejection control is a control method that does not rely on an accurate model. It improves the control effect by estimating and compensating for disturbances in the system, but it cannot fully utilize these nonlinear characteristics to simplify control design and improve control performance. Summary of the invention

[0003] Aiming at the limitation of a single control method, the present invention proposes an ADRC optimization compensation control method based on the partial differential flatness characteristics of the controlled object for a system with partial differential flatness characteristics, which can improve the response speed, tracing effect and robustness to disturbances of the system.

[0004] The present invention is achieved through the following technical solutions:

[0005] An ADRC optimization compensation control method based on partial differential flatness characteristics of a controlled object comprises the following steps:

[0006] Step 1: Establish a control model of the controlled system with partial differential flatness characteristics;

[0007] Step 2: Divide the model into a differential flat part and a non-differential flat part according to the model characteristics;

[0008] Step 3: Determine the input-output relationship between the differential flat part and the non-differential flat part, and design a double closed-loop control structure;

[0009] Step 4: According to the differential flatness theory, the differential flatness part is processed by linear feedback.

[0010] The system state variables and input and output variables are all represented by flat outputs and their finite-order derivatives;

[0011] Step 5: Design the time domain basis function of differential flat output and solve the expected trajectory according to the boundary conditions;

[0012] Step 6: Based on the desired trajectory obtained in step 5, design the inner loop linear anti-disturbance controller and finally obtain the actual control quantity of the inner loop.

[0013] Step 7: According to the actual control output of the inner loop obtained in step 6, an outer loop linear anti-disturbance controller of corresponding order is designed for the non-differential flat part of the outer loop. The specific steps are the same as step 5, and finally the final control quantity under the double closed-loop control structure is obtained.

[0014] Furthermore, the controlled object has partial differential flatness, and the differential flatness control theory can be applied to this part.

[0015] Furthermore, the differential flatness part applies the differential flatness control theory, which includes four steps: determining the differential flatness output, constructing the flattening map, generating the desired trajectory and outputting the actual trajectory.

[0016] Furthermore, the desired trajectory of the controlled object having the differential flatness part is expressed in a polynomial manner, and the degree of the polynomial is determined by the number and properties of the boundary conditions.

[0017] Furthermore, the controlled object has a differential flat part and a non-differential flat part, and the output of one part should be the input of the other part, so a double closed-loop control structure can be realized.

[0018] Furthermore, the closed-loop control and disturbance rejection of the desired trajectory of the differential flat part are achieved through a linear active disturbance rejection controller, and the controller design includes a linear extended state observer and a linear feedback control law.

[0019] Furthermore, the bandwidth of the observer and controller of the inner-loop linear ADRC is greater than the bandwidth of the observer and controller of the corresponding outer-loop linear ADRC.

[0020] Furthermore, the control model is a Laval nozzle model based on a proportional solenoid valve, the differential flat part is the voltage-valve core displacement part of the proportional solenoid valve link, and the non-differential flat part is the valve core displacement-flow-thrust part of the Laval nozzle link.

[0021] On the other hand, the present invention provides an ADRC optimization compensation control system based on partial differential flatness characteristics of a controlled object, the system comprising:

[0022] A controlled system model building module is used to establish a control model of a controlled system with partial differential flatness characteristics;

[0023] A dual closed-loop control structure building module is used to divide the model into a differential flat part and a non-differential flat part according to the model characteristics; determine the input-output relationship between the differential flat part and the non-differential flat part, and design a dual closed-loop control structure;

[0024] The inner loop control solution module is used to perform linear feedback processing on the differential flat part according to the differential flatness theory, and all system state variables and input and output variables are represented by flat outputs and their finite-order derivatives; the time domain basis function of the differential flat output is designed, and the expected trajectory is solved according to the boundary conditions; the inner loop linear anti-disturbance controller is designed according to the expected trajectory to obtain the actual control quantity of the inner loop;

[0025] The outer loop control solution module is used to design an outer loop linear anti-disturbance controller for the non-differential flat part of the outer loop according to the actual control output of the inner loop, and finally obtain the final control quantity under the double closed-loop control structure.

