CN109507878A - State based on average residence time switching feeds back switch controller design method - Google Patents
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Abstract
The present invention relates to a kind of states based on average residence time switching to feed back switch controller design method, is modeled for every kind of failure of controlled device, obtains corresponding subsystem model；Set H∞The initial value of parameter index is as storage value；Matrix and Lyapunov Jacobian matrix to be solved is set, and constructs linear matrix inequality；Increase damped expoential according to step value and averagely station the value of time parameter, obtains matrix and H to be solved∞Parameter index；Time and controller matrix are averagely stationed in solution.The controller and switching law design method for the average residence time strategy that application model of the present invention relies on, using the controller design under redundancy backup flying wheel feature design error failure generating state, satellite controller is set steadily to switch to the control law of backup flying wheel when flying wheel breaks down, interference suppression level with higher simultaneously, improves the safety and reliability of satellite transit.
Description
Technical Field
The invention relates to the field of satellite fault-tolerant control, in particular to a state feedback switching controller design method based on average residence time switching.
Background
The inertia wheel is an actuating mechanism of a satellite control system, is an indispensable basic device for controlling the attitude of the satellite, and is also a basic guarantee that the satellite can run in orbit, and the reliability and the safety of the inertia wheel are necessary preconditions for the stable running of the satellite. In the attitude control of the satellite, the attitude needs to be modeled and controlled by an euler method or a four-element method. In the operation of the satellite, the requirements on reliability and safety are extremely high, and the inertia wheel design comprises a backup inertia wheel so that a fault attitude system of a certain working inertia wheel can still work normally. Therefore, the fault-tolerant controller can be designed through the switching controller, so that the system can be switched to the backup inertia wheel to continue stable operation when the inertia wheel fails.
Handover strategies have been extensively studied in the field of linear variable parameters. The switching control makes the design of the variable parameter controller more flexible and practical. Current research has applied this switched variable parameter control strategy to missile systems, aircraft systems, power generation systems, inverted pendulum systems, and the like.
The mode dependent mean dwell method is a common method in handover strategies. The principle is that the activation time conditions of different subsystems are designed, the conditions which are required to be met by the activation time of the different subsystems are guaranteed, and the descending property of the overall Lyapunov function of the system is guaranteed. Let the residence time of switching signal in different subsystems meet the condition of average residence time, i.e. Ti＞τa,iThe stability of the switching system is ensured. The switching system divergence caused by too frequent switching is avoided.
H∞The method is a common method in robust control, and ensures the stability of the systemMeanwhile, the suppression parameters of the system to disturbance input are optimized, the solved controller enables the system to be stable, and the closed-loop system has disturbance resistance. The specific form of the controller is obtained by solving the unknown matrix usually by using a linear matrix inequality constraint method.
In the conventional fault-tolerant control method, the same switching conditions are generally used for the fault cut-in and cut-out. The switching strategy may cause frequent switching near a switching surface, and the fault-tolerant controller design based on the mode-dependent average residence time switching strategy ensures the performance of a switching system by ensuring the average residence time of different subsystems, so that the switching-in time and the switching-out time meet the average residence time condition, and the design can effectively avoid performance reduction caused by switching among different subsystems.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a state feedback switching controller design method based on average residence time switching.
The technical scheme adopted by the invention for realizing the purpose is as follows:
a design method of a state feedback switching controller based on average residence time switching comprises the following steps:
step 1: modeling is carried out aiming at each fault of a controlled object to obtain a corresponding subsystem model;
step 2: setting the position of switching surface of fault-tolerant controller, the upper limit value, the lower limit value and the step value of attenuation index, the upper limit value, the lower limit value and the step value of average residence time parameter according to fault factor, and setting H∞The initial value of the parameter index is used as a storage value;
and step 3: setting a matrix to be solved and a Lyapunov function matrix according to the form of a controller to be solved, and constructing a linear matrix inequality according to a bounded real guiding principle;
and 4, step 4: within the upper and lower limits of the attenuation index and the average residence time parameter, increasing the values of the attenuation index and the average residence time parameter according to the step value to obtain a matrix to be solved and H∞A parameter index; if H is obtained∞If the parameter index is less than the stored value, H is updated∞Parameter indexes, and storing a solving matrix, a decay index and an average residence time parameter; otherwise, the H is abandoned∞A parameter index;
and 5: the average dwell time and controller matrix are solved.
