CN106647584A - Fault tolerant control method of four-rotor-wing aircraft based on optimal sliding mode - Google Patents

Abstract

The invention discloses a fault tolerant control method of a four-rotor-wing aircraft based on an optimal sliding mode. The optimal fault tolerant control method is provided by considering time lag caused by wireless network transmission, aiming at actuator faults of the four-rotor-wing aircraft and combining optimal control and sliding mode control. According to the fault tolerant control method, a sliding mode surface with time lag compensation is designed, and sufficient conditions of asymptotical stability of an ideal sliding mode is given by utilizing a linear matrix inequality principle; an optimal control concept is introduced, and quadratic form optimal performance indexes are adopted; and the sliding model control is combined to finally form a complete fault tolerant controller. According to the method disclosed by the invention, the sliding mode surface with the time lag compensation is configured and influences caused by the time lag can be eliminated; the quadratic form optimal performance indexes are designed so that a control rule of a nominal system can be optimized; and the control precision of the four-rotor-wing aircraft is effectively improved, and design evidences of the fault tolerant controller are provided for a complicated four-rotor-wing aircraft with the actuator faults. The fault tolerant control method is used for carrying out passive fault tolerant control on the four-rotor-wing aircraft with the time invariant time lag.

Description

A kind of fault tolerant control method of the quadrotor based on Optimal Sliding Mode

Technical field

The present invention relates to a kind of fault tolerant control method of the quadrotor based on Optimal Sliding Mode, belongs to aircraft failure Diagnosis and faults-tolerant control field.

Background technology

Helicopter type has a lot, mainly includes：Single-rotor helicopter, twin-rotor helicopter (lap siding, cross-arranging type) and Four-rotor helicopter.Wherein four-rotor helicopter, as a new branch of Helicopter Development, its structure and flight theory with Conventional helicopters are different, with before and after and the two sets screws in left and right, by change propeller lift size, Jin Ergai changed Become position and attitude.The actions such as it can be easily carried out taking off vertically and land, hover, horizontal and vertical flight.With it is normal Rule layout helicopter is compared, and structure is simpler, and the anti-twisted torque of four rotor generations can cancel each other out, and not special is anti-twisted Pitch.At the same time, four-rotor helicopter has the advantages that small volume, lightweight, low cost, uses flexible, good concealment, because This is widely used in dual-use field.Four-rotor helicopter is the controlled device of a complexity, with multiple-input and multiple-output And the various challenges such as non-linear, close coupling, time lag, and wind can be inevitably run in flight course Disturb, the uncertain factor such as engine luggine, artificial real time management is lacked in addition, helicopter once breaks down, it will cause calamity Difficulty consequence.Therefore fault-tolerant controller needs still to possess in the case where system has time lag and uncertainty stronger fault-tolerant Ability.

At present active tolerant control and passive fault tolerant control are broadly divided into the fault tolerant control method of quadrotor, its Middle active tolerant control is by fault accommodation or signal reconstruction, it is ensured that the stability of system after failure generation, the method design spirit Living, fault-tolerant ability is strong, but controller architecture is complex, and needs to obtain clear and definite fault message, and system design is relatively costly. Relative to active tolerant control, passive fault tolerant control is under conditions of controller architecture and parameter is not changed, using controller Itself robustness making closed-loop system that there is insensitivity to some failures, to realize that system still can be in original after breaking down Have under performance indications and run, this design of control method is relatively simple and cost is relatively low, it is not necessary to know clear and definite fault message, It is more particularly suitable using passive fault tolerant control especially in the nonlinear system containing various uncertain factors

It is because the sliding mode of sliding formwork control has completely adaptivity to systematic parameter perturbation and additional interference therefore non- Often it is adapted to process the passive fault tolerant control problem of four-rotor helicopter flight control system.Its control is discontinuous, control process In, the structure of closed-loop system ceaselessly changes, and forces system mode to be moved along pre-designed sliding-mode surface, gradually " cunning " to State balance point, i.e. Asymptotic Stability.Its topmost advantage is once system state amount arrival sliding-mode surface, system is just by parameter Change and the impact of external disturbance.Sliding formwork control is widely used in flight control system, and the faults-tolerant control for flight control system is provided newly Thinking.

