CN111413872A - Air cavity pressure rapid active disturbance rejection method based on extended state observer - Google Patents
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Abstract
The invention provides an air cavity pressure rapid active disturbance rejection method based on an extended state observer, which is suitable for air intake and exhaust pressure control of a typical engine transition state test task, and mainly comprises the following steps: constructing a control model of an air cavity pressure system based on linear active disturbance rejection control, and estimating total disturbance (sum of internal disturbance and external disturbance) influencing controlled quantity in real time by an extended state observer; dynamically modifying the original uncertain system into an ideal integral series system through a special state feedback mechanism; estimating the disturbance by utilizing the natural dominance predictability and the immunity of the linear active disturbance rejection controller; the improved whale algorithm is used for updating the convergence rate and the global search capability, and disturbance is eliminated immediately by using a control quantity, so that the aim of fast active disturbance rejection is fulfilled. The method can provide technical support for the research of complex control technologies such as subsequent aircraft engine transition state test environment simulation multivariable control, dynamic decoupling control and the like.
Description
Technical Field
The invention belongs to the technical field of control of an electric power system, and particularly relates to a rapid active disturbance rejection method for air cavity pressure based on an extended state observer.
Background
The active disturbance rejection control of the air cavity pressure system is a necessary condition for establishing an aerial working environment of an engine test, and the bottleneck problem of quality improvement of control at the present stage is particularly prominent because the engine transition state assessment test has the remarkable characteristics of short time, large disturbance impact, difficulty in accurately obtaining a disturbance source characteristic model and the like. Foreign scholars mainly carry out engineering application research on the aspects of parameter self-tuning control technology, gain scheduling, valve step adjustment, self-adaptive control, combination control, feedforward control and the like, and the transition state adjustment performance of a control system is greatly improved. At present, Chinese scholars mainly adopt a model-based feedforward + feedback classical control mode for controlling the transition state of an air cavity pressure system and combine methods such as fuzzy control and the like, so that the control quality of the cavity pressure system in a transition state test is improved.
In the actual process, because the environment simulation system has a large amount of model uncertainty and unmodeled dynamics, the active disturbance rejection technology at the present stage can only complete the local optimization of the control quality, and the universality is insufficient. In addition, for disturbance links which are difficult to model and cannot be measured, but have significant influence on a controlled object, a model-based classical active disturbance rejection method cannot play a role. The above factors severely restrict the effective improvement of the control quality of the air cavity pressure system.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides the rapid active disturbance rejection method of the air cavity pressure based on the extended state observer, which solves the problem that the PID in the prior control technology has serious lag in the phase of a tracking system.
In order to achieve the above purpose, the invention adopts the technical scheme that:
the scheme provides a rapid active disturbance rejection method for air cavity pressure based on an extended state observer, which comprises the following steps:
s1, constructing an air cavity pressure system control model based on linear active disturbance rejection control, and estimating total disturbance in real time by using a linear extended state observer according to the air cavity pressure system control model;
s2, dynamically modifying the original uncertain system into an integral series system by using an expansion state feedback mechanism according to the total disturbance;
s3, estimating disturbance by using a linear active disturbance rejection controller according to the integral series system;
and S4, updating by using an improved whale algorithm according to the estimated value to obtain an optimized result, and realizing rapid active disturbance rejection of the air cavity pressure.
Further, the expression of the air cavity pressure system control model in S1 is as follows:
wherein the content of the first and second substances,representing the second derivative of the air volume pressure,representing the total disturbance of the air reservoir pressure system, a1And a2Are all representative of the parameters of the model,differentiation of the controlled pressure, t represents a time constant, y represents the controlled pressure, w represents an external unknown disturbance, b represents the control input gain0Denotes a control gain, and u denotes a control input amount.