The subsystem model is as follows:
z＝C1x+D11ω+D12,iF(ρ)u,
y＝C2x+D21ω,
wherein x ∈ RnIs the system state;is controlled output;is a disturbance input;outputting for measurement;is a control input;is the fault parameter vector, rho ∈ omegaρAnd rate of change of its derivativeF (rho) is a fault factor matrix in the subsystem; a is the state gain in the state equation in the subsystem; b is1Inputting a gain for disturbance in a state equation in a subsystem; b is2,iControlling input gain in a state equation in a subsystem; c1The state gain in the controlled output equation in the subsystem is obtained; d11For perturbing the input gain in the controlled output equation in the subsystem, D12,iControlling input gain in a controlled output equation in a subsystem; c2Measuring state gain in an output equation for the subsystem; d21And (4) disturbance input gain in an output equation is measured in the subsystem.
The fault factor matrix is:
wherein, T0The moment when the fault occurs; rhoiAs a fault factor, ρi(t-T0，i) Is T0，iRepresents the effect of the fault on the control input.
The fault factors are:
wherein, aiIs a rate of decay of the fault to be determined, and ai＞0；T0，iThe moment when the fault occurs; rhoiIs a fault factor; and t is the time for which the system is running.
The decay exponent is greater than 0; the average residence time parameter is greater than 1; the step value is greater than 0; h∞The initial value of the parameter index is greater than 0.
The linear matrix inequality is:
Xi(ρ)-μiXj(ρ)≤0
wherein, Xi(rho) is a Lyapunov function matrix of the subsystem i; xj(ρ) is the Lyapunov function matrix of the subsystem j; a is the state gain in the state equation in the subsystem; b is1Inputting a gain for disturbance in a state equation in a subsystem; b is2,iControlling input gain in a state equation in a subsystem; c1Obtaining the state gain in the output equation in the subsystem; d11Inputting the gain for the disturbance in the output equation in the subsystem; d12,iControlling input gain in an output equation in the subsystem;is a matrix to be solved;is nzA dimension unit matrix;is nωA dimension unit matrix; f (rho) is a fault factor matrix in the subsystem.
The solving result comprises a Lyapunov function matrix, a matrix to be solved, a decay exponent and average residence time.
The average residence time is:
wherein λ is0，iTo decay index, μiTo be the average residence time parameter,is the average residence time minimum.
The controller matrix is:
wherein,for the matrix to be solved, XiAnd (rho) is a Lyapunov function matrix.
The invention has the following beneficial effects and advantages:
the invention applies the controller and the switching law design method of the mode-dependent average residence time strategy, and applies the characteristic of the redundant backup inertia wheel to design the controller design in the fault occurrence state, so that the satellite controller can be stably switched to the control law of the backup inertia wheel when the inertia wheel has faults, and meanwhile, the invention has higher interference suppression level and improves the safety and the reliability of the satellite operation.
Drawings
FIG. 1 is a flow chart of a method of the present invention;
FIG. 2 is a schematic diagram of the mode dependent average dwell time switching plane setting of the present invention;
fig. 3 is a schematic view of a satellite backup flywheel of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples.
Fig. 1 shows a flow chart of the method of the present invention.
The invention provides a design method of a fault diagnosis controller based on a mode-dependent average residence time switching strategy, which comprises the following steps:
(1) modeling a controlled object as a switching linear variable parameter system, wherein each fault mode is modeled as a subsystem; the system model is of the form:
z＝C1x+D11ω+B12,σF(ρ)u,
y＝C2x+D21ω, (1)
wherein x ∈ RnIn order to be in the state of the system,is the output of the controlled machine, and,in order to disturb the input of the input,is the measurement output of the optical fiber,is a control input.Is a fault parameter vector belonging to a superset rho epsilon omegaρAnd its inverse rate of change also belongs to the superset
In the system (1) of the present invention,is a fault factor in the system. T is0Time of occurrence of the failure, ρiIs T0Represents the effect of the fault on the control input. Model of F (ρ) is
Wherein a isi> 0 is an unknown rate of decay of the fault.
