Gas-fired boiler multivariable active-disturbance-rejection control method based on LQR optimal state error feedback

Abstract

The invention discloses a gas-fired boiler multivariable active-disturbance-rejection control method based on LQR optimal state error feedback. The gas-fired boiler multivariable active-disturbance-rejection control method is used for comprehensive control over steam pressure, steam flow and steam drum liquid level. In a gas-fired boiler control system, steam pressure, flow and steam drum liquid level fluctuation can be caused by gas demand changes of downstream users, and the system stability is further affected by the coupling effect between variables. A traditional PID controller cannot meet process requirements during anti-interference and variable coupling coping, and traditional active-disturbance-rejection control is poor in control effect under object time lag and observer bandwidth limitation. In order to solve the problems, an extended state observer is assisted by multivariable decoupling and model information, an optimal control law based on LQR is designed, and an LQR-PI controller architecture and output first-order differential and disturbance estimation of the extended state observer are combined. The control method not only ensures that the system can track the set value quickly without overshoot, but also has good disturbance suppression performance, can adjust and control the input quantity in time, and ensures that the output of the gas-fired boiler system is stable.

Description

Technical Field

[0001] The present invention relates to the field of advanced control technology, and in particular to a multivariable anti-disturbance control method for gas boilers based on optimal state error feedback of a linear quadratic regulator (LQR). Aiming at the multivariable strong coupling scenario of gas boilers, the decoupling control strategy, model information-assisted extended state observer and LQR optimal control idea are combined to achieve the given tracking of the reaction process and the suppression effect of random variable load disturbances. Background Art

[0002] In the industrial production process, the use of gas boilers as a new type of steam supply equipment has many impacts. Gas boilers have good thermal stability, high energy density, and relatively easy adjustment of gas volume, so they can maintain a relatively stable heat output. However, compared with the large time lag of coal-fired boilers, the gas boiler system is a multivariable control system with small time lag and strong coupling. Its control strategy is often relatively simple and cannot adapt to complex working conditions. For example, in some cases, the system may not be able to make real-time adjustments based on load changes, fuel quality and other factors, resulting in low combustion efficiency and increased energy consumption.

[0003] The structure of the traditional PID control algorithm is relatively simple and does not require complex mathematical models, so it is easy to understand and implement. In the steam pressure control of gas boilers, due to the nonlinear and time-varying characteristics of the system, the adjustment of PID parameters may become complicated and time-consuming. When the steam load of downstream equipment changes rapidly, the PID controller cannot respond and adjust the steam pressure in time. In some cases, the output of the PID control system has a large overshoot problem, which in turn affects the stability of the system and even triggers the shutdown alarm mechanism, which is not conducive to the normal operation of the production process.

[0004] In the face of randomly changing load disturbances, an extended state observer can be used to estimate the total disturbance, and based on this, a feedback control law can be designed to compensate for the disturbance in real time, which is an effective response strategy. However, the traditional extended state observer is limited in bandwidth when facing the time lag problem of the controlled object, resulting in inaccurate state and total disturbance estimation, untimely output of the feedback control law based on the estimated value, slow recovery of steam pressure when the load changes, and untimely adjustment of gas volume, so the control effect is not satisfactory. In view of this, in the context of randomly changing loads, engineering researchers urgently need to explore a method that can quickly and efficiently regulate the main steam pressure of the gas boiler based on the estimated system state variables and load disturbance values ​​to ensure its stable supply to downstream equipment. Summary of the invention

[0005] In view of the shortcomings and problems existing in the above-mentioned existing methods, the technical problem to be solved by the present invention is: to provide a gas boiler multivariable anti-disturbance control method based on LQR optimal state error feedback, to make full use of model identification information, to effectively alleviate the observer bandwidth burden, and to integrate the linear state error feedback law with the LQR optimal PI controller architecture, to speed up the response speed and effectively suppress the overshoot of the dynamic process output.