Still further, the expression established by the linear extended state observer in S1 is as follows:
wherein the content of the first and second substances,the first derivative of the controlled pressure is shown,the second derivative of the pressure is shown,the derivative, z, representing the total disturbance1、z2And z3All represent system state variables, β1,β2And β3All represent the gain of the observer, y represents the controlled pressure, b0Denotes a control gain, and u denotes a control input amount.
Still further, the process of simplifying to the integral cascade system in S2 is as follows:
u0=kp(rset-z1)-kdz2
wherein the content of the first and second substances,representing the total disturbance of the air volume pressure system,differentiation of the controlled pressure, t representing the time constant, y representing the controlled pressurePressure, w represents an external unknown disturbance, z1、z2And z3All represent system state variables, u0Denotes a proportional-derivative controller, kpAnd kdRespectively, the controller proportional gain and the derivative gain.
Still further, the parameter adjustment of the linear active disturbance rejection controller in S3 includes the following steps:
a1, determining a control gain b according to the air cavity pressure system control model0;
A2, according to the control gain b0Selecting the bandwidth omega of the parameter controllercAnd observer bandwidth ω0Taking the initial value of the parameter controller bandwidth omegacAnd the observer bandwidth ω is gradually increased while keeping the minimum value constant0;
A3, judging observer bandwidth omega0Whether the state tracking requirement is met, if so, entering the step A4, otherwise, returning to the step A2;
a4, gradually increasing the bandwidth omega of parameter controllercAnd reducing the observer bandwidth omega when the system output fluctuates0Then gradually increasing the bandwidth omega of the parameter controllerc;
A5, judging the bandwidth omega of parameter controllercAnd if the control requirement is met, finishing the parameter adjustment of the linear active disturbance rejection controller, otherwise, returning to the step A4.
Still further, in the parameter adjustment process of the linear active disturbance rejection controller, if large amplitude oscillation occurs, the control gain b is adjusted0。
Still further, the S4 includes the following steps:
b1, initializing parameters of the whale algorithm according to the estimated value;
b2, randomly generating the position of the initial whale according to the limited range;
b3, defining the position of the whale, and calculating the adaptation value of the current whale colony to obtain the optimal position of the whale;
b4, according to the optimal position of the whale, performing optimal neighborhood disturbance updating by using a self-adaptive inertia weight and position updating method;
b5, judging whether the global optimal position probability is less than or equal to 0.5 according to the optimal neighborhood disturbance updating, if so, performing variable spiral updating by using spiral searching, and entering the step B7, otherwise, entering the step B6;
b6, judging whether the weight system is less than or equal to 1, if so, performing contraction enclosure updating by using spiral searching, and entering the step B7, otherwise, randomly searching and updating the position by using a whale position updating formula, and entering the step B7;
b7, judging whether the iteration times reach a preset value, if so, obtaining an optimization result, and realizing the rapid active disturbance rejection of the air cavity pressure, otherwise, returning to the step B3.
The invention has the beneficial effects that:
(1) the linear active disturbance rejection controller parameter setting module is integrated, the dynamic response speed of a control system is obviously improved, the adjusting time and the dynamic deviation of the system are greatly reduced, meanwhile, the linear active disturbance rejection controller parameter setting is simple and the universality is stronger, so that the control quality of the air cavity pressure control system can be effectively improved under the disturbance link that the cavity pressure environment simulation system is difficult to model and cannot measure, but has obvious influence on a controlled object, and technical support can be provided for the subsequent complex control technical researches such as aircraft engine transition state test environment simulation multivariable control, dynamic decoupling control and the like;
(2) the invention constructs a control model of the air cavity pressure system based on linear active disturbance rejection control, and can estimate the total disturbance (the sum of internal disturbance and external disturbance) influencing the controlled quantity in real time through an extended state observer;
(3) the linear extended state observer can accurately identify the total disturbance acting on the controlled object, and the linear active disturbance rejection controller can predict and compensate a series of uncertain and unknown disturbances in the system, so that a universal rapid disturbance rejection control method suitable for an air cavity incomplete dependence model is formed;
(4) the linear active disturbance rejection control can track the flow change dynamic (disturbance amount) of the air cavity without error in the process of adjusting the flow change dynamic (control amount), and the linear active disturbance rejection control controller can observe disturbance in real time and greatly improve the quality of air inlet pressure control in a transition state test of the air cavity;
(5) the active disturbance rejection control idea of the linear active disturbance rejection control controller completely meets the engineering actual requirement of the air cavity inlet pressure environment simulation control system. The technology has obvious engineering practical value and good application prospect for an aircraft engine simulation test actual system with a large amount of model uncertainty and unmodeled dynamics;
(6) the improved whale algorithm is used for updating the convergence rate and the global search capability, the optimization capability of the algorithm is improved, disturbance can be eliminated in time by using a control quantity, and the purpose of rapid active disturbance rejection is achieved.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
FIG. 2 is a block diagram of the extended state observer based intake plenum pressure control system of the present invention.