However, still there is many problems to need to solve in sliding formwork faults-tolerant control.For example, the robust of sliding mode how is improved Property, the convergence time how is reduced, and how to ensure that preferable sliding mode is optimum.In order to ensure the robustness of sliding mode And the effect of faults-tolerant control is improved, the thought of optimum control can be introduced.With reference to sliding formwork control, Optimal Sliding Mode Control rule can Effectively simplify control device, cost-effective.

Existing method can not consider comprehensively real system time lag that may be present, uncertainty, failure etc. it is various because Element, to complicated flight control system good control effect has been difficult, therefore the present invention has good practicality.

The content of the invention

Goal of the invention：For above-mentioned prior art, a kind of fault-tolerant control of the quadrotor based on Optimal Sliding Mode is proposed Method processed, can effectively eliminate the negative effect that time lag is brought so that preferable sliding mode best performance, and faults-tolerant control rule can Overcome impact of the failure to system.

Technical scheme：A kind of fault tolerant control method of the quadrotor based on Optimal Sliding Mode, it is characterised in that：Consider There are time lag and actuator failures in quadrotor, with reference to optimum control and sliding formwork control, propose a kind of optimum faults-tolerant control Method so that aircraft can continue to safe flight after it there are actuator failures, and ensure good flight quality.According to institute The model parameter of the aircraft of acquisition, designs a kind of Integral Sliding Mode face with time lag compensation, eliminates the impact of time lag, for mark Claim system design quadratic optimal performance index, obtain optimum ideal sliding mode, and then design corresponding sliding formwork control ratio, finally Constitute optimum fault-tolerant controller.Comprise the following specific steps that：

Step 1) set up the Mathematical Modeling of quadrotor：

Wherein A ∈ R^n×n, A_d∈R^n×n, B ∈ R^n×m, C ∈ R^p×n, x ∈ RⁿIt is the state variable of system, Δ A (t) and Δ A_d T () is that modeling is uncertain, x (t- τ) represents the state variable of time lag, u (t) ∈ R^mIt is the control input of system, f (x, t)∈RⁿRepresent actuator failures.

Step 2) there are four rotor flight control systems of time lag and actuator failures for more than, carry out the optimum of nominal system Sliding mode design：

The nominal system of system (1) is：

In nominal system (2), u=u is made₀, then define quadratic optimal performance index as follows：

Here Q ∈ R^n×nIt is positive semidefinite state weight matrix, and R ∈ R^n×mIt is the weight matrix of a positive definite.

According to n times alternative manner, the approximate solution of optimal control law is：

Wherein, matrix P is the steady-state solution of following Riccati equation：

PA+A^TP-PBR^-1B^TP+Q=0 (4)

AndIt is the front n items solution sum of one group of differential equation.Control law (3) can ensure that the robust of whole nominal system Property.

Step 3) in step 1), step 2) on the basis of, construct the integral form sliding-mode surface with time lag compensation：

Wherein matrix G ∈ R^m×nMeeting GB, nonsingular (due to matrix B sequency spectrum, therefore the selection of matrix G here is not only One).K=R^-1B^TP∈R^m×nIt is a constant matrices to be designed, it can be obtained by solving by LMI (5) Go out.

May certify that, if there is matrix Y ∈ R^m×n, positive definite matrix X ∈ R^n×nWith normal number ε₁, ε₂, ε₃So that linear moment Battle array inequality (5) is set up：

Then standard sliding mode is asymptotically stability.

Wherein

Step 4) the discontinuous sliding formwork control ratio of construction so that with faulty and probabilistic time lag system state trajectory with Nominal system track is the same.

According to the method for designing of sliding formwork control, fault controller is into following form：

U=u_con+u_dis, (6)

Wherein u_conIt is the continuous part of sliding formwork control ratio, and discontinuous part u_disIt is then for maintaining system in sliding-mode surface On preferable sliding mode.