[0026] Beneficial effects of the present invention:

[0027] The present invention makes full use of the model characteristics of the system with a differential flatness part, realizes feedback linearization for the differential flat part according to endogenous dynamic feedback, and designs a feedforward trajectory to improve control accuracy and system response speed; introduces active disturbance rejection control to simplify the dependence on the system model, making the control design more flexible and intuitive; for the non-differential flat part, the inaccurate part of the model, internal and external disturbances, uncertainties, etc. are all considered as disturbances suffered by the system and a controller is designed to control it, thereby compensating for the total disturbance of the system and enhancing the robustness of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 It is a design flow chart of the present invention.

[0029] Figure 2 This is the system control block diagram based on differential flat control.

[0030] Figure 3 This is the block diagram of ADRC control based on the second-order system.

[0031] Figure 4 Schematic diagram of the Laval nozzle model based on a proportional solenoid valve.

[0032] Figure 5 It is a time domain variation curve diagram of various variables of the proportional solenoid valve link based on the present invention.

[0033] Figure 6 This is a flow closed-loop control result diagram based on the control method of the present invention. DETAILED DESCRIPTION

[0034] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments.

[0035] like Figure 1 As shown, the ADRC optimization compensation control method based on the partial differential flatness characteristics of the controlled object of the present invention takes the Laval nozzle model based on the proportional solenoid valve as an example, and includes the following steps:

[0036] Step 1: Establish a Laval nozzle model based on a proportional solenoid valve:

[0037] The model is described as follows:

[0038] For the structure of the proportional solenoid valve, its output model can be simplified as:

[0039]

[0040] Where F is the electromagnet thrust; is the current-force coefficient; i is the electromagnet coil current.

[0041] The electromagnet outputs displacement and force at the same time, driving the valve core to move. The valve core motion equation of the proportional solenoid valve is:

[0042]

[0043] Where m is the valve core mass; is the displacement change of the valve core over time t, represents the electromagnet coil current over time t; is the velocity damping coefficient; k is the spring stiffness coefficient; is the spring preload displacement; It is the reaction force on the valve core.

[0044] The flow model at the Laval nozzle outlet is:

[0045]

[0046] Where G is the mass flow rate through the valve; is the flow coefficient; is the nozzle throat area; is the inlet pressure; R is the gas constant; T is the absolute temperature; K is the adiabatic index.

[0047] Needle valve structure Figure 4 As shown in C, the relationship between the throttling area and the valve core displacement is:

[0048]

[0049] Where r is the radius of the throat aperture; is the needle valve half angle; x is the valve core displacement.

[0050] The nozzle thrust calculation is approximated using Laval nozzle theory, assuming that the entire flow process is a one-dimensional isentropic flow state. Compared with the expansion The following relationship exists ( The nozzle throat area is The nozzle outlet area is ):

[0051]

[0052] Nozzle injection mass flow rate:

[0053]

[0054] Average nozzle exit velocity:

[0055]

[0056] Thrust calculation:

[0057]

[0058] In the formula The thrust output of the nozzle is is the working fluid specific heat ratio, R is the nitrogen gas constant, and are the gas pressures at the nozzle outlet and inlet, respectively, is the nozzle inlet gas temperature.

[0059] Step 2: Identify the differential flat part and the non-differential flat part of the system:

[0060] According to the model information in the first step, it is determined that the voltage-spool displacement part of the proportional solenoid valve link is a differential flat part, while the valve core displacement-flow-thrust part of the Laval nozzle link is a non-differential flat part.

[0061] Step 3: Determine the input-output relationship between the differential flat part and the non-differential flat part, and design a double closed-loop control structure:

[0062] Depend on Figure 4 From the model information of the first step, it can be known that the output of the proportional solenoid valve link is the valve core displacement, and the input of the Laval nozzle link is also the valve core displacement. Therefore, the proportional solenoid valve link based on differential flatness can be designed as the inner loop to realize the closed-loop control of the valve core displacement and serve as the input of the outer loop; at the same time, the Laval nozzle link is designed as the outer loop to realize the closed-loop control of the flow / thrust, and finally realize the overall closed-loop control of the current-flow. The flow closed-loop control result is shown in the figure Figure 6 shown.

[0063] Step 4: Perform linear feedback processing on the differential flat part, such as Figure 2 As shown, the mapping relationship between system state variables, input and output variables, flat output and its finite order derivative is established:

[0064] From the experiment, we can get the valve core motion equation of the proportional solenoid valve: It can be approximately expressed by the following polynomial about the valve core displacement:

[0065]

[0066] In the formula , , , is the polynomial coefficient of valve core displacement, so the original formula can be rewritten as:

[0067]

[0068] At this time, the valve core motion model of the proportional solenoid valve can find a flat output as

[0069] y=x

[0070] Where x is the valve core displacement.