FIG. 3 is a schematic cross-sectional view of the mission of the engine according to this embodiment.
Fig. 4 is a control effect diagram of the linear active disturbance rejection controller in this embodiment.
Fig. 5 is a diagram illustrating the effect of the linear extended state observer in this embodiment.
Fig. 6 is a diagram showing the effect of PID control in the present embodiment.
Detailed Description
The following description of the embodiments of the present invention is provided to facilitate the understanding of the present invention by those skilled in the art, but it should be understood that the present invention is not limited to the scope of the embodiments, and it will be apparent to those skilled in the art that various changes may be made without departing from the spirit and scope of the invention as defined and defined in the appended claims, and all matters produced by the invention using the inventive concept are protected.
Example 1
The invention provides an expansion state observer-based rapid active disturbance rejection method for air cavity pressure, which is suitable for controlling air intake and exhaust pressure of a typical engine transition state test task, and as shown in figure 1, the method mainly comprises the following steps:
s1, constructing an air cavity pressure system control model based on linear active disturbance rejection control, and estimating total disturbance in real time by using a linear extended state observer according to the air cavity pressure system control model;
s2, dynamically modifying the original uncertain system into an integral series system by using an expansion state feedback mechanism according to the total disturbance;
s3, estimating disturbance by using a linear active disturbance rejection controller according to the integral series system;
the parameter adjustment of the linear active disturbance rejection controller comprises the following steps:
a1, determining a control gain b according to the air cavity pressure system control model0;
A2 according to control gain b0Selecting the bandwidth omega of the parameter controllercAnd observer bandwidth ω0Taking the initial value of the parameter controller bandwidth omegacAnd the observer bandwidth ω is gradually increased while keeping the minimum value constant0;
A3, judging observer bandwidth omega0Whether the state tracking requirement is met, if so, entering the step A4, otherwise, returning to the step A2;
a4, gradually increasing the bandwidth omega of parameter controllercAnd reducing the observer bandwidth omega when the system output fluctuates0Then gradually increasing the bandwidth omega of the parameter controllerc;
A5, judging the bandwidth omega of parameter controllercIf the control requirement is met, finishing the parameter adjustment of the linear active disturbance rejection controller if the control requirement is met, otherwise, returning to the step A4;
s4, updating by using an improved whale algorithm according to the estimated value to obtain an optimized result, and realizing the rapid active disturbance rejection of the air-containing cavity pressure, wherein the realization method comprises the following steps:
b1, initializing parameters of the whale algorithm according to the estimated value;
b2, randomly generating the position of the initial whale according to the limited range;
b3, defining the position of the whale, and calculating the adaptation value of the current whale colony to obtain the optimal position of the whale;
b4, according to the optimal position of the whale, performing optimal neighborhood disturbance updating by using a self-adaptive inertia weight and position updating method;
b5, judging whether the global optimal position probability is less than or equal to 0.5 according to the optimal neighborhood disturbance updating, if so, performing variable spiral updating by using spiral searching, and entering the step B7, otherwise, entering the step B6;
b6, judging whether the weight system is less than or equal to 1, if so, performing contraction enclosure updating by using spiral searching, and entering the step B7, otherwise, randomly searching and updating the position by using a whale position updating formula, and entering the step B7;
b7, judging whether the iteration times reach a preset value, if so, obtaining an optimization result, and realizing the rapid active disturbance rejection of the air cavity pressure, otherwise, returning to the step B3.