Step 4.1) linear segment of fault-tolerant controller can determine with equivalent optimum control method, due to step 3) in The particularity of sliding-mode surface structure, the linear segment design of controller is as follows：

Step 4.2) the discontinuous control section of design：

The discontinuous portion of control law sets up the upper bound that meter needs know uncertain and failure separately, and probabilistic upper bound is Know, but fault message is but unknown, and this also complies with actual conditions.We can define two adaptive quantity to estimate online Meter unknown parameter：

Then the discontinuous portion of faults-tolerant control rule is divided into：

Wherein η is a little normal number.

Convolution (7) and (9), can obtain complete Optimal Sliding Mode faults-tolerant control rule as follows：

Step 5) according to the state of flight of quadrotor, suitable parameter is selected, complete the faults-tolerant control to it.Have Beneficial effect：A kind of fault tolerant control method of quadrotor based on Optimal Sliding Mode proposed by the present invention, construct with when The sliding-mode surface of stagnant compensation, according to optimum control thought quadratic optimal performance index is designed, and obtains optimum ideal sliding mode, knot Sliding Mode Control Design Method is closed, complete Optimal Sliding Mode fault-tolerant controller is finally constituted.

Have the advantage that：

(1) by integral form sliding-mode surface of the design with time lag compensation, the impact that time lag is brought is effectively eliminated；

(2) dividing value in the time lag of guarantee system asymptotically stability is given using LMI, four rotations are fully taken into account Rotor aircraft time delay that may be present during practical flight so that the design of controller has more preferable practicality；

(3) quadratic optimal performance index is designed, it is ensured that the preferable sliding mode of system is best performance；

(4) method for introducing adaptive boundary estimation estimates the size of quadrotor actuator failures, fault-tolerant control Rule processed is constantly changing parameter so that system conservative is less, and control effect is more preferably.

Method therefor of the present invention as a kind of fault tolerant control method of quadrotor, with certain practical application valency Value, it is easy to accomplish, fault-tolerant ability is strong, can effectively improve the flight safety of quadrotor.The method is workable, Using convenient, reliable.

Description of the drawings

Fig. 1 is the flow chart of the inventive method；

Fig. 2 is the quadrotor simulating experimental system of Quanser；

Fig. 3 is quadrotor schematic diagram；

Fig. 4 is four-rotor aircraft control system theory diagram；

Fig. 5 is X-axis dynamic respond curve comparison figure；

Fig. 6 is X-axis velocity-response curve comparison diagram；

Fig. 7 is carried out device dynamic response curve comparison diagram；

Fig. 8 is preferable sliding mode response curve comparison diagram；

Fig. 9 is simulink analogous diagrams.

Specific embodiment

The present invention is done below in conjunction with the accompanying drawings further is explained.

As shown in Figure 1, it is considered to which quadrotor has time lag and actuator failures, with reference to optimum control and sliding formwork control System, proposes a kind of optimum fault tolerant control method so that aircraft can continue to safe flight after it there are actuator failures, and protect The good flight quality of card.According to the model parameter of acquired aircraft, a kind of Integral Sliding Mode with time lag compensation is designed Face, eliminates the impact of time lag, and for nominal system quadratic optimal performance index is designed, and obtains optimum ideal sliding mode, enters And corresponding sliding formwork control ratio is designed, finally constitute optimum fault-tolerant controller.Comprise the following specific steps that：

Step 1) set up the Mathematical Modeling of quadrotor：

Wherein A ∈ R^n×n, A_d∈R^n×n, B ∈ R^n×m, C ∈ R^p×n, x ∈ RⁿIt is the state variable of system, Δ A (t) and Δ A_d T () is that modeling is uncertain, x (t- τ) represents the state variable of time lag, u (t) ∈ R^mIt is the control input of system, f (x, t)∈RⁿRepresent actuator failures.

Step 2) there are four rotor flight control systems of time lag and actuator failures for more than, carry out the optimum of nominal system Sliding mode design：

The nominal system of system (1) is：

In nominal system (2), u=u is made₀, then define quadratic optimal performance index as follows：

Here Q ∈ R^n×nIt is positive semidefinite state weight matrix, and R ∈ R^m×mIt is the weight matrix of a positive definite.