[0006] To achieve the above-mentioned invention object, the present invention adopts the following technical scheme: a multivariable active disturbance rejection control method for a gas boiler based on LQR optimal state error feedback, comprising the following steps:

[0007] Step 1: Identify the transfer function expressions between different inputs / outputs of the gas boiler by using the recursive least squares method and combine them into a transfer function matrix;

[0008] Step 2: Set the steam pressure setting value, steam flow setting value and drum liquid level setting value of the gas boiler, and measure the actual output signals of the gas boiler system: steam pressure, steam flow and drum liquid level;

[0009] Step 3: Pre-plan to decouple the multivariable system into three independent channels: gas flow-steam pressure, induced draft-steam flow, and water inlet-drum liquid level. Based on this plan, design the inverse decoupler module;

[0010] Step 4: Design a model information assisted extended state observer (MESO) based on the model parameter information identified in step 1 and the actual output of the system;

[0011] Step 5: Based on the model parameter information identified in step 1, construct the LQR-PI architecture to search for the optimal control parameters of each independent channel; then combine the output first-order derivative estimate and total disturbance estimate of the MESO output in step 4 to generate the LQR optimal linear state error feedback law (LQR-LESF) for the three independent channels. The obtained controller output corresponds to the virtual control input of the inverse decoupler module in step 3.

[0012] Step 6: Further according to the actual process requirements, the actual control signal is converted into the corresponding gas valve, induced draft valve and water inlet valve opening; the upper and lower limits of the valve opening are determined and then the actual control quantity is limited. If the value exceeds the allowable range of the process, the limit value is used instead and transmitted to the actuator.

[0013] Furthermore, the specific method of step 1 is as follows:

[0014] Step 1.1: Fit the high-order hysteresis relationship of different input / output of the gas boiler into the transfer function form of first-order inertia plus hysteresis by recursive least squares method:

[0015]

[0016] Where s is a complex frequency domain operator, They are the static gain, time constant and lag time of different input / output relationships of the gas boiler system;

[0017] Step 1.2: To match the subsequent parameter tuning of MESO and optimal controller, the second-order inertia plus hysteresis transfer functions of the three input / output relationships of gas volume-steam pressure, induced draft volume-steam flow, and water inlet volume-steam drum level need to be additionally identified:

[0018]

[0019] Furthermore, the specific design method of the inverse decoupler in step 3 is as follows:

[0020] Step 3.1: Based on the system transfer function matrix Design of forward all-pass matrix , the feedforward compensation matrix ;

[0021] Step 3.2: Design the inverse decoupler matrix:

[0022] ;

[0023] Step 3.3: The generalized decoupled three-independent channel system after the introduction of the inverse decoupler is expressed as:

[0024]

[0025] Furthermore, the specific design method of MESO in step 4 is as follows:

[0026] Step 4.1: Assume that the lumped perturbation is a type of unknown differentiable but first-order derivative is bounded;

[0027] Step 4.2: Due to the introduction of the inverse decoupler module in step 3, the following MESO can be established based on the second-order time-domain expressions of each independent channel identified in step 1.2 and ignoring the small delay link:

[0028]

[0029] in, They represent the estimation of gas flow, induced draft, drum level and their first-order differentials respectively. Express an estimate of the total disturbance for each independent channel; is the gain coefficient, which is a key parameter in the design of the reduced-order observer and affects the speed and accuracy of disturbance estimation;

[0030] Step 4.3: Based on the MESO designed above, use the bandwidth method to determine the observer parameters: ,in, is the observer bandwidth of each independent channel MESO;

[0031] Furthermore, the specific design method of LQR-LSEF in step 5 is as follows:

[0032] Step 5.1: For each independent channel, set the expected closed-loop equation and determine the closed-loop system matrix:

[0033] ;

[0034] ;

[0035] in, The matrix is ​​obtained based on the second-order model parameters identified in step 1. are the expected closed-loop damping ratio, natural frequency and relative dominant multiple of each channel respectively;

[0036] Step 5.2: Define the semi-positive definite state weight matrix according to the LQR strategy , the positive definite control weight matrix and the symmetric positive definite Riccati coefficient matrix ;

[0037] Step 5.3: According to the closed-loop expected system matrix And Riccati equation calculation matrix:

[0038] ;

[0039] Step 5.4: Get the optimal control vector expression based on the LQR strategy:

[0040] ;

[0041] Step 5.5: Select PID three channels as system state variables ,Right now: Then step 5.4 is converted to calculate the optimal parameters of the PID controller :

[0042] ;

[0043] Step 5.6: Error Signal Estimated by MESO Generated with a given reference value for proportional and integral components; the differential component is used Instead, is the controller bandwidth; finally, we introduce As the disturbance compensation of the control signal, LQR-LSEF is finally generated:

[0044] . BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 It is a principle diagram of the process of a gas boiler in an embodiment of the present invention;

[0046] Figure 2 Schematic diagram of the control system structure in an embodiment of the present invention;

[0047] Figure 3 A control process flow chart in an embodiment of the present invention;

[0048] Figure 4 This is a steam pressure tracking effect diagram in an embodiment of the present invention;

