CN105045105A - State-delay four-rotor helicopter fault tolerant control device and method - Google Patents

Abstract

The invention discloses a state-delay four-rotor helicopter fault tolerant control device and method. The device comprises a fault injection module, a helicopter system platform, a data acquisition module, a fault diagnosis module and a power amplifier. The fault injection module is connected with the helicopter system platform and injects the simulated fault information to the helicopter system platform; the data acquisition module collects status information and error information of a helicopter; the fault diagnosis module receives the status information and the error information to obtain a fault-tolerant control law, and resends the fault-tolerant control law to the data acquisition module; and after the data acquisition module processes the fault-tolerant control law, a control instruction is transmitted through the power amplifier to a motor in the helicopter system platform for carry out fault-tolerant adjustment until the error is zero. The fault tolerant control device and method, on the basis of an established four-rotor helicopter linear mathematic model, and by adopting an improved guaranteed cost controller and a model reference self-adaption controller, solve the problem of fault-tolerant control of the system under the conditions of interference, state delay and multiple faults.

Description

A kind of four-rotor helicopter faults-tolerant control device and method for states with time-delay

Technical field

The invention belongs to helicopter Fault Tolerance Control Technology field, particularly a kind of four-rotor helicopter faults-tolerant control device and method for states with time-delay.

Background technology

In recent years, four-rotor helicopter is widely used in rescue, the fields such as search and supervision.The kinetic model of four-rotor helicopter is a drive lacking, the nonlinear system of highly coupling, so the control research of four rotors has certain challenging popular project.Usually due to external disturbance, the problems such as time delay and actuator performance decay, can cause four rotors to send out the raw various fault of helicopter.For ensureing the Ability of emergency management of system, guaranteeing system safety operation, assessment of failure, analysis and faults-tolerant control carrying out to system most important.

In order to realize four-rotor helicopter Fault-tolerant Control System Design, generally adopt the method based on hardware redundancy to improve the reliability of system at present, but also can increase cost, the weight of four-rotor helicopter and the complicacy of control system simultaneously.And the position utilizing advanced control theory to estimate fault to occur based on the fault diagnosis of Analysis design, size and system state vector, the Redundancy Design control law of digging system own, cost-saving, effective suppression failure effect, supervisory system is normally run, but there is no associated description in prior art.

Due to the delay of information transmission and measurement, all kinds of control system ubiquity Time Delay, so obtaining larger concern in recent years for the control problem of time lag system.For the four-rotor helicopter of existence time lag, because time lag will cause the concussion of control system, its flying quality will inevitably be subject to larger impact.In order to ensure the flying quality that helicopter is good, solve its Time Delay very crucial.

Summary of the invention

For above-mentioned the deficiencies in the prior art, the object of this invention is to provide a kind of four-rotor helicopter faults-tolerant control device and method for states with time-delay, to solve the faults-tolerant control problem of four-rotor helicopter system under interference, state time delay and multiple faults condition.。

For achieving the above object, the present invention is by the following technical solutions:

For a four-rotor helicopter faults-tolerant control device for states with time-delay, comprise direct fault location module, Helicopter System platform, data acquisition module, fault diagnosis module and power amplifier, wherein,

Direct fault location module is connected with Helicopter System platform, and the failure message of simulation is injected Helicopter System platform;

Data acquisition module, by the built-in sensors of Helicopter System platform, gathers status information and the control information of helicopter;

Fault diagnosis module is connected with data acquisition module, and the status information that reception data acquisition module spreads out of and control information, obtain faults-tolerant control rule, and resend to data acquisition module by faults-tolerant control rule;

Power amplifier is connected with Helicopter System platform with data acquisition module, and after data acquisition module process faults-tolerant control rule, through power amplifier, by steering order, the motor be transferred in Helicopter System platform performs fault-tolerant adjustment, until error is zero.

Described data acquisition module comprises data collector, signal compiling and modular converter, wherein,

Data collector is for gathering voltage input information and the attitude angle angle of Helicopter System platform;

Signal compiling and conversion equipment operate for the treatment of the encoding and decoding between Helicopter System platform and fault diagnosis module and analog to digital conversion;

Signal compiling and conversion equipment and data collector are linked in sequence.

Described fault diagnosis module comprises status information module, control information module, the Guaranteed Cost Controller of improvement, model reference adaptive controller, wherein,

Status information module and control information module obtain status information and the control information of data acquisition module output;

The Guaranteed Cost Controller improved and model reference adaptive controller utilize the status information and control information determination faults-tolerant control rule that gather, and are sent to data acquisition module.

The Guaranteed Cost Controller of described improvement is made up of model reference linear quadratic regulator and Guaranteed Cost Controller two parts; Model reference linear quadratic regulator is used for track reference system, disturbance suppression and solve the problem that Guaranteed Cost Controller can not be used for the coefficient of regime matrix not linear model of full rank; Guaranteed Cost Controller is for solving state delay problem.

Described Helicopter System platform is 3-DOFhover platform.

Based on the four-rotor helicopter faults-tolerant control installation method for states with time-delay of above-mentioned device, comprise the following steps:

Step 1, set up four-rotor helicopter body axis system, determine the definition of pitching, driftage and wobble shaft, and set up the linear kinetic model of dynamics attitude angle under normal circumstances;

Step 2, state-space expression when determining four-rotor helicopter dynamics attitude angle system failure; By in fault injection system, the state-space expression under certainty annuity fault;

Step 3, on the basis of step 2, from data acquisition module, obtain the status information of system, status information comprises pitching, driftage, roll angle size, subtract each other with reference to the quantity of state reference value in model and above-mentioned status information, obtain control information, construct four-rotor helicopter flight attitude fault-tolerant controller thus, actuator failures on Real-Time Monitoring pitching, driftage and rolling direction and other interference, and export faults-tolerant control rule to data acquisition module, through power amplifier, control signal is transferred to motor and performs.