Injecting fault versus ρ of fault factor by input controliDamping parameter αiEvaluation was performed. Fault factor evaluation is carried out on the input which is possibly faulted in each dimension to obtain a matrix F (rho) and a corresponding matrix B of each fault condition2,iAnd B12,iIs used for the functional expression of (1).
Fig. 3 is a schematic diagram of a satellite backup flywheel of the present invention.
According to the characteristics of the inertia wheels in fig. 3, the inertia wheels on the three axes x, y and z are all normal working inertia wheels, and the inertia wheels not on the axes are backup inertia wheels. For a satellite system, when the system operates normally, a normal model is established, and at this time, F (ρ) ═ I. And (3) respectively establishing 3 fault models aiming at the fault condition of each inertia wheel to form a switching variable parameter system with 4 subsystems.
(2) Designing a switching surface of the fault-tolerant controller according to the fault factors; failure of different control inputs will result in a change in the attenuation of the failure factor, but according to function (2), the failure factor range is 0 ≦ ρiLess than or equal to 1. According to a mode-dependent mean residence time switching strategy design method, according to rhoiThe attenuation margin sets the switching plane.
Fig. 2 is a schematic diagram of the design of the mode-dependent average dwell time switching plane of the present invention.
The health subsystem and the fault subsystem are divided by a switching plane. In order to avoid the situation of frequent switching, the switching-in time and the switching-out time of each subsystem are determined as different switching times. FIG. 3 shows a design of a normal, failed subsystem plunge-cut plane of the present invention. Maintaining average residency between switching times of a normal subsystem to a failed system and switching times of the failed system to a normal systemThe time remaining is also beneficial for the system to recover from the failure. In step (d), the average residence time is τaThe difference of (a). At the same time, λ is set0,i,min＝0，λ0,i,max＝2，μi,min＝1，μi,maxWith 3 and a step length of λ0,i,step＝0.01，μi,step＝0.01。
(3) Constructing a subsystem H from a controller to be solved∞Linear matrix inequality constraint, selecting solving parameters according to linear growth; according to the controlled object model, setting the form of the state feedback controller to be solved as follows:
u＝Kσ(ρ)x (3)
setting a matrix to be solved according to the form of the controllerAnd positive definite matrix Xi(ρ) constructing a linear matrix inequality constraint of the subsystem:
(4) and constructing a linear matrix inequality of the switching surface according to the selected switching surface, wherein the inequality is as follows:
Xi(ρ)-μiXj(ρ)≤0. (5)
inequality (5) is a constraint on the switching plane. In the system switching aspect, each subsystem system has average residence time
The switching strategy ensures that the system can be stably switched to a fault state, namely a backup inertia wheel working state, when a single inertia wheel breaks down, and simultaneously ensures that the system can be stably switched to a normal working state from the backup inertia wheel working state when the system recovers from the fault. As long as the switching meets the requirement of the average residence time, the switching is frequent for a plurality of times adjacent in time, and the overall performance of the switching system can still be ensured by the characteristic of the average residence time.
(5) Solving the linear matrix inequality constraint constructed in the step (3) and the step (4) to obtain H∞Parametric result gamma∞And the parameter gamma obtained by solving in the previous step∞,lastBy comparison, if γ∞＜γ∞,lastSaving the solved matrixAnd Xi(p), if γ∞≥γ∞,lastThen matrix is discardedAnd Xi(ρ). Judging whether the fault parameter rho reaches an upper limit, namely rhol＝ρl,maxIf yes, performing the step (6), otherwise, increasing the number of times of iteration completion by 1, and returning to the step (3);
(6) a matrix of handover controllers obtained by solving the matrix. Obtaining a matrix through the solution of the step (5)And positive definite matrix Xi(ρ) by the formula
And solving to obtain the state feedback controller.