In this embodiment, the linear extended state observer accurately observes the controlled pressure (Z) in real time1) Pressure differential signal (Z)2) And total disturbance (Z)3) In the process, the linear active disturbance rejection controller can realize a phase advance control mechanism while finishing the dynamic modification of the controlled object. For the control of the air cavity pressure system, we build the following control model:
in formula (1): u is the control input, y is the controlled pressure, w is the external unknown disturbance, a1,a2Model parameters, and b control input gain.
If it is provided withFor the total disturbance of the system, it is an internal disturbance (uncertainty of the system model and uncertainty of the control input gain)Qualitative) and external unknown disturbance, then
If will totally disturbExpand to a new state variable x3Then the equation of state of system (2) can be expressed as:
in the formula (3), x1,x2,x3Is a system state variable which respectively represents the controlled pressure, the differential of the controlled pressure and the total disturbance of the system. Establishing a linear extended state observer for the system, including:
provided that observer gain β is1,β2,β3If the selection is proper, the linear extended state observer can realize the real-time estimation of each state variable of the system, namely
If total disturbanceIf the estimation is successful, it can be ignoredThen equation (2) can be simplified to an integral cascade system:
for dynamically modified integral series systems (5), a proportional-derivative (PID) controller is designed:
u0=kp(rset-z1)-kdz2(6)
in formula (6): r issetIs a pressure set value, kpAnd kdRespectively, a controller proportional gain and a differential gain. The closed loop transfer function of the control system is established by equations (5) and (6):
the basic architecture of the linear active disturbance rejection controller (L ADRC) is composed of the linear extended state observer formula (4), the integration series system formula (5) after system dynamic modification and the PD controller formula (6), and whether the key of the linear active disturbance rejection controller L ADRC technology is real-time and effective or not is to observe the total disturbance of the system, and the original controlled system is dynamically modified into a simple integration series system process.
An error equation can be obtained by the second-order controlled object (3) and the linear extended state observer (4):
e=Aee+Eh (8)
from equation (8), the characteristic polynomial of the linear extended state observer (L ESO) can be obtained as:
l ESO is BIBO stable when the roots of the feature polynomial (9)) are all in the left half plane of the S domain, so the observer gain β1,β2,β3Can be obtained by a pole allocation method, and the observer bandwidth of L ESO is defined as omega0All poles of the formula (9) are arranged at- ω0Where, i.e. λ(s) ═ s + ω0)3Then, there are:
similarly, the bandwidth of the PD controller is defined as omegacAll poles of the characteristic equation of the closed loop system (7) are configured at-omega0Where, i.e. D(s) ═ s2+kds+kp=(s+ωc)2Then there is
The expressions (10) and (11) show that only the observer bandwidth omega needs to be adjusted in the actual parameter adjusting process0And controller bandwidth ωcThe observation speed of the state observer and the parameters of the controller can be quickly adjusted, so that the parameter adjusting process of L ADRC is greatly simplified, and the stability of a control system can be ensured.
In this embodiment, as shown in fig. 2, one of the core ideas of the present invention is to estimate the total disturbance (sum of internal disturbance and external disturbance) affecting the controlled quantity in real time by an extended state observer (L ESO), and then dynamically modify the original uncertain system into an ideal integral series system (shown in the dashed line frame in fig. 2) by a special state feedback mechanism, which greatly simplifies the design difficulty of the controller1) Pressure differential signal (Z)2) And total disturbance (Z)3) Furthermore, L ADRC can realize a phase advance control mechanism while completing dynamic modification of the controlled object, which is the essential reason that L ADRC can greatly improve the control qualityThus, the method is simple and easy to operate.