The invention has the beneficial effects as follows:

(1) adopt software fault injection method, do not destroy the integrality of attitude control system, and can the position of unrestricted choice direct fault location and size, without the need to extra hardware device, to direct fault location, topworks does not cause physical damage;

(2) Guaranteed Cost Controller improved is by the combination of model reference linear quadratic regulator and Guaranteed Cost Controller, solve the problem that Guaranteed Cost Controller is not suitable for four-rotor helicopter linear model, and effectively ensure that the robust stability of time lag Helicopter System;

(3) Guaranteed Cost Controller of improvement and model reference adaptive controller are combined, effectively solve the faults-tolerant control ability of time lag four-rotor helicopter system to fault;

(4) real-time faults injection condition, current topworks duty and attitudes vibration in human-computer interaction interface, realize fault pre-alarming and Real-Time Monitoring;

(5) the present invention is used for verifying the reliability of attitude control system and troubleshooting capability, easy to operate, cost is low, cost performance is high, realizability is strong;

(6) the present invention may be used for actuator failure analysis and the systems reliability analysis in helicopter attitude control system semi-physical simulation stage.

Accompanying drawing explanation

Fig. 1 is the four-rotor helicopter faults-tolerant control schematic diagram of device for time lag of the present invention;

Fig. 2 is the naive model of four-rotor helicopter system;

System pitching curve when Fig. 3 is non-fault;

System deviation curve when Fig. 4 is non-fault;

System roll angle curve when Fig. 5 is non-fault;

System pitching curve when Fig. 6 is for there being a fault;

System deviation curve when Fig. 7 is for there being a fault;

System roll angle curve when Fig. 8 is for there being a fault.

Embodiment

Below in conjunction with accompanying drawing, the present invention is further described.

As shown in Figure 1, the four-rotor helicopter faults-tolerant control device for states with time-delay of the present invention comprises direct fault location module, Helicopter System platform, data acquisition module, fault diagnosis module and power amplifier, wherein,

Direct fault location module is connected with Helicopter System platform, and the failure message of simulation is injected Helicopter System platform;

Data acquisition module, by the built-in sensors of Helicopter System platform, gathers status information and the control information of helicopter;

Fault diagnosis module is connected with data acquisition module, and the status information that reception data acquisition module spreads out of and control information, obtain faults-tolerant control rule, and resend to data acquisition module by faults-tolerant control rule;

Power amplifier is connected with Helicopter System platform with data acquisition module, and after data acquisition module process faults-tolerant control rule, through power amplifier, by steering order, the motor be transferred in Helicopter System platform performs fault-tolerant adjustment, until error is zero.

Data acquisition module comprises data collector, signal compiling and modular converter, wherein,

Data collector is for gathering voltage input information and the attitude angle angle of Helicopter System platform;

Signal compiling and conversion equipment operate for the treatment of the encoding and decoding between Helicopter System platform and fault diagnosis module and analog to digital conversion;

Signal compiling and conversion equipment and data collector are linked in sequence.

Fault diagnosis module comprises status information module, control information module, the Guaranteed Cost Controller of improvement, model reference adaptive controller, wherein,

Status information module and control information module obtain status information and the control information of data acquisition module output;

The Guaranteed Cost Controller improved and model reference adaptive controller utilize the status information and control information determination faults-tolerant control rule that gather, and are sent to data acquisition module.

The Guaranteed Cost Controller improved is made up of model reference linear quadratic regulator and Guaranteed Cost Controller two parts; Model reference linear quadratic regulator is used for track reference system, disturbance suppression and solve the problem that Guaranteed Cost Controller can not be used for the coefficient of regime matrix not linear model of full rank; Guaranteed Cost Controller is for solving state delay problem.

Direct fault location module uses MATLAB software simulating, by the adjustment to output voltage, and simulation partial loss fault and the stuck fault of motor.

Helicopter System platform, power amplifier and data acquisition module are that outsourcing 3-DOFhover platform (comprises four-rotor helicopter fuselage, model is the power amplifier of the highest exportable 24V linear voltage of UPM2405,5A electric current, model is the signal acquiring board of Q8, and computing machine is provided with matlab, LABVIEW, real-time control software QuaRC etc.);

Fault diagnosis module realizes controlling in real time and man-machine interaction, and designed software algorithm, by matlab, LABVIEW, QuaRC software simulating, comprises the input of image data and analysis, the design of faults-tolerant control rule and output.The input of image data and analysis comprise to decode and to obtain state and control information from data collecting card; The design of faults-tolerant control rule and output comprise Guaranteed Cost Controller and the model reference adaptive controller of improvement.Helicopter running state data can show, to realize Real-Time Monitoring and the control of fault by the interface portion of designed software.

Encoders0-2 port white wire on data collecting card is connected on (ENC0) on 3-DOF platform-(ENC2), AnlogOutputs0-3 port black line is connected on the FromD/A of four power amplifiers, and the line of corresponding power supply ToLoad black is connected on (D/A0)-(D/A3) of 3-DOF platform.

With reference to Fig. 2-8, based on the four-rotor helicopter faults-tolerant control installation method for states with time-delay of above-mentioned device, comprise the following steps:

Step 1, set up body axis system, determine the definition of pitching, driftage and wobble shaft, and set up the linear kinetic model of dynamics attitude angle under normal circumstances;

Four-rotor helicopter pitching, driftage and roll angle equation are:

$\left\{\begin{array}{c}{J}_p\stackrel{\·\·}{\mathrm{\θ}}={\mathrm{lK}}_f(U_f-U_b)\\ J_y\stackrel{\·\·}{\mathrm{\ψ}}=K_{tc}(U_f+U_b)+K_{tn}(U_l+U_r)\\ J_r\stackrel{\·\·}{\mathrm{\φ}}={\mathrm{lK}}_f(U_l-U_r)\end{array}\right.---\left(1\right)$

Implication in formula representated by parameter is: θ, ψ, φ are respectively the angle of pitch, crab angle and roll angle, K _ffor rotor lift coefficient, K _tn, K _tcbe respectively rotor clockwise, be rotated counterclockwise moment coefficient, J _pthe moment of inertia of body around pitch axis, J _ythe moment of inertia of body around yaw axis, J _rthe moment of inertia of body around wobble shaft, U _f, U _b, U _l, U _rbe respectively four-rotor helicopter forward direction motor, backward motor, left-hand motor and dextrad motor driven voltage value, l is the length of true origin to motor center point;

Above-mentioned equation is determined under following hypothesis relation:

(1) structure of aircraft be all rigidity with Striking symmetry;

(2) just heart place in the structure, aircraft center;

(3) be linear relationship between the voltage of direct current generator and moment;

(4) change of attitude of flight vehicle angle is very little, is namely less than 10 °.