[0071] At this time, the state variable is represented by the flat output and its finite-order derivative:

[0072]

[0073] Step 5: Design the time domain basis function of differential flat output and solve the expected trajectory:

[0074] Set the time domain expression (polynomial form, Bezier curve, etc.) of the differential flat output y of the corresponding order. Take the sixth-order polynomial as an example.

[0075]

[0076] In the formula , , , , , are the polynomial coefficients of the time domain expression, t is the time, and the boundary conditions are set at this time:

[0077] The valve core preload displacement is , ; The initial displacement of the valve core is , ; The initial valve core speed is 2, ;The displacement of the valve core at time t=0.5s is ,Right now ; The displacement of the valve core at time t=0.8s is , at this time, the target valve core position is ; ; ; The time domain variation curves of the variables in the proportional solenoid valve link are as follows: Figure 5 As shown;

[0078] Therefore, the time domain expression coefficients of the flat output y at this time can be solved as follows:

[0079] ; ; ; ; ;

[0080] Step 6: Design a linear active disturbance rejection controller based on the desired trajectory obtained in step 5:

[0081] For the time domain expression of the flat output y obtained in the fifth step, a second-order linear anti-disturbance controller is designed according to the order of the proportional solenoid valve spool motion equation, as shown in Figure 3 As shown, it mainly includes two aspects: linear extended state observer and linear feedback control law.

[0082] Introducing its state space equation,

[0083]

[0084] in is the disturbance compensation parameter, u is the system control input, and h is the total disturbance of the system.

[0085] The corresponding continuous linear extended state observer,

[0086]

[0087] Where z is the state vector of the observer, L is the observer error feedback gain matrix, , , They are respectively related to the observer response speed, observer stability and observer high-order dynamic characteristics.

[0088] At this time, the state observer state equation can be expressed as:

[0089]

[0090] Introducing the Hurwitz matrix,

[0091]

[0092] Solving the characteristic equation and placing the poles yields:

[0093]

[0094]

[0095] in is the observer bandwidth.

[0096] At the same time, after performing Laplace transformation on the system function, the closed-loop transfer function can be obtained:

[0097]

[0098] Similarly, configuring the controller poles yields

[0099]

[0100] in is the controller bandwidth.

[0101] Step 7: Design an auto-disturbance rejection controller of the corresponding order for the differential flat part:

[0102] Based on the actual control output of the inner loop obtained in step 6, the corresponding order linear anti-disturbance control controller is designed according to the experimental relationship between valve core displacement and output flow and order identification. The specific steps are the same as step 6 to obtain the final control quantity under the double closed-loop control structure. It is also ensured that the observer and controller bandwidth of the final inner loop linear anti-disturbance control controller are greater than the observer and controller bandwidth of the corresponding outer loop linear anti-disturbance control controller.

[0103] On the other hand, the present invention also provides an ADRC optimization compensation control system based on the partial differential flatness characteristics of the controlled object, the system including a controlled system model building module, a dual closed-loop control structure building module, an inner loop control solution module and an outer loop control solution module; for the specific implementation process of each module, please refer to the sight steps of the aforementioned ADRC optimization compensation control method based on the partial differential flatness characteristics of the controlled object.

[0104] The controlled system model building module is used to establish a control model of a controlled system having a partial differential flatness characteristic;

[0105] The dual closed-loop control structure building module is used to divide the model into a differential flat part and a non-differential flat part according to the model characteristics; determine the input-output relationship between the differential flat part and the non-differential flat part, and design a dual closed-loop control structure;

[0106] The inner loop control solution module is used to perform linear feedback processing on the differential flat part according to the differential flatness theory, and all the system state variables and input and output variables are represented by the flat output and its finite order derivatives; design the time domain basis function of the differential flat output, and solve the expected trajectory according to the boundary conditions; design the inner loop linear anti-disturbance controller according to the expected trajectory, and obtain the actual control quantity of the inner loop;

[0107] The outer loop control solution module is used to design an outer loop linear anti-disturbance controller for the outer loop non-differential flat part according to the actual control output of the inner loop, and finally obtain the final control quantity under the double closed-loop control structure.