According to n times alternative manner, the approximate solution of optimal control law is：

Wherein, matrix P is the steady-state solution of following Riccati equation：

PA+A^TP-PBR^-1B^TP+Q=0 (4)

AndIt is the front n items solution sum of one group of differential equation.Control law (3) can ensure that the robust of whole nominal system Property.

Step 3) in step 1), step 2) on the basis of, construct the integral form sliding-mode surface with time lag compensation：

Wherein matrix G ∈ R^m×nMeeting GB, nonsingular (due to matrix B sequency spectrum, therefore the selection of matrix G here is not only One).

K=R^-1B^TP∈R^m×nIt is a constant matrices to be designed, it can be by solving by LMI (5) Draw.

May certify that, if there is matrix Y ∈ R^m×n, positive definite matrix X ∈ R^n×nWith normal number ε₁, ε₂, ε₃So that linear moment Battle array inequality (5) is set up：

Then standard sliding mode is asymptotically stability.

Wherein

Step 4) the discontinuous sliding formwork control ratio of construction so that with faulty and probabilistic time lag system state trajectory with Nominal system track is the same.

According to the method for designing of sliding formwork control, fault controller is into following form：

U=u_con+u_dis, (6)

Wherein u_conIt is the continuous part of sliding formwork control ratio, and discontinuous part u_disIt is then for maintaining system in sliding-mode surface On preferable sliding mode.

Step 4.1) linear segment of fault-tolerant controller can determine with equivalent optimum control method, due to step 3) in The particularity of sliding-mode surface structure, the linear segment design of controller is as follows：

Step 4.2) the discontinuous control section of design：

The discontinuous portion of control law sets up the upper bound that meter needs know uncertain and failure separately, and probabilistic upper bound is Know, but fault message is but unknown, and this also complies with actual conditions.We can define two adaptive quantity to estimate online Meter unknown parameter：

Then the discontinuous portion of faults-tolerant control rule is divided into：

Wherein η is a little normal number.

Convolution (7) and (9), can obtain complete Optimal Sliding Mode faults-tolerant control rule as follows：

Step 5) according to the state of flight of quadrotor, suitable parameter is selected, complete the faults-tolerant control to it.

The above is only the preferred embodiment of the present invention, it is noted that for the ordinary skill people of the art For member, under the premise without departing from the principles of the invention, some improvements and modifications can also be made, these improvements and modifications also should It is considered as protection scope of the present invention,

Emulate the validity of explanation embodiment with real case below.

Using the Qball-X4 quadrotor semi-physical simulation platforms of Canadian quanser companies production as concrete Algorithm experimental simulation object.Fig. 2 is the quadrotor simulating experimental system of Quanser, and Fig. 3 is quadrotor appearance State motion schematic diagram.The simulating experimental system is made up of ground control station, camera locating systems and aircraft, and master controller leads to Cross WLAN to be communicated with each unmanned instrument, mainly system is positioned and mission planning.Once whole control The control algorithm design of system is completed, and control station can be made to function only as positioning action, so as to carry out unmanned instrument from master control Coordination control research between system and multiple instruments.System realizes that space three-dimensional is positioned by six infrared cameras, so as to obtain Take desired parameters.

The Mathematical Modeling of quadrotor is as follows：

Wherein, each coefficient matrix is as follows：

In emulation experiment, by hard ware measure it is found that being generally 80-120 millis by the time lag that causes is wirelessly transferred Second, in order to prove that this chapter proposes the validity of method, it is assumed that time lag is τ=1s.

In simulation process, the model of controlled system is built with matlab simulink, can easily change control The type of rule and failure.

There is the catastrophic failure of following form in t=11s in hypothesis system：

The quantity of state vector for taking initial time system is：

x₀=[x₁ x₂ x₃]^T=[1 1 1.1]^T

According to the inventive method, the quadrotor to there are actuator failures carries out faults-tolerant control.According to step 1)- Step 5), wherein parameter value undetermined is as follows：Sliding-mode surface coefficient matrix G=[0 0 1], upper bound a=0.8602, a_d=0.5, solution obtains feedback of status coefficient matrix K=[1.6263 0.5438 4.9179].