Step 2, state-space expression when determining four-rotor helicopter dynamics attitude angle system failure; By in fault injection system, the state-space expression under certainty annuity fault;

The dynamic model of certainty annuity when fault is actuator damage fault, described model is:

$\left\{\begin{array}{c}\stackrel{\·}{x}\left(t\right)=Ax\left(t\right)+A_{\mathrm{\τ}}x(t-\mathrm{\τ})+B\[(f\left(t\right)-\mathrm{\σ}\left(t\right))v\left(t\right)+\mathrm{\σ}\left(t\right)\stackrel{\‾}{v}\left(t\right)\]+Bd\left(t\right)\\ y\left(t\right)=Cx\left(t\right)\end{array}\right.---\left(2\right)$

In formula for state vector, v (t) ∈ R ^{4 × 1}for control inputs vector, for output vector, τ is that system state postpones, d (t) ∈ R ⁴for the external disturbance of unknown bounded, for stuck fault input vector, f (t) ∈ R ^{4 × 4}for partial failure failure coefficient matrix, σ (t) ∈ R ^{4 × 4}for stuck failure coefficient matrix, it meets respectively:

$\begin{array}{cc}f\left(t\right)=\left\{\begin{array}{cc}diag(1,1,...,1),& t<T_1\\ diag(f_1,f_2,...,f_p),& t\&GreaterEqual;T_1\end{array}\right.& \mathrm{\&sigma;}\left(t\right)=\left\{\begin{array}{cc}0,& t<T_2\\ diag({\mathrm{\&sigma;}}_1,{\mathrm{\&sigma;}}_2,...,{\mathrm{\&sigma;}}_p),& t\&GreaterEqual;T_2\end{array}\right.\end{array}$

A, B, C are system matrix, A _tfor state time delay matrix, wherein

$\begin{array}{cc}A=\left[\begin{array}{cccccc}0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\end{array}\right]& B=\left[\begin{array}{cccc}0& 0& 0& 0\\ 0& 0& 0& 0\\ 0& 0& 0& 0\\ 0.4235& -0.4235& 0& 0\\ -0.0326& -0.0326& 0.0326& 0.0326\\ 0& 0& 0.4235& -0.4235\end{array}\right]\\ C=\left[\begin{array}{cccccc}1& 0& 0& 0& 0& 0\\ 0& 1& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0\end{array}\right]& A_{\mathrm{\&tau;}}=A\end{array}$

Step 3, the pitching that the basis of step 2 obtains system from data time acquisition module, driftage, roll angle size, i.e. status information, subtract each other with reference to the quantity of state reference value in model and above-mentioned status information, obtain control information, construct four-rotor helicopter flight attitude fault-tolerant controller thus, actuator failures on Real-Time Monitoring pitching, driftage and rolling direction and other interference, and export faults-tolerant control rule to data acquisition module, through power amplifier, control signal is transferred to motor and performs;

Four rotor flying attitude fault-tolerant controllers, comprise Guaranteed Cost Controller and the model reference adaptive controller of improvement, quantity of state, the margin of error of system import status information module and control information module into respectively by data acquisition module, utilize the data of two modules, the Guaranteed Cost Controller be improved respectively and the output of model reference adaptive controller.Improve Guaranteed Cost Controller can disturbance suppression on the impact of system, the robust stability of guarantee system under state time delay, model reference adaptive can reconfigurable control system, the tracking performance that guarantee system is good under multiple faults condition, following process is that trouble-shooter specifically performs step:

The reference model that step 31, selecting system are followed the tracks of, is defined as:

$\{\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_m\left(t\right)=A_m{x}_m\left(t\right)+B_{m}r\left(t\right)\\ y_m\left(t\right)=C_m{x}_m\left(t\right)\end{array}---\left(3\right)$

X in formula _mt () is the quantity of state that system is expected to follow the tracks of, r (t) is the input that system is expected, y _mthe output that system is expected, A _m, B _m, C _mit is the suitable matrix of dimension.

The design of the Guaranteed Cost Controller of step 32, improvement.Under the Guaranteed Cost Controller improved is used for fault-free conditions, maintain the tracking performance of system, the robust stability of Guarantee Status time-delay system.Under fault-free conditions, system (2) can be expressed as:

$\stackrel{\&CenterDot;}{x}\left(t\right)=Ax\left(t\right)+A_{\mathrm{\&tau;}}x(t-\mathrm{\&tau;})+Bv\left(t\right)+Bd\left(t\right)---\left(4\right)$

The Guaranteed Cost Controller improved comprises model reference linear quadratic regulator and Guaranteed Cost Controller two parts.Model reference linear quadratic regulator is mainly used to track reference system, disturbance suppression and solve the problem that Guaranteed Cost Controller can not be used for the coefficient of regime matrix not linear model of full rank.Guaranteed Cost Controller is mainly used in solution state delay problem.

First the design of model reference linear quadratic regulator is carried out.Choose performance index function as follows:

$J_{lqr}={\&Integral;}_{t_0}^{\mathrm{\&infin;}}\&lsqb;{\left(x\right(t)-x_m(t\left)\right)}^{T}Q\left(x\right(t)-x_m(t\left)\right)+v^T\left(t\right)Rv\left(t\right)\&rsqb;dt---\left(5\right)$

Q ∈ R in formula ^{6 × 6}for symmetric positive semidefinite matrix, R ∈ R ^{4 × 4}for symmetric positive definite matrix.