[0049] Figure 5 This is a steam flow tracking effect diagram in an embodiment of the present invention;

[0050] Figure 6 This is a diagram showing the effect of tracking the drum liquid level in an embodiment of the present invention;

[0051] Figure 7 The gas volume control change in the embodiment of the present invention;

[0052] Figure 8 The change of the induced air volume control in the embodiment of the present invention;

[0053] Fig. 9 The water inlet control change in the embodiment of the present invention; DETAILED DESCRIPTION

[0054] The specific implementation of the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. Obviously, the examples described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0055] Figure 2 The structure block diagram of the multivariable active disturbance rejection control of a gas boiler based on the LQR optimal linear control law in an embodiment of the present invention is shown. Figure 3 To control the process flow of the operation, including:

[0056] Step 1: Use the recursive least squares method to identify the transfer function expression of the first-order inertia plus time delay between different inputs / outputs of the gas boiler and combine them into a transfer function matrix:

[0057]

[0058] In addition, for the three input / output relationships of gas volume-steam pressure, induced draft volume-steam flow, and water intake volume-drum liquid level, the second-order inertia plus time lag transfer function expression is identified:

[0059]

[0060] Step 2, assuming that the gas boiler actually requires a stable steam pressure of 0.55MPa, a steam flow of 0.5t / h, and a drum liquid level of 120mm in a stable state. When the gas load of downstream users changes, the changing load is regarded as a disturbance signal of the system output steam pressure. When the downstream load changes, the manipulated variables, namely the gas volume, induced draft volume, and water inlet volume, are required to be input in a timely manner to ensure the rapid recovery and stability of the control output.

[0061] Step 3: Design an inverse decoupler based on the model parameter information identified in step 1. The specific design method is as follows:

[0062] Step 3.1: Based on the system transfer function matrix Design of forward all-pass matrix , the feedforward compensation matrix ;

[0063] Step 3.2: Design the inverse decoupler matrix .

[0064] Step 3.3: The generalized decoupled three-independent channel system after the introduction of the inverse decoupler is expressed as:

[0065] , in this case it can be replaced by the second-order inertia delay transfer function.

[0066] Step 4: Design a model information assisted extended state observer (MESO) based on the model parameter information identified in step 1 and the actual output of the system. The specific design method is as follows:

[0067] Step 4.1: Assume that the lumped perturbation is a type of unknown differentiable but first-order derivative is bounded;

[0068] Step 4.2: Due to the introduction of the inverse decoupler module in step 3, the following MESO can be established based on the second-order time-domain expressions of each independent channel identified in step 1.2 and ignoring the small delay link:

[0069]

[0070] in, They represent the estimation of gas flow, induced draft, drum level and their first-order differentials respectively. Express an estimate of the total disturbance for each independent channel; is the gain coefficient, which is a key parameter in the design of reduced-order observer and affects the speed and accuracy of disturbance estimation.

[0071] Step 4.3: Based on the MESO designed above, use the bandwidth method to determine the observer parameters: ,in, is the observer bandwidth of each independent channel MESO. In this example, the MESO observer bandwidths designed for the three independent channels are all set to 1.3.

[0072] Step 5: Build the optimal linear state error feedback control law (LQR-LSEF) based on the LQR strategy. The specific design method is as follows:

[0073] Step 5.1: For each independent channel, set the expected closed-loop equation and determine the closed-loop system matrix:

[0074]

[0075]

[0076] in, The matrix is ​​obtained based on the second-order model parameters identified in step 1. are the expected closed-loop damping ratio, natural frequency and relative dominant multiple of each channel respectively.

[0077] Step 5.2: Define the semi-positive definite state weight matrix according to the LQR strategy , the positive definite control weight matrix and the symmetric positive definite Riccati coefficient matrix .

[0078] Step 5.3: According to the closed-loop expected system matrix And Riccati equation calculation matrix:

[0079]

[0080] Step 5.4: Get the optimal control vector expression based on the LQR strategy:

[0081]

[0082] Step 5.5: Select PID three channels as system state variables ,Right now: Then step 5.4 is converted to calculate the optimal parameters of the PID controller :

[0083]

[0084] In this example, the LQR-PI optimal parameter setting results corresponding to the three independent channels are:

[0085]

[0086] Step 5.6: Error Signal Estimated by MESO Generated with a given reference value for proportional and integral components; the differential component is used Instead, is the controller bandwidth; finally, we introduce As disturbance compensation for the control signal. In this example, the controller bandwidths set for the three independent channels are .

