A backstepping control method based on disturbance observer

Abstract

The present invention discloses a backstepping control method based on a disturbance observer to control the internal temperature of a polymerization kettle. In a nonlinear system with a relative order greater than 1, the control quantity cannot directly act on the controlled quantity. Therefore, the present invention uses backstepping control to convert the control problem of the controlled quantity into the control problem of the system intermediate variable, and step by step retreats to the control of the previous system variable, and finally the final system controlled quantity can be indirectly controlled by the actual control quantity. That is, the jacket temperature is controlled by controlling the flow rate of the jacket cooling water, and then the polymerization kettle wall and the internal temperature of the polymerization kettle are controlled. The present invention compensates the expanded state terms estimated by multiple disturbance observers in the backstepping controller, thereby reducing the impact of external disturbances on the system.

Description

Technical Field

[0001] The invention relates to a back-stepping control method based on a disturbance observer, which is used for controlling the internal temperature of a semi-batch polymerization kettle. Background Art

[0002] Semi-batch polymerization is an important production method in chemical process control. Usually, due to factors such as uncertainty, nonlinearity, and external disturbances in model parameters, the robustness of the control algorithm is difficult to guarantee. The automation level of most semi-batch production processes in China is generally low. The actual temperature control of semi-batch polymerization mainly adopts the traditional cascade PID structure, with the kettle temperature as the main control variable and the jacket inlet temperature as the secondary control variable, but the control effect is usually difficult to guarantee.

[0003] Backstepping control is widely used in nonlinear systems with a relative order greater than 1, but there is currently no controller with stronger anti-disturbance ability applied to semi-batch polymerization reactions. In order to cope with various external disturbances, such as fluctuations in cooling water temperature and feed temperature, the extended state observer is widely used in uncertain systems, which includes all uncertainties and external disturbances into an extended state. Summary of the invention

[0004] At the beginning of the batch reaction, the steam valve is opened to pass steam into the jacket, and the temperature in the kettle is raised to the preset temperature T using steam.

[0005] After reaching the preset temperature, close the steam valve, open the raw material monomer feed valve, and continuously add monomer raw materials into the kettle. The raw materials are a mixture of monomers and water, and initiators are added to increase the polymerization reaction rate.

[0006] Since the polymerization reaction is a strongly exothermic process, cooling water must be continuously injected into the jacket during the constant temperature stage to ensure that the temperature in the kettle remains at the set value.

[0007] Use high-precision temperature sensor to measure the temperature T in the kettle R , kettle wall temperature T S and jacket temperature T M .

[0008] In order to design a disturbance observer, it is necessary to assume that the external disturbance term is a continuous smooth curve, is differentiable, and the absolute value of its first derivative is less than a constant term.

[0009] Assuming the actual monomer material feed T F The temperature fluctuates around its nominal value:

[0010] Assume that the actual temperature of the cooling water inlet to the jacket is Fluctuates around its nominal value:

[0011] For the external disturbance term mentioned above, a high-gain state observer based on Lie derivative is used to measure its expanded state, which includes the external disturbance.

[0012] The following expanded state is calculated, which contains the intermediate state of the system and the unknown external disturbance term. This expanded state is designed for the first external disturbance ω1 of the system, that is, the disturbance of the monomer feed temperature:

[0013]

[0014] The second expanded state is obtained, which contains the intermediate state of the system and the unknown external disturbance term. This expanded state is designed for the second external disturbance ω3 of the system, that is, the disturbance of the cooling water inlet temperature in the jacket:

[0015]

[0016] The first expanded state η1 is estimated in the following way. The main method is to use the estimated value of the expanded state, the system model parameters, the difference between the actual value of the system state and its estimated value, and the high gain constant term Γ1κ 1，1 Wait for a pair of T R Estimated value:

[0017]

[0018] Among them, the estimated value of the expansion state η1 is updated by the following formula, using the high gain term T R and its estimated value.

[0019]

[0020] The second expansion state η3 is estimated using the following formula, using the estimated value of the expansion state The nominal value of cooling water temperature, cooling water flow rate (i.e., control quantity), the difference between jacket temperature and its estimated value, and the high gain constant term Γ3κ 3，1 Wait for a pair of T M Estimated value:

[0021]

[0022] Among them, the estimated value of the expansion state η3 is updated by the following formula.