In order to obtain model reference linear quadratic regulator feedback gain, choose Hamilton function as follows:

$\begin{array}{c}H(x,\mathrm{\&lambda;},u)=\frac{1}{2}\&lsqb;{\left(x\right(t)-x_m(t\left)\right)}^{T}Q(x-x_m)+v^T\left(t\right)Rv\left(t\right)\&rsqb;\\ +{\mathrm{\&lambda;}}^T\left(t\right)\left(Ax\right(t)+A_{\mathrm{\&tau;}}x(t-\mathrm{\&tau;})+Bv(t)+Bd(t\left)\right)\end{array}---\left(6\right)$

According to obtain the optimum control of model reference linear quadratic regulator to be input as:

u _lqr(t)＝K _lqr(x(t)-x _m(t))＝-R ^-1B ^TP(x(t)-x _m(t))(7)

Next designs Guaranteed Cost Controller.The control inputs of Guaranteed Cost Controller

$u_{gcc}\left(t\right)=K_{gcc}\left(x\right(t)+{\&Integral;}_{t-\mathrm{\&tau;}}^{t}x\left(s\right)ds)---\left(8\right)$

Make v (t)=u _lqr(t)+u _gcct () substitutes into system (4) and obtains

$\stackrel{\&CenterDot;}{x}\left(t\right)=(A_{lqr}+{\mathrm{BK}}_{gcc})x\left(t\right)+A_{\mathrm{\&tau;}}x(t-\mathrm{\&tau;})+{\mathrm{BK}}_{gcc}{\&Integral;}_{t-\mathrm{\&tau;}}^{t}x\left(s\right)ds+Bd\left(t\right)-{\mathrm{BK}}_{lqr}{x}_m\left(t\right)---\left(9\right)$

A in formula _lqr=A+BK _lqr.

Suppose to there is positive definite symmetric matrices with the matrix of a suitable dimension meet following LMI

$\left[\begin{array}{ccc}{\mathrm{\&Phi;}}_{11}& A_{\mathrm{\&tau;}}{\stackrel{\&OverBar;}{P}}_1& {B\stackrel{\&OverBar;}{K}}_{gcc}\\ {\stackrel{\&OverBar;}{P}}_1{A}_{\mathrm{\&tau;}}^T& -{\stackrel{\&OverBar;}{Q}}_1& 0\\ {{\stackrel{\&OverBar;}{K}}_{gcc}}^T{B}^T& 0& -{\mathrm{\&tau;}}^{-1}{\stackrel{\&OverBar;}{Q}}_2\end{array}\right]<0---\left(10\right)$

In formula ${\mathrm{\&Phi;}}_{11}=A_{lqr}{\stackrel{\&OverBar;}{P}}_1+{\stackrel{\&OverBar;}{P}}_1{A_{lqr}}^T+B{\stackrel{\&OverBar;}{K}}_{gcc}+{{\stackrel{\&OverBar;}{K}}_{gcc}}^T{B}^T+{\stackrel{\&OverBar;}{Q}}_1+\mathrm{\&tau;}{\stackrel{\&OverBar;}{Q}}_2.$

And disturbance meets as lower inequality

X ^t(t) P ₁bd (t)-x ^t(t) P ₁bK _lqrx _mt the input of () <0 (11) then Guaranteed Cost Controller can be expressed as

$u_{gcc}\left(t\right)={\stackrel{\&OverBar;}{K}}_{gcc}{\stackrel{\&OverBar;}{P}}^{-1}\left(x\right(t)+\underset{t-\mathrm{\&tau;}}{\overset{t}{\&Integral;}}x\left(s\right)ds)---\left(12\right)$

And system (9) has robust stability.

Choose following Lyapunov function

$V_1(x,t)=x^T\left(t\right)P_{1}x\left(t\right)+{\&Integral;}_{t-\mathrm{\&tau;}}^t{x}^T\left(s\right)Q_{1}x\left(s\right)ds+{\&Integral;}_{t-\mathrm{\&tau;}}^t(s-t+\mathrm{\&tau;})x^T\left(s\right)Q_{2}x\left(s\right)ds---\left(13\right)$

P in formula ₁∈ R ^{n × n}, Q ₁∈ R ^{n × n}and Q ₁∈ R ^{n × n}for positive definite symmetric matrices.

Formula (13) differentiate is obtained

$\begin{array}{c}{\stackrel{\&CenterDot;}{V}}_1(x,t)=2x^T\left(t\right)P_1\stackrel{\&CenterDot;}{x}\left(t\right)+x^T\left(t\right)Q_{1}x\left(t\right)-x^T(t-\mathrm{\&tau;})Q_{1}x(t-\mathrm{\&tau;})\\ +{\mathrm{\&tau;x}}^T\left(t\right)Q_{2}x\left(t\right)-{\&Integral;}_{t-\mathrm{\&tau;}}^t{x}^T\left(s\right)Q_{2}x\left(s\right)ds\end{array}---\left(14\right)$

Can obtain according to formula (11)

${\stackrel{\&CenterDot;}{V}}_1(x,t)\&le;{\mathrm{\&xi;}}^T\left(t\right)\mathrm{\&Psi;}\mathrm{\&xi;}\left(t\right)---\left(15\right)$

In formula ${\mathrm{\&xi;}}^T\left(t\right)=\left[\begin{array}{ccc}{x}^T\left(t\right)& x^T(t-\mathrm{\&tau;})& {\left({\&Integral;}_{t-\mathrm{\&tau;}}^{t}x\left(s\right)ds\right)}^T\end{array}\right],\mathrm{\&Psi;}=\left[\begin{array}{ccc}{\mathrm{\&Psi;}}_{11}& P_1{A}_{\mathrm{\&tau;}}& P_1{\mathrm{BK}}_{gcc}\\ {A_{\mathrm{\&tau;}}}^T{P}_1& -Q_1& 0\\ {K_{gcc}}^T{B}^T{P}_1& 0& -{\mathrm{\&tau;}}^{-1}{Q}_2\end{array}\right],$

Ψ ₁₁＝P ₁(A _lqr+BK _gcc)+(A _lqr+BK _gcc) ^TP ₁+Q ₁+tQ ₂

Because $\mathrm{\&Psi;}<0\&DoubleLeftRightArrow;\widehat{\mathrm{\&Psi;}}<0,$

$\begin{array}{c}\widehat{\mathrm{\&Psi;}}=diag({P_1}^{-1},{P_1}^{-1},{P_1}^{-1})\mathrm{\&Psi;}diag(P_1^{-1},P_1^{-1},{P_1}^{-1})\\ =\left[\begin{array}{ccc}{\widehat{\mathrm{\&Psi;}}}_{11}& A_{\mathrm{\&tau;}}{\stackrel{\&OverBar;}{P}}_1& B{\stackrel{\&OverBar;}{K}}_{gcc}\\ {\stackrel{\&OverBar;}{P}}_1{A}_{\mathrm{\&tau;}}^T& -{\stackrel{\&OverBar;}{Q}}_1& 0\\ {{\stackrel{\&OverBar;}{K}}_{gcc}}^T{B}^T& 0& -{\mathrm{\&tau;}}^{-1}{\stackrel{\&OverBar;}{Q}}_2\end{array}\right]\end{array}---\left(16\right)$