Claims (9)
1. A state feedback switching controller design method based on average residence time switching is characterized in that: the method comprises the following steps:
step 1: modeling is carried out aiming at each fault of a controlled object to obtain a corresponding subsystem model;
step 2: setting the position of switching surface of fault-tolerant controller, the upper limit value, the lower limit value and the step value of attenuation index, the upper limit value, the lower limit value and the step value of average residence time parameter according to fault factor, and setting H∞The initial value of the parameter index is used as a storage value;
and step 3: setting a matrix to be solved and a Lyapunov function matrix according to the form of a controller to be solved, and constructing a linear matrix inequality according to a bounded real guiding principle;
and 4, step 4: within the upper and lower limits of the attenuation index and the average residence time parameter, increasing the values of the attenuation index and the average residence time parameter according to the step value to obtain a matrix to be solved and H∞A parameter index; if H is obtained∞If the parameter index is less than the stored value, H is updated∞Parameter indexes, and storing a solving matrix, a decay index and an average residence time parameter; otherwise, the H is abandoned∞A parameter index;
and 5: the average dwell time and controller matrix are solved.
2. The method according to claim 1, wherein the subsystem model is:
z＝C1x+D11ω+D12,iF(ρ)u,
y＝C2x+D21ω,
wherein x ∈ RnIs the system state;is controlled output;is a disturbance input;outputting for measurement;is a control input;is the fault parameter vector, rho ∈ omegaρAnd rate of change of its derivativeF (rho) is a fault factor matrix in the subsystem; a is the state gain in the state equation in the subsystem; b is1Inputting a gain for disturbance in a state equation in a subsystem; b is2,iControlling input gain in a state equation in a subsystem; c1The state gain in the controlled output equation in the subsystem is obtained; d11For perturbing the input gain in the controlled output equation in the subsystem, D12,iControlling input gain in a controlled output equation in a subsystem; c2Measuring state gain in an output equation for the subsystem; d21And (4) disturbance input gain in an output equation is measured in the subsystem.
3. The method according to claim 2, wherein the fault factor matrix is:
wherein, T0The moment when the fault occurs; rhoiAs a fault factor, ρi(t-T0，i) Is T0，iRepresents the effect of the fault on the control input.
4. The method according to claim 1 or 3, wherein the failure factor is:
wherein, aiIs a rate of decay of the fault to be determined, and ai＞0；T0，iThe moment when the fault occurs; rhoiIs a fault factor; and t is the time for which the system is running.
5. The method of claim 1, wherein the decay exponent is greater than 0; the average residence time parameter is greater than 1; the step value is greater than 0; h∞The initial value of the parameter index is greater than 0.
6. The method of claim 1, wherein the linear matrix inequality is:
Xi(ρ)-μiXj(ρ)≤0
wherein, Xi(rho) is a Lyapunov function matrix of the subsystem i; xj(ρ) is the Lyapunov function matrix of the subsystem j; a is the state gain in the state equation in the subsystem; b is1Inputting a gain for disturbance in a state equation in a subsystem; b is2,iControlling input gain in a state equation in a subsystem; c1Obtaining the state gain in the output equation in the subsystem; d11Inputting the gain for the disturbance in the output equation in the subsystem; d12,iControlling input gain in an output equation in the subsystem;is a matrix to be solved;is nzA dimension unit matrix;is nωA dimension unit matrix; f (ρ) isA fault factor matrix in the subsystem.
7. The method according to claim 1, wherein the solution result comprises a Lyapunov function matrix, a matrix to be solved, a decay exponent, and an average dwell time.
8. The method according to claim 1, wherein the average dwell time is:
wherein λ is0，iTo decay index, μiTo be the average residence time parameter,is the average residence time minimum.
9. The method of claim 1, wherein the controller matrix is:
wherein,for the matrix to be solved, XiAnd (rho) is a Lyapunov function matrix.
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