Example 2
To further illustrate the present invention, the following takes a certain period of flight mission of a certain type of engine as an example:
the flight mission comprises two working conditions: 1) the engine throttle rod is unchanged, and the Mach number of the engine is changed under the test working condition (within 0-80 seconds); 2) and (4) transition state test working conditions (80-160 seconds) with sudden change of air inlet flow and unchanged Mach number are caused by change of an engine throttle lever. FIG. 3 shows, in sequence from top to bottom, the real-time variation of the throttle lever of the engine, the flight Mach number, the engine air flow and the inlet pressure.
1) Working condition 1 (within 0-80 seconds): in the process, the throttle lever of the engine is always in a slow driving area. The change of the flight Mach number of the engine is realized by adjusting the air inlet pressure, namely adjusting the air inlet pressure within 7sInternal variation to achieve engine Mach number atTo change in time. With the change of Mach number, the air flow of the engine is changed, and the change range is
2) Working condition 2 (80-160 seconds): the engine flight mach number remains unchanged during this process. Cause the engine air flow to beAn internal variation. The flow of the engine is in a typical nonlinear change process in the states of a push rod and a pull rod, the integral change time of the flow does not exceed 6 seconds, and the maximum flow change rate in the dynamic process reaches every secondSecond 20 kg/s. The disturbance of the control system during the transition state test is very serious.
The air volume pressure control adopts a linear active disturbance rejection control method to obtain a simulation result as shown in FIG. 4. FIG. 5 shows a part of the observation effect of a linear extended state observer (L ESO) of the linear active disturbance rejection controller, Z1Can accurately track the actual controlled pressure Z2Differential signal, Z, effective to track controlled pressure3The total disturbance of the system can be accurately identified, so that the observation reliability and effectiveness of the linear extended state observer are reflected.
Example 3
And comparing the disturbance rejection capacities of the controllers under the working conditions of the engine throttle lever quick control test by using an air cavity pressure quick active disturbance rejection method based on an extended state observer.
The linear active disturbance rejection controller is applied to the air cavity pressure control system, the problem that the air inlet pressure is difficult to control in the transition state test of the engine is solved, the test is carried out according to the most challenging test working condition in the simulation, and the system disturbance rejection capability control effects of the linear active disturbance rejection controller and the PID in the transition state test of the engine are respectively shown in the figures 4 and 6. The maximum deviation value of the controlled pressure under the action of the PID controller is 6.91kPa (the maximum instantaneous fluctuation amount is 9.21%), the adjusting time is 20s, the maximum deviation value of the controlled pressure under the action of the linear active disturbance rejection controller is greatly reduced to 0.9kPa (the maximum instantaneous fluctuation amount is 1.2%), and the adjusting time is not more than 6 s. The result shows that the anti-interference capability of the system is greatly improved after the linear active-interference-rejection controller is adopted, and the simulation result completely meets the precision requirement of the engine intake pressure transition state test simulation. Meanwhile, the real-time change conditions of the opening degree and the flow of the regulating valve under the action of the linear active disturbance rejection controller and the PID controller are respectively shown in FIG. 4 and FIG. 6.
Claims (7)
1. The method for fast active disturbance rejection of the air cavity pressure based on the extended state observer is characterized by comprising the following steps:
s1, constructing an air cavity pressure system control model based on linear active disturbance rejection control, and estimating total disturbance in real time by using a linear extended state observer according to the air cavity pressure system control model;
s2, dynamically simplifying the original uncertain system into an integral series system by utilizing an expansion state feedback mechanism according to the total disturbance;
s3, estimating disturbance by using a linear active disturbance rejection controller according to the integral series system;
and S4, updating by using an improved whale algorithm according to the estimated value to obtain an optimized result, and realizing rapid active disturbance rejection of the air cavity pressure.