In formula ${\widehat{\mathrm{\&Psi;}}}_{11}=A_{lqr}{\stackrel{\&OverBar;}{P}}_1+{\stackrel{\&OverBar;}{P}}_1{A_{lqr}}^T+B{\stackrel{\&OverBar;}{K}}_{gcc}+{{\stackrel{\&OverBar;}{K}}_{gcc}}^T{B}^T+{\stackrel{\&OverBar;}{Q}}_1+\mathrm{\&tau;}{\stackrel{\&OverBar;}{Q}}_2,\stackrel{\&OverBar;}{P}={P_1}^{-1},{\stackrel{\&OverBar;}{K}}_{gcc}=K_{gcc}{P_1}^{-1},$

${\stackrel{\&OverBar;}{Q}}_1={P_1}^{-1}{Q}_1{P_1}^{-1},{\stackrel{\&OverBar;}{Q}}_2={P_1}^{-1}{Q}_2{P_1}^{-1}.$

According to LMI (10), can show that system robust is stablized.

According to above-mentioned, the control inputs of the Guaranteed Cost Controller of improvement can be expressed as

$u_{igcc}\left(t\right)=K_{lqr}\left(x\right(t)-x_m(t\left)\right)+K_{gcc}\left(x\right(t)+{\&Integral;}_{t-\mathrm{\&tau;}}^{t}x\left(s\right)ds)---\left(17\right)$

The design of step 33, model reference adaptive system.Model reference adaptive is mainly used to reconfigurable control system, compensates the actuator failures of four-rotor helicopter.

Suppose to there is constant value matrix with meet following condition

$\begin{array}{c}A+B\left(f\right(t)-\mathrm{\&sigma;}(t\left)\right)K_1^{*}=A_m\\ B\left(f\right(t)-\mathrm{\&sigma;}(t\left)\right)K_2^{*}=B_m\\ B\left(f\right(t)-\mathrm{\&sigma;}(t\left)\right)K_3^{*}+B\mathrm{\&sigma;}\left(t\right)\stackrel{\&OverBar;}{v}\left(t\right)=0\end{array}---\left(18\right)$

The Model Reference Adaptive Control that then can design a model rule is as follows

u _ac(t)＝K ₁(t)x(t)+K ₂(t)r(t)+K ₃(t)(19)

K in formula ₁(t) ∈ R ^{4 × 6}, K ₂(t) ∈ R ^{4 × 4}and K ₃(t) ∈ R ^{4 × 1}be respectively and estimated value, and ${\tilde{K}}_1\left(t\right)=K_1\left(t\right)-K_1^{*},{\tilde{K}}_2\left(t\right)=K_2\left(t\right)-K_2^{*},{\tilde{K}}_3\left(t\right)=K_3\left(t\right)-K_3^{*}.$

The Guaranteed Cost Controller control inputs (17) of associating improvement and the control inputs (19) of model reference adaptive, can obtain following input control rule

$v\left(t\right)=K_1\left(t\right)x\left(t\right)+K_2\left(t\right)r\left(t\right)+K_3\left(t\right)+K_{lqr}\left(x\right(t)-x_m(t\left)\right)+K_{gcc}\left(x\right(t)+{\&Integral;}_{t-\mathrm{\&tau;}}^{t}x\left(s\right)ds)---\left(20\right)$

Control law (20) is substituted into system (2) obtain

$\begin{array}{c}\stackrel{\&CenterDot;}{x}\left(t\right)=Ax\left(t\right)+A_{\mathrm{\&tau;}}x(t-\mathrm{\&tau;})+B\{\left(f\right(t)-\mathrm{\&sigma;}(t\left)\right)\&lsqb;K_1\left(t\right)x\left(t\right)+K_2\left(t\right)r\left(t\right)+K_3\left(t\right)\\ +K_{lqr}\left(x\right(t)-x_m(t\left)\right)+K_{gcc}\left(x\right(t)+{\&Integral;}_{t-\mathrm{\&tau;}}^{t}x\left(s\right)ds)\&rsqb;+\mathrm{\&sigma;}\left(t\right)\stackrel{\&OverBar;}{v}\left(t\right)\}+Bd\left(t\right)\\ =Ax\left(t\right)+B\left(f\right(t)-\mathrm{\&sigma;}(t\left)\right)\left(K_1\right(t\left)x\right(t)+K_2(t\left)r\right(t\left)\right)+B\left(f\right(t)-\mathrm{\&sigma;}(t\left)\right)K_3\left(t\right)\\ +B\mathrm{\&sigma;}\left(t\right)\stackrel{\&OverBar;}{v}\left(t\right)+B\left(f\right(t)-\mathrm{\&sigma;}(t\left)\right)\&lsqb;K_{lqr}\left(x\right(t)-x_m(t\left)\right)+K_{gcc}\left(x\right(t)+{\&Integral;}_{t-\mathrm{\&tau;}}^{t}x\left(s\right)ds)\&rsqb;\\ +A_{\mathrm{\&tau;}}x(t-\mathrm{\&tau;})+Bd\left(t\right)\end{array}---\left(21\right)$

Because the Guaranteed Cost Controller improved can the impact of compensating disturbance and state time delay, so

$\begin{array}{c}\underset{t\&RightArrow;\mathrm{\&infin;}}{\lim }B\left(f\right(t)-\mathrm{\&sigma;}(t\left)\right)[K_{lqr}\left(x\right(t)-x_m(t\left)\right)+K_{gcc}\left(x\right(t)+{\&Integral;}_{t-\mathrm{\&tau;}}^{t}x\left(s\right)ds)\&rsqb;\\ +A_{\mathrm{\&tau;}}x(t-\mathrm{\&tau;})+Bd\left(t\right)=0\end{array}---\left(22\right)$