[0023]

[0024] Use a backstepping controller based on ηi 的 Estimated value calculation intermediate state Ts The expected value of (i.e., the controller's expected temperature of the reactor wall under the currently measured internal temperature of the polymerization reactor):

[0025]

[0026] Use a backstepping controller according to η i The estimated value of the intermediate state T M The expected value (i.e., the expected temperature of the jacket by the controller when the expected temperature of the kettle wall is calculated in the previous step and the actual value of the system intermediate variable is measured):

[0027]

[0028] Finally, according to the previous step, we can calculate In the case of , the final control quantity can be obtained as:

[0029]

[0030] After limiting the calculated value according to the actual process, it is set as the jacket cooling water inlet flow rate, and the cooling water valve opening is calculated accordingly. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 The semi-batch polymerization process of the present invention

[0032] Figure 2 This is the control effect diagram of the backstepping controller based on the disturbance observer of the present invention

[0033] Figure 3 is the expanded state including the disturbance term and its estimated value 1 of the present invention

[0034] Figure 4 is the expanded state and its estimated value including the disturbance term of the present invention 2

[0035] Figure 5 Schematic diagram of the backstepping control of the present invention

[0036] Figure 6 Flowchart of the present invention DETAILED DESCRIPTION

[0037] The present invention is described in detail below in conjunction with the accompanying drawings:

[0038] The present invention discloses a backstepping control method based on a disturbance observer. The specific control block diagram of the method is as follows: Figure 5 As shown in the figure, the actual semi-batch polymerization reactor model is as follows Figure 1 shown.

[0039] The reaction model consists of the following six ordinary differential equations:

[0040]

[0041] The first three formulas are mass conservation equations, and the last three are energy conservation equations. The first formula is the mass conservation equation for water, the second formula is the mass conservation equation for monomer A, the third formula is the mass conservation equation for polymer, the fourth formula is the energy conservation equation for internal temperature, the fifth formula is the energy conservation equation for kettle wall, and the sixth formula is the energy conservation equation for jacket temperature.

[0042] When the temperature inside the polymerization reactor is lower than the set point, the optimal jacket temperature should be a larger value so that heat can be transferred from the jacket to the polymerization reactor. This step is usually a preparatory action before the start of the polymerization reaction, that is, using Figure 1 The heating mode in the polymerization kettle is used to heat the polymerization kettle to the set point. At the beginning of the batch reaction, the steam valve is opened (valve opening 100%), and steam is introduced into the jacket to heat the polymerization kettle to a suitable temperature to facilitate the chemical reaction. Then, the reaction process is started under the action of the initiator. After reaching the set temperature, the steam valve is closed.

[0043] like Figure 5 As shown in the figure, the control logic of the backstepping control method is similar to the cascade structure. The robust adaptive backstepping controller is designed based on the Lyapunov stability theory.

[0044] In semi-batch polymerization control, the control target is to stabilize the internal temperature of the polymerization reactor at the set point or track a step-change set point. The controllable variable is the flow rate of jacket cooling water.

[0045] For the semi-batch polymerization reactor model in this paper, the relative order is calculated to be 3.

[0046] During the reaction, because the polymerization reaction is a violent exothermic process, it is usually necessary to add a large amount of cooling water in the jacket to remove the excess heat in the kettle. However, since the temperature of the cooling water is not a fixed value, it will fluctuate within a certain range. This will eventually lead to fluctuations in the temperature of the polymerization kettle.

[0047] The corresponding control law is the sum of the proportional feedback term and the feedforward compensation term. If there is an uncertainty term in the feedforward term, that is, there is an uncertain parameter in the feedforward term, it will lead to a deviation in the control amount and eventually lead to overshoot.

[0048] We assume that the intermediate state variables are completely observable, and the two intermediate state variables are the polymerization reactor wall temperature and the jacket temperature.

[0049] like Figure 3, as shown in Figure 4, the backstepping control based on the disturbance observer can first estimate the expansion state term and then accurately control the reactor temperature, which can solve the control error problem caused by external disturbances in traditional backstepping control. If the nonlinear system is as follows:

[0050]

[0051] y=h(x)

[0052] Design the state observer as follows:

[0053]

[0054] Since in the actual production process, the controllable variable, i.e., the cooling water flow rate, has an upper limit, the calculated output value must be limited in actual control to ensure that the controllable variable has practical significance.

[0055] When the cooling water valve opening reaches 100%, the upper limit of the cooling water flow rate in an actual process is 83kg / s.

[0056] In controlling the internal temperature of the reactor, the optimal state values ​​of the two intermediate state variables are first calculated. Then, Lyapunov functions are designed to obtain the control quantities for the control problems of the two variables. The final control effect is as follows: Figure 2 As shown, compared with the traditional backstepping control, the method of the present invention can effectively suppress the influence of external interference.