Fig. 5-Fig. 8 is faults-tolerant control result.Fig. 5-Fig. 7 is respectively the response of X-direction displacement, speed and Actuator dynamic Curve, and contrasted with the method without time lag treatment, Fig. 8 is the contrast song of optimum faults-tolerant control and traditional sliding formwork control Line.

From Fig. 5-Fig. 7, after system occurs actuator failures, the displacement of aircraft X-axis and speed there occurs obvious ripple Dynamic, but under the faults-tolerant control of the present invention, can tend towards stability in the short period of time, and fast response time, overshoot is little, also It is say that after system jam aircraft remains able to maintain original state of flight, it is to avoid the generation of accident, and Good flight quality can be kept.From the preferable sliding mode curve comparison of Fig. 8, compared to the fault-tolerant control of traditional sliding formwork System, the inventive method is obtained in that the preferable sliding mode of optimum.Therefore, the faults-tolerant control rule can well ensure aircraft Control accuracy and security.

Claims (1)

1. a kind of fault tolerant control method of the quadrotor based on Optimal Sliding Mode, it is characterised in that：Consider four rotor flyings There are time lag and actuator failures in device, with reference to optimum control and sliding formwork control, propose a kind of optimum fault tolerant control method so that fly Row device can continue to safe flight after it there are actuator failures, and ensure good flight quality.According to acquired flight The model parameter of device, designs a kind of Integral Sliding Mode face with time lag compensation, eliminates the impact of time lag, for nominal system design Quadratic optimal performance index, obtains optimum ideal sliding mode, and then designs corresponding sliding formwork control ratio, finally constitutes most beutiful face Wrong controller.Comprise the following specific steps that：

Step 1) set up the Mathematical Modeling of quadrotor：

$\left\{\begin{array}{c}\stackrel{\·}{x}\left(t\right)=(A+\mathrm{\Δ}A(t\left)\right)x\left(t\right)+(A_d+{\mathrm{\ΔA}}_d(t\left)\right)x(t-\mathrm{\τ})+B\left(u\right(t)+f(x,t\left)\right)\\ y\left(t\right)=Cx\left(t\right)\end{array}\right.---\left(1\right)$

Wherein A ∈ R^n×n, A_d∈R^n×n, B ∈ R^n×m, C ∈ R^p×n, x ∈ RⁿIt is the state variable of system, Δ A (t) and Δ A_dT () is Modeling is uncertain, and x (t- τ) represents the state variable of time lag, u (t) ∈ R^mIt is the control input of system, f (x, t) ∈ Rⁿ Represent actuator failures.

Step 2) there are four rotor flight control systems of time lag and actuator failures for more than, carry out the Optimal Sliding Mode of nominal system Design：

The nominal system of system (1) is：

In nominal system (2), u=u is made₀, then define quadratic optimal performance index as follows：

$J=\frac{1}{2}{\∫}_0^{\mathrm{\∞}}\left(x^T\left(t\right)Qx\left(t\right)+{u_0}^T{\mathrm{Ru}}_0\left(t\right)\right)dt$

Here Q ∈ R^n×nIt is positive semidefinite state weight matrix, and R ∈ R^m×mIt is the weight matrix of a positive definite.

According to n times alternative manner, the approximate solution of optimal control law is：

$u_{oN}\left(t\right)=-R^{-1}{B}^T\left(Px\left(t\right)+{\tilde{h}}_N\left(t\right)\right)---\left(3\right)$

Wherein, matrix P is the steady-state solution of following Riccati equation：

PA+A^TP-PBR^-1B^TP+Q=0 (4)

AndIt is the front n items solution sum of one group of differential equation.Control law (3) can ensure that the robustness of whole nominal system.

Step 3) in step 1), step 2) on the basis of, construct the integral form sliding-mode surface with time lag compensation：

$\mathrm{\σ}(x,t)=G\left(x\right(t)-x(0\left)\right)-G{\∫}_0^t\[\left(A-BK\right)x\left(s\right)+A_{d}x(s-\mathrm{\τ})-{\mathrm{BR}}^{-1}{B}^T{\tilde{h}}_N\left(s\right)\]ds$

Wherein matrix G ∈ R^m×nMeet GB nonsingular (due to matrix B sequency spectrum, therefore the selection of matrix G here is not unique).K =R^-1B^TP∈R^m×nIt is a constant matrices to be designed, it can be drawn by solving by LMI (5).