According to formula (22), system (21) can be reduced to

$\begin{array}{c}\stackrel{\&CenterDot;}{x}\left(t\right)=Ax\left(t\right)+B\left(f\right(t)-\mathrm{\&sigma;}(t\left)\right)\left(K_1\right(t\left)x\right(t)+K_2(t\left)r\right(t\left)\right)+\\ B\left(f\right(t)-\mathrm{\&sigma;}(t\left)\right)K_3\left(t\right)+B\mathrm{\&sigma;}\left(t\right)\stackrel{\&OverBar;}{v}\left(t\right)\end{array}---\left(23\right)$

Definition status error is

e(t)＝x(t)-x _m(t)(24)

Formula (24) differentiate is obtained

$\begin{array}{c}\stackrel{\&CenterDot;}{e}\left(t\right)=\stackrel{\&CenterDot;}{x}\left(t\right)-{\stackrel{\&CenterDot;}{x}}_m\left(t\right)\\ =A_{m}e\left(t\right)+B_m\&lsqb;K_2^{*-1}{\tilde{K}}_1\left(t\right)x\left(t\right)+K_2^{*-1}{\tilde{K}}_2\left(t\right)r\left(t\right)+K_2^{*-1}{\tilde{K}}_3\&rsqb;\end{array}---\left(25\right)$

Suppose to there is matrix M _s, Γ ∈ R ^{4 × 4}, meet

$M_s=K_2^{*}\mathrm{\&Gamma;}={\left(K_2^{*}\mathrm{\&Gamma;}\right)}^T={\mathrm{\&Gamma;}}^T{K}_2^{*T}>0---\left(26\right)$

Design following adaptive control laws

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{\tilde{K}}}_1\left(t\right)={\stackrel{\&CenterDot;}{K}}_1\left(t\right)=-{\mathrm{\&Gamma;}}^T{B_m}^T{P}_{2}e\left(t\right)x^T\left(t\right)\\ {\stackrel{\&CenterDot;}{\tilde{K}}}_2\left(t\right)={\stackrel{\&CenterDot;}{K}}_2\left(t\right)=-{\mathrm{\&Gamma;}}^T{B}_m^T{P}_{2}e\left(t\right)r^T\left(t\right)\\ {\stackrel{\&CenterDot;}{\tilde{K}}}_3\left(t\right)={\stackrel{\&CenterDot;}{K}}_3\left(t\right)=-{\mathrm{\&Gamma;}}^T{B}_m^T{P}_{2}e\left(t\right)\end{array}\right.---\left(27\right)$

P in formula ₂∈ R ^{6 × 6}for positive definite symmetric matrices, for any constant value symmetric positive definite matrix Q ₃∈ R ^{6 × 6}meet

$P_2{A}_m+A_m^T{P}_2=-Q_3---\left(28\right)$

Choose following Lyapunov function

$V_2=e^{T}Pe+tr\&lsqb;{\tilde{K}}_1^T{M_s}^{-1}{\tilde{K}}_1\&rsqb;+tr\&lsqb;{\tilde{K}}_2{M}_s^{-1}{\tilde{K}}_2^T\&rsqb;+tr\&lsqb;{\tilde{K}}_3^T{M}_s^{-1}{\tilde{K}}_3\&rsqb;---\left(29\right)$

Formula (29) differentiate is obtained

$\begin{array}{c}{\stackrel{\&CenterDot;}{V}}_2=2e^T{P}_2\stackrel{\&CenterDot;}{e}+2tr\&lsqb;{\tilde{K}}_1^T{M}_s^{-1}{\stackrel{\&CenterDot;}{\tilde{K}}}_1\&rsqb;+2tr\&lsqb;{\tilde{K}}_2{M}_s^{-1}{\stackrel{\&CenterDot;}{\tilde{K}}}_2^T\&rsqb;+2tr\&lsqb;{\tilde{K}}_3^T{M}_s^{-1}{\stackrel{\&CenterDot;}{\tilde{K}}}_3\&rsqb;\\ =-e^T{Q}_{3}e+2e^T{P}_2{B}_m\&lsqb;K_2^{*-1}{\tilde{K}}_{1}x+K_2^{*-1}{\tilde{K}}_{2}r+K_2^{*-1}{\tilde{K}}_3\&rsqb;+2tr\&lsqb;{\tilde{K}}_1^T{M}_s^{-1}{\stackrel{\&CenterDot;}{\tilde{K}}}_1\&rsqb;\\ +2tr\&lsqb;{\tilde{K}}_2{M}_s^{-1}{\stackrel{\&CenterDot;}{\tilde{K}}}_2^T\&rsqb;+2tr\&lsqb;{\tilde{K}}_3^T{M}_s^{-1}{\stackrel{\&CenterDot;}{\tilde{K}}}_3\&rsqb;\\ =-e^T{Q}_{3}e+2tr\&lsqb;{\tilde{K}}_1^T{M}_s^{-1}{\mathrm{\&Gamma;}}^T{B}_m^T{P}_2{\mathrm{ex}}^T\&rsqb;+2tr\&lsqb;{\tilde{K}}_2{M}_s^{-1}{\mathrm{\&Gamma;}}^T{B}_m^T{P}_2{\mathrm{er}}^T\&rsqb;\\ +2tr\&lsqb;{\tilde{K}}_3^T{M}_s^{-1}{\mathrm{\&Gamma;}}^T{B}_m^T{P}_{2}e\&rsqb;+2tr\&lsqb;{\tilde{K}}_1^T{M}_s^{-1}{\stackrel{\&CenterDot;}{\tilde{K}}}_1\&rsqb;+2tr\&lsqb;{\tilde{K}}_2{M}_s^{-1}{\stackrel{\&CenterDot;}{\tilde{K}}}_2^T\&rsqb;+2tr\&lsqb;{\tilde{K}}_3^T{M}_s^{-1}{\stackrel{\&CenterDot;}{\tilde{K}}}_3\&rsqb;\\ -e^T{Q}_{3}e\&le;0\end{array}---\left(30\right)$

Obtained by Barbalat theorem illustrative system, under the effect of control law (20), can keep stable.

Simulating, verifying is carried out to the present invention below.