[0057]

[0058] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A backstepping control method based on disturbance observer, characterized in that: The following steps are involved: Step 1: For a given nonlinear system model with a relative order greater than 1, determine the external disturbances that exist, and determine the quantity and form of the external disturbances, and design a disturbance estimation method based on an extended state observer for each disturbance term; Step 2: Design disturbance observer: Assume that in the nonlinear system There is a disturbance in the f(x) part of , and assuming that the disturbance is unknown but continuous, smooth and differentiable, the following disturbance observer can be designed: Where η represents the expansion state, which includes the unknown disturbance, and Γ represents the high gain coefficient, which is a key parameter in the design of the disturbance observer and affects the speed and accuracy of the disturbance estimation. Step 3: Set the temperature setting value of the semi-batch polymerization reactor And measure the temperature T in the kettle R , kettle wall temperature T S and jacket temperature T M ; Step 4: Estimate the expansion state using the disturbance observer: For all external disturbance terms ω i , using the disturbance observer to estimate its expansion state η i ; Step 5: Convert the controlled quantity control problem into the control problem of the intermediate state of the nonlinear system: According to the model parameters and the expanded state vector obtained in step 4 and the process state measurement value, use the backstepping controller to calculate the expected value of the intermediate state of the system The relative order of the nonlinear system is 3, and the solution to its expected state is: Step 6: Calculate the error between the expected value of the intermediate process state variable of the nonlinear system and its true measured value Step 7: Find the controller output: Based on the above error vector, expanded state vector and the expected value of the system intermediate state obtained in step 5 Use the backstepping controller to find the final controller output: The specific method is to calculate the expansion state: It contains the intermediate state of the system and the unknown external disturbance term. This expanded state is designed for the first external disturbance ω1 of the system, that is, the disturbance of the monomer feed temperature, and then the second expanded state is obtained: It contains the intermediate state of the system and the unknown external disturbance term. This expanded state is designed for the second external disturbance ω3 of the system, that is, the disturbance of the cooling water inlet temperature in the jacket. Then the first expanded state η1 is estimated, and the estimated value of the expanded state, the system model parameters, the difference between the actual value of the system state and its estimated value, and the high gain constant term Γ1κ are used. 1，1 Establish a T R Estimated value: Among them, the estimated value of the expansion state η1 uses the high gain term T R Update by the difference between the estimated value and the Estimate the second expansion state η3 and use the estimated value of the expansion state The nominal value of cooling water temperature, cooling water flow rate, the difference between the jacket temperature and its estimated value, and the high gain constant term Γ3κ 3，1 Establish a T M Estimated value: Among them, the estimated value of the expansion state η3 is updated: Use a backstepping controller according to η i The estimated value of the intermediate state T S The expected value is the expected temperature of the reactor wall by the controller under the current measured internal temperature of the polymerization reactor: Use a backstepping controller according to η i The estimated value of the intermediate state T M The expected value of the controller is the expected temperature of the jacket when the expected temperature of the kettle wall is calculated in the previous step and the actual value of the system intermediate variable is measured: Finally, according to and Substitute the parameters of the reactor and the first-order derivative of the expected temperature of the reactor wall, combined with the reactor temperature change model: The final control quantity is: Step 8: Convert the controller output value according to the actual process: The purpose of this step is to calculate the cooling water flow The corresponding valve opening determines the maximum cooling water flow rate when the cooling water valve opening is maximum according to the actual process requirements, and limits the calculated value according to the maximum flow rate. If the calculated value is not within the range allowed by the process, the calculated value is set to the upper or lower limit of the process range, and this value is transmitted to the valve actuator, and this value is used as the cooling water valve opening to control the internal temperature of the reactor.

2. The backstepping control method based on disturbance observer according to claim 1 has strong robustness and anti-interference ability, characterized in that: Step 4 specifically includes the following steps: Step 4.1 Use Lie derivatives to establish the expansion state η for each term in the system that has external disturbances i , which contains the intermediate state of the system and the unknown external disturbance term ω i ; Step 4.2 Use the high-gain extended state observer to calculate the controlled quantity T of the system R and the intermediate state T M Make an estimate and get and The observer uses a high-gain constant coefficient and multiplies this coefficient by the difference between the actual value measured by the system and the predicted value; Step 4.3 Determine the expansion state η including the disturbance term based on the difference between the actual value measured by the system and the predicted value i The rate of change of the estimated value of Step 4.4 updates the expansion state with the change rate obtained in step 4.3, and keeps repeating the above steps 4.2, 4.3 and this step.

3. The backstepping control method based on disturbance observer according to claim 1 is characterized in that: The step 7 specifically includes the following steps: Step 7.1 First, determine the expected temperature of the reactor wall based on the estimated value of the expansion state obtained in step 4, the difference between the estimated value of the system state and its optimal expected value, the set value of the polymerization reactor temperature, and the system model parameters. Step 7.2 Based on step 7.1 System model parameters, system state error value, kettle wall temperature T s To calculate the desired jacket temperature Step 7.3: Based on the calculation in step 7.2 The system model parameters, system state error value, cooling water temperature, total mass of cooling water in the jacket, and the expansion state estimate obtained in step 4 are used to calculate the final controller output, i.e., the cooling water flow rate.

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