May certify that, if there is matrix Y ∈ R^m×n, positive definite matrix X ∈ R^n×nWith normal number ε₁, ε₂, ε₃So that linear matrix inequality technique Formula (5) is set up：

$\left[\begin{array}{ccc}{W}_0& A_d^T& PD\\ A_d& -{\mathrm{\&epsiv;}}_{2}I& 0\\ D^{T}P& 0& -\left({\mathrm{\&epsiv;}}_1+{\mathrm{\&epsiv;}}_3\right)I\end{array}\right]<0---\left(5\right)$

Then standard sliding mode is asymptotically stability.

Wherein

Step 4) the discontinuous sliding formwork control ratio of construction so that with faulty and probabilistic time lag system state trajectory and nominally System trajectory is the same.

According to the method for designing of sliding formwork control, fault controller is into following form：

U=u_con+u_dis, (6)

Wherein u_conIt is the continuous part of sliding formwork control ratio, and discontinuous part u_disIt is then for maintaining system on sliding-mode surface Preferable sliding mode.

Step 4.1) linear segment of fault-tolerant controller can determine with equivalent optimum control method, due to step 3) in sliding formwork The particularity of face structure, the linear segment design of controller is as follows：

$u_{con}\left(t\right)=-Kx\left(t\right)-R^{-1}{B}^T{\tilde{h}}_N---\left(7\right)$

Step 4.2) the discontinuous control section of design：

The discontinuous portion of control law sets up the upper bound that meter needs know uncertain and failure separately, and probabilistic upper bound is known , but fault message is but unknown, this also complies with actual conditions.We can define two adaptive quantity and carry out On-line Estimation Unknown parameter：

${\stackrel{\&CenterDot;}{\widehat{\mathrm{\&gamma;}}}}_1=\left|\right|\mathrm{\&sigma;}\left|\right|\left|\right|G\left|\right|\left|\right|B\left|\right|,{\stackrel{\&CenterDot;}{\widehat{\mathrm{\&gamma;}}}}_2=\left|\right|\mathrm{\&sigma;}\left|\right|\left|\right|G\left|\right|\left|\right|B\left|\right|\left|\right|x\left(t\right)\left|\right|---\left(8\right)$

Then the discontinuous portion of faults-tolerant control rule is divided into：

$u_{dis}=-{\left(GB\right)}^{-1}\left|\right|G\left|\right|\&lsqb;\mathrm{\&eta;}+a\left|\right|x\left(t\right)\left|\right|+a_d\left|\right|x(t-\mathrm{\&tau;})\left|\right|+\left|\right|B\left|\right|({\widehat{\mathrm{\&gamma;}}}_1+{\widehat{\mathrm{\&gamma;}}}_2|\left|x\right(t\left)\right|\left|\right)\&rsqb;\frac{\mathrm{\&sigma;}}{\left|\right|\mathrm{\&sigma;}\left|\right|}---\left(9\right)$

Wherein η is a little normal number.

Convolution (7) and (9), can obtain complete Optimal Sliding Mode faults-tolerant control rule as follows：

$u=-Kx\left(t\right)-R^{-1}{B}^T{\tilde{h}}_N-{\left(GB\right)}^{-1}\left|\right|G\left|\right|\{\mathrm{\&eta;}+a|\left|x\left(t\right)\right||+a_d|\left|x(t-\mathrm{\&tau;})\right||+|\left|B\right|\left|({\widehat{\mathrm{\&gamma;}}}_1+{\widehat{\mathrm{\&gamma;}}}_2|\left|x\right(t\left)\right|\left|\right)\right\}\frac{\mathrm{\&sigma;}}{\left|\right|\mathrm{\&sigma;}\left|\right|}---\left(10\right)$

Step 5) according to the state of flight of quadrotor, suitable parameter is selected, complete the faults-tolerant control to it.