2. The extended state observer-based air volume pressure fast active disturbance rejection method according to claim 1, wherein the expression of the air volume pressure system control model in S1 is as follows:
wherein the content of the first and second substances,representing the second derivative of the air volume pressure,representing the total disturbance of the air reservoir pressure system, a1And a2Are all representative of the parameters of the model,representing the derivative of the controlled pressure, t representing the time constant, y representing the controlled pressure, w representing the external unknown disturbance, b representing the control input gain, b0Denotes a control gain, and u denotes a control input amount.
3. The extended state observer-based air volume pressure fast active disturbance rejection method according to claim 1, wherein the linear extended state observer in S1 establishes the following expression:
wherein the content of the first and second substances,the first derivative of the controlled pressure is shown,the second derivative of the pressure is shown,the derivative, z, representing the total disturbance1、z2And z3All represent system state variables, β1,β2And β3All represent the gain of the observer, y represents the controlled pressure, b0Denotes a control gain, and u denotes a control input amount.
4. The extended state observer-based air volume pressure fast active disturbance rejection method according to claim 1, wherein the process of simplifying to an integral series system in S2 is as follows:
u0=kp(rset-z1)-kdz2
wherein the content of the first and second substances,representing the total disturbance of the air volume pressure system,representing the second derivative of the air volume pressure,differentiation of the controlled pressure, t represents a time constant, y represents the controlled pressure, w represents an external unknown disturbance, z1、z2And z3All represent system state variables, u0Denotes a proportional-derivative controller, kpAnd kdRespectively representing the proportional and differential gains of the controller, rsetIndicating the pressure set point.
5. The extended state observer-based air volume pressure fast active disturbance rejection method according to claim 1, wherein the parameter adjustment of the linear active disturbance rejection controller in S3 comprises the following steps:
a1, determining a control gain b according to the air cavity pressure system control model0;
A2, according to the control gain b0Selecting the bandwidth omega of the parameter controllercAnd observer bandwidth ω0Taking the initial value of the parameter controller bandwidth omegacAnd maintaining the parameter controller bandwidth ωcGradually increasing observer bandwidth omega with unchanged minimum value0;
A3, judging observer bandwidth omega0Whether the state tracking requirement is met, if so, entering the step A4, otherwise, returning to the step A2;
a4, gradually increasing the bandwidth omega of parameter controllercAnd reducing the observer bandwidth omega when the system output fluctuates0Then gradually increasing the bandwidth omega of the parameter controllerc;
A5, judging the bandwidth omega of parameter controllercAnd if the control requirement is met, finishing the parameter adjustment of the linear active disturbance rejection controller, otherwise, returning to the step A4.
6. The extended state observer-based air volume pressure sensor of claim 5The fast active disturbance rejection method is characterized in that in the parameter adjustment process of the linear active disturbance rejection controller, if large amplitude oscillation occurs, the control gain b is adjusted0。
7. The extended state observer-based air volume pressure fast active disturbance rejection method according to claim 1, wherein the S4 comprises the steps of:
b1, initializing parameters of the whale algorithm according to the estimated value;
b2, randomly generating the position of the initial whale according to the limited range;
b3, defining the position of the whale, and calculating the adaptation value of the current whale colony to obtain the optimal position of the whale;
b4, according to the optimal position of the whale, performing optimal neighborhood disturbance updating by using a self-adaptive inertia weight and position updating method;
b5, judging whether the global optimal position probability is less than or equal to 0.5 according to the optimal neighborhood disturbance updating, if so, performing variable spiral updating by using spiral searching, and entering the step B7, otherwise, entering the step B6;
b6, judging whether the weight system is less than or equal to 1, if so, performing contraction enclosure updating by using spiral searching, and entering the step B7, otherwise, randomly searching and updating the position by using a whale position updating formula, and entering the step B7;
b7, judging whether the iteration times reach a preset value, if so, obtaining an optimization result, and realizing the rapid active disturbance rejection of the air cavity pressure, otherwise, returning to the step B3.
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