Under fault-free conditions, interference d=[1.211.21] is injected ^twith state time delay τ=0.5s.The Guaranteed Cost Controller that checking improves is to trouble-free time lag four-rotor helicopter control effects.The pitching of four rotors, driftage and roll angle response curve are shown in Fig. 3-5.

Having under fault condition, f (t)=[0.20.50.51] ^t, σ (t)=[0000] ^t, 10s<t<20s, f (t)=[0.20.50.51] ^t, σ (t)=[0001] ^t, t>20s.Simulation is when 10s, and 20% loss of voltage occurs forward direction motor, and 50% loss of voltage occurs backward motor, and 50% loss of voltage occurs left motor; When 20s, there is stuck fault in right motor.The Guaranteed Cost Controller that checking improves and model reference adaptive controller are to the time lag four-rotor helicopter control effects that actuator failures occurs.The pitching of four rotors, driftage and roll angle response curve are shown in Fig. 6-8.

From above step and accompanying drawing, the present invention effectively can realize the faults-tolerant control that actuator failures time lag four-rotor helicopter occurs, and ensures the tracking performance that system is good, to monitoring in real time and fault pre-alarming significant.

The above is only the preferred embodiment of the present invention; be noted that for those skilled in the art; under the premise without departing from the principles of the invention, can also make some improvements and modifications, these improvements and modifications also should be considered as protection scope of the present invention.

Claims (9)

1. for a four-rotor helicopter faults-tolerant control device for states with time-delay, it is characterized in that: comprise direct fault location module, Helicopter System platform, data acquisition module, fault diagnosis module and power amplifier, wherein,

Direct fault location module is connected with Helicopter System platform, and the failure message of simulation is injected Helicopter System platform;

Data acquisition module, by the built-in sensors of Helicopter System platform, gathers status information and the control information of helicopter;

Fault diagnosis module is connected with data acquisition module, and the status information that reception data acquisition module spreads out of and control information, obtain faults-tolerant control rule, and resend to data acquisition module by faults-tolerant control rule;

Power amplifier is connected with Helicopter System platform with data acquisition module, and after data acquisition module process faults-tolerant control rule, through power amplifier, by steering order, the motor be transferred in Helicopter System platform performs fault-tolerant adjustment, until error is zero.

2. the four-rotor helicopter faults-tolerant control device for states with time-delay according to claims 1, is characterized in that: described data acquisition module comprises data collector, signal compiling and modular converter, wherein,

Data collector is for gathering voltage input information and the attitude angle angle of Helicopter System platform;

Signal compiling and conversion equipment operate for the treatment of the encoding and decoding between Helicopter System platform and fault diagnosis module and analog to digital conversion;

Signal compiling and conversion equipment and data collector are linked in sequence.

3. the four-rotor helicopter faults-tolerant control device for states with time-delay according to claims 1, it is characterized in that: described fault diagnosis module comprises status information module, control information module, the Guaranteed Cost Controller of improvement, model reference adaptive controller, wherein

Status information module and control information module obtain status information and the control information of data acquisition module output;

The Guaranteed Cost Controller improved and model reference adaptive controller utilize the status information and control information determination faults-tolerant control rule that gather, and are sent to data acquisition module.

4. the four-rotor helicopter faults-tolerant control device for states with time-delay according to claims 1, is characterized in that: the Guaranteed Cost Controller of described improvement is made up of model reference linear quadratic regulator and Guaranteed Cost Controller two parts; Model reference linear quadratic regulator is used for track reference system, disturbance suppression and solve the problem that Guaranteed Cost Controller can not be used for the coefficient of regime matrix not linear model of full rank; Guaranteed Cost Controller is for solving state delay problem.

5. the four-rotor helicopter faults-tolerant control device for states with time-delay according to claims 1, is characterized in that: described Helicopter System platform is 3-DOFhover platform.

6., based on the four-rotor helicopter faults-tolerant control installation method for states with time-delay of the arbitrary described device of claim 1-5, it is characterized in that: comprise the following steps:

Step 1, set up four-rotor helicopter body axis system, determine the definition of pitching, driftage and wobble shaft, and set up the linear kinetic model of dynamics attitude angle under normal circumstances;

Step 2, state-space expression when determining four-rotor helicopter dynamics attitude angle system failure; By in fault injection system, the state-space expression under certainty annuity fault;

Step 3, on the basis of step 2, from data acquisition module, obtain the status information of system, status information comprises pitching, driftage, roll angle size, subtract each other with reference to the quantity of state reference value in model and above-mentioned status information, obtain control information, construct four-rotor helicopter flight attitude fault-tolerant controller thus, actuator failures on Real-Time Monitoring pitching, driftage and rolling direction and other interference, and export faults-tolerant control rule to data acquisition module, through power amplifier, control signal is transferred to motor and performs.

7. the four-rotor helicopter faults-tolerant control installation method for states with time-delay according to claims 6, is characterized in that: four-rotor helicopter pitching in step 1, driftage and roll angle equation are:

$\left\{\begin{array}{c}{J}_p\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}={\mathrm{lK}}_f(U_f-U_b)\\ J_y\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&psi;}}=K_{tc}(U_f+U_b)+K_{tn}(U_l+U_r)\\ J_r\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&phi;}}={\mathrm{lK}}_f(U_l-U_r)\end{array}\right.$

Implication in formula representated by parameter is: θ, ψ, φ are respectively the angle of pitch, crab angle and roll angle, K _ffor rotor lift coefficient, K _tn, K _tcbe respectively rotor clockwise, be rotated counterclockwise moment coefficient, J _pthe moment of inertia of body around pitch axis, J _ythe moment of inertia of body around yaw axis, J _rthe moment of inertia of body around wobble shaft, U _f, U _b, U _l, U _rbe respectively four-rotor helicopter forward direction motor, backward motor, left-hand motor and dextrad motor driven voltage value, l is the length of true origin to motor center point;

Above-mentioned equation is determined under following hypothesis relation:

(1) structure of aircraft is all rigidity and Striking symmetry;

(2) just heart place in the structure, aircraft center;

(3) be linear relationship between the voltage of direct current generator and moment;

(4) change of attitude of flight vehicle angle is less than 10 °.