[0108] Although the present invention has been disclosed as above with preferred embodiments, it is not intended to limit the present invention. A person with ordinary knowledge in the technical field to which the present invention belongs may make various changes and modifications without departing from the spirit and scope of the present invention. Therefore, the protection scope of the present invention shall be determined by the definition of the claims.

Claims

1. An ADRC optimization compensation control method based on the partial differential flatness characteristics of the controlled object, characterized in that: The following steps are involved: Step 1: Establish a control model of the controlled system with partial differential flatness characteristics; Step 2: Divide the model into a differential flat part and a non-differential flat part according to the model characteristics; Step 3: Determine the input-output relationship between the differential flat part and the non-differential flat part, and design a double closed-loop control structure; Step 4: According to the differential flatness theory, the differential flat part is processed by linear feedback, and the system state variables and input and output variables are all represented by the flat output and its finite-order derivative; Step 5: Design the time domain basis function of differential flat output and solve the expected trajectory according to the boundary conditions; Step 6: Design the inner loop linear anti-disturbance controller according to the expected trajectory to obtain the actual control quantity of the inner loop; Step 7: According to the actual control output of the inner loop, design an outer loop linear anti-disturbance controller for the non-differential flat part of the outer loop, and finally obtain the final control quantity under the double closed-loop control structure.

2. The ADRC optimization compensation control method based on the partial differential flatness characteristics of the controlled object according to claim 1 is characterized in that: The controlled object has partial differential flatness, and differential flatness control theory can be applied to this part.

3. The ADRC optimization compensation control method based on the partial differential flatness characteristics of the controlled object according to claim 1 is characterized in that: The differential flat part applies differential flat control theory, including four steps: determining differential flat output, constructing flattening map, generating expected trajectory and outputting actual trajectory.

4. The ADRC optimization compensation control method based on the partial differential flatness characteristics of the controlled object according to claim 1 is characterized in that: The expected trajectory of the differentially flat part of the controlled object is expressed in a polynomial, and the degree of the polynomial is determined by the number and nature of the boundary conditions.

5. The ADRC optimization compensation control method based on the partial differential flatness characteristics of the controlled object according to claim 1 is characterized in that: The controlled object has a differential flat part and a non-differential flat part. The output of one part should be the input of the other part, and a double closed-loop control structure can be realized.

6. The ADRC optimization compensation control method based on the partial differential flatness characteristics of the controlled object according to claim 1 is characterized in that: The closed-loop control and disturbance rejection of the desired trajectory of the differential flat part are achieved through a linear active disturbance rejection controller. The controller design includes a linear extended state observer and a linear feedback control law.

7. The ADRC optimization compensation control method based on the partial differential flatness characteristics of the controlled object according to claim 1 is characterized in that: The observer and controller bandwidth of the inner-loop linear ADRC should be larger than the observer and controller bandwidth of the corresponding outer-loop linear ADRC.

8. The ADRC optimization compensation control method based on the partial differential flatness characteristics of the controlled object according to claim 1 is characterized in that: The control model is a Laval nozzle model based on a proportional solenoid valve. The differential flat part is the voltage-valve core displacement part of the proportional solenoid valve link, and the non-differential flat part is the valve core displacement-flow-thrust part of the Laval nozzle link.

9. An ADRC optimization compensation control system based on the partial differential flatness characteristics of a controlled object for implementing the control method according to any one of claims 1 to 8, characterized in that: The system includes: A controlled system model building module is used to establish a control model of a controlled system with partial differential flatness characteristics; A dual closed-loop control structure building module is used to divide the model into a differential flat part and a non-differential flat part according to the model characteristics; determine the input-output relationship between the differential flat part and the non-differential flat part, and design a dual closed-loop control structure; The inner loop control solution module is used to perform linear feedback processing on the differential flat part according to the differential flatness theory, and all system state variables and input and output variables are represented by flat outputs and their finite-order derivatives; the time domain basis function of the differential flat output is designed, and the expected trajectory is solved according to the boundary conditions; the inner loop linear anti-disturbance controller is designed according to the expected trajectory to obtain the actual control quantity of the inner loop; The outer loop control solution module is used to design an outer loop linear anti-disturbance controller for the non-differential flat part of the outer loop according to the actual control output of the inner loop, and finally obtain the final control quantity under the double closed-loop control structure.

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