[0087] Finally, LQR-LSEF is generated:

[0088]

[0089] Figure 4-6 Refer to the given effect diagram for tracking the output of each channel system. Figure 7-9 In the simulation, the method of the present invention is compared with LQR-PID control and traditional ADRC control, and the control parameters of the controller of the present invention corresponding to LQR-PID and ADRC are set to be consistent, so as to illustrate the fusion of the above two methods and the effectiveness of the present method in terms of given tracking and disturbance suppression.

Claims

1. A multivariable active disturbance rejection control method for a gas boiler based on LQR optimal state error feedback, characterized in that: The following steps are involved: Step 1: Identify the transfer function expression between different inputs / outputs of the gas boiler by recursive least squares method, where the input , output , They are gas volume, induced draft volume and water intake volume respectively; They are steam pressure, steam flow and drum liquid level, which are combined into a transfer function matrix model: in represents the channel index, is the static gain, is the time constant, is the lag time, s is the complex frequency domain operator; Step 2: Set the steam pressure setting value, steam flow setting value and drum liquid level setting value of the gas boiler, and measure the actual output signals of the gas boiler system: steam pressure, steam flow and drum liquid level; Step 3: Pre-plan to decouple the multivariable system into three independent channels: gas flow-steam pressure, induced draft-steam flow, and water inlet-drum liquid level. Based on this plan, design the inverse decoupler module : Step 4: Design a model information assisted extended state observer (MESO) based on the model parameter information identified in step 1 and the actual output of the system; Step 5: Based on the model parameter information identified in step 1, the optimal PI controller architecture of the linear quadratic regulator (LQR) is constructed to search for the optimal control parameters of each independent channel; then, combined with the output first-order derivative estimate and total disturbance estimate of the MESO output in step 4, the LQR optimal linear state error feedback law (LQR-LESF) for the three independent channels is generated; Step 6: Further according to the actual process requirements, the actual control signal is converted into the corresponding gas valve, induced draft valve and water inlet valve opening; the upper and lower limits of the valve opening are determined and then the actual control quantity is limited. If the value exceeds the allowable range of the process, the limit value is used instead and transmitted to the actuator.

2. According to the multivariable active disturbance rejection control method for a gas boiler based on LQR optimal state error feedback described in claim 1, the design of the proposed MESO fully utilizes the parameter information expressed by the independent channel transfer function, and is characterized in that: Step 4 specifically includes the following steps: Step 4.1 Assume the lumped disturbance It is a class of unknown differentiable but bounded first-order derivatives; Step 4.2 Due to the introduction of the inverse decoupler module in step 3, the following MESO can be established based on the second-order time domain expressions of each independent channel identified in step 1, ignoring the small delay link: in, The second-order transfer function parameters identified for each independent channel; They represent the estimation of gas flow, induced draft, drum level and their first-order differentials respectively. Express an estimate of the total disturbance for each subchannel; is the gain coefficient, which is a key parameter in the design of the reduced-order observer and affects the speed and accuracy of disturbance estimation; Step 4.3 Based on the MESO designed above, use the bandwidth method to determine the observer parameters: ,in, is the observer bandwidth of each independent channel MESO.

3. According to the multivariable active disturbance rejection control method for a gas boiler based on LQR optimal state error feedback as described in claim 1, the proposed LQR-LSEF optimal control law combines the control structure of the LQR optimal PI controller and the linear state error feedback law, and is characterized in that: Step 5 specifically includes the following steps: Step 5.1 For each independent channel, set the expected closed-loop equation and determine the closed-loop system matrix: in, The matrix is ​​obtained based on the second-order model parameters identified in step 1. are the expected closed-loop damping ratio, natural frequency and relative dominant multiple of each channel respectively; Step 5.2 Define the semi-positive definite state weight matrix according to the LQR strategy , the positive definite control weight matrix and the symmetric positive definite Riccati coefficient matrix ; Step 5.3 Based on the closed-loop expected system matrix And Riccati equation calculation matrix: Step 5.4 Obtain the optimal control vector expression based on the LQR strategy, where The hysteresis time constant identified for each channel: Step 5.5 Select PID three channels as system state variables ,Right now: , then step 5.4 is converted to calculate the optimal parameters of the PID controller : Step 5.6 Error signal Estimated by MESO Generated with a given reference value for proportional and integral components; the differential component is used Instead, is the controller bandwidth; finally, As the disturbance compensation of the control signal, LQR-LSEF is finally generated: 。

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