8. the four-rotor helicopter faults-tolerant control installation method for states with time-delay according to claims 6, it is characterized in that: the state-space expression of step 2 certainty annuity when fault is actuator damage fault, described state-space expression is:

$\left\{\begin{array}{c}\stackrel{\&CenterDot;}{x}\left(t\right)=Ax\left(t\right)+A_{\mathrm{\&tau;}}x(t-\mathrm{\&tau;})+B\&lsqb;(f\left(t\right)-\mathrm{\&sigma;}\left(t\right))v\left(t\right)+\mathrm{\&sigma;}\left(t\right)\stackrel{\&OverBar;}{v}\left(t\right)\&rsqb;+Bd\left(t\right)\\ y\left(t\right)=Cx\left(t\right)\end{array}\right.$

In formula, for state vector, v (t) ∈ R ^{4 × 1}for control inputs vector, for output vector, τ is that system state postpones, d (t) ∈ R ⁴for the external disturbance of unknown bounded, for stuck fault input vector, f (t) ∈ R ^{4 × 4}for partial failure failure coefficient matrix, σ (t) ∈ R ^{4 × 4}for stuck failure coefficient matrix, it meets respectively:

$f\left(t\right)=\left\{\begin{array}{cc}diag(1,1,...,1),& t<T_1\\ diag(f_1,f_2,...,f_p),& t\&GreaterEqual;T_1\end{array}\right.$ $\mathrm{\&sigma;}\left(t\right)=\left\{\begin{array}{cc}0,& t<T_2\\ diag({\mathrm{\&sigma;}}_1,{\mathrm{\&sigma;}}_2,...,{\mathrm{\&sigma;}}_p),& t\&GreaterEqual;T_2\end{array}\right.$

A, B, C are system matrix, A _tfor state time delay matrix, wherein

$A=\left[\begin{array}{cccccc}0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\end{array}\right]$ $B=\left[\begin{array}{cccc}0& 0& 0& 0\\ 0& 0& 0& 0\\ 0& 0& 0& 0\\ 0.4235& -0.4235& 0& 0\\ -0.0326& -0.0326& 0.0326& 0.0326\\ 0& 0& 0.4235& -0.4235\end{array}\right]$

$C=\left[\begin{array}{cccccc}1& 0& 0& 0& 0& 0\\ 0& 1& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0\end{array}\right]$ A _τ＝A。

9. the four-rotor helicopter faults-tolerant control installation method for states with time-delay according to claims 6, is characterized in that: the concrete execution step of the four-rotor helicopter flight attitude fault-tolerant controller of step 3 is:

The reference model that step 31, selecting system are followed the tracks of, is defined as:

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_m\left(t\right)=A_m{x}_m\left(t\right)+B_{m}r\left(t\right)\\ y_m\left(t\right)=C_m{x}_m\left(t\right)\end{array}\right.$

X in formula _mt () is the quantity of state that system is expected to follow the tracks of, r (t) is the input that system is expected, y _mthe output that system is expected, A _m, B _m, C _mit is the suitable matrix of dimension;

The design of the Guaranteed Cost Controller of step 32, improvement:

The Guaranteed Cost Controller improved is for maintaining the tracking performance of states with time-delay four-rotor helicopter under fault-free conditions, and the control inputs of the Guaranteed Cost Controller of improvement represents and is:

$u_{igcc}\left(t\right)=K_{lqr}\left(x\right(t)-x_m(t\left)\right)+K_{gcc}\left(x\right(t)+{\&Integral;}_{t-\mathrm{\&tau;}}^{t}x\left(s\right)ds)$

The design of step 33, model reference adaptive system:

Model reference adaptive is used for reconfigurable control system, compensates the actuator failures of four-rotor helicopter, supposes to there is constant value matrix with meet following condition:

$A+B\left(f\right(t)-\mathrm{\&sigma;}(t\left)\right)K_1^{*}=A_m$

$B\left(f\right(t)-\mathrm{\&sigma;}(t\left)\right)K_2^{*}=B_m$

$B\left(f\right(t)-\mathrm{\&sigma;}(t\left)\right)K_3^{*}+B\mathrm{\&sigma;}\left(t\right)\stackrel{\&OverBar;}{v}\left(t\right)=0$

Then the design of model reference self-adapting control rule is as follows:

u _ac(t)＝K ₁(t)x(t)+K ₂(t)r(t)+K ₃(t)

K in formula ₁(t) ∈ R ^{4 × 6}, K ₂(t) ∈ R ^{4 × 4}and K ₃(t) ∈ R ^{4 × 1}be respectively and estimated value, and ${\tilde{K}}_1\left(t\right)=K_1\left(t\right)-K_1^{*},{\tilde{K}}_2\left(t\right)=K_2\left(t\right)-K_2^{*},{\tilde{K}}_3\left(t\right)=K_3\left(t\right)-K_3^{*};$

Adaptive control laws is:

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{\tilde{K}}}_1\left(t\right)={\stackrel{\&CenterDot;}{K}}_1\left(t\right)=-{\mathrm{\&Gamma;}}^T{B_m}^T{P}_{2}e\left(t\right)x^T\left(t\right)\\ {\stackrel{\&CenterDot;}{\tilde{K}}}_2\left(t\right)={\stackrel{\&CenterDot;}{K}}_2\left(t\right)=-{\mathrm{\&Gamma;}}^T{B}_m^T{P}_{2}e\left(t\right)r^T\left(t\right)\\ {\stackrel{\&CenterDot;}{\tilde{K}}}_3\left(t\right)={\stackrel{\&CenterDot;}{K}}_3\left(t\right)=-{\mathrm{\&Gamma;}}^T{B}_m^T{P}_{2}e\left(t\right)\end{array}\right.$

P in formula ₂∈ R ^{6 × 6}for positive definite symmetric matrices, for any constant value symmetric positive definite matrix Q ₃∈ R ^{6 × 6}meet

$P_2{A}_m+A_m^T{P}_2=-Q_3;$

After reconstruct, input control rule is:

$v\left(t\right)=K_1\left(t\right)x\left(t\right)+K_2\left(t\right)r\left(t\right)+K_3\left(t\right)+K_{lqr}\left(x\right(t)-x_m(t\left)\right)+K_{gcc}\left(x\right(t)+{\&Integral;}_{t-\mathrm{\&tau;}}^{t}x\left(s\right)ds).$