CN107121977B - Mechanical arm actuator failures fault-tolerant control system and its method based on double-layer structure - Google Patents
Mechanical arm actuator failures fault-tolerant control system and its method based on double-layer structure Download PDFInfo
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B23/00—Testing or monitoring of control systems or parts thereof
- G05B23/02—Electric testing or monitoring
- G05B23/0205—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults
- G05B23/0218—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults characterised by the fault detection method dealing with either existing or incipient faults
- G05B23/0243—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults characterised by the fault detection method dealing with either existing or incipient faults model based detection method, e.g. first-principles knowledge model
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B2219/00—Program-control systems
- G05B2219/20—Pc systems
- G05B2219/24—Pc safety
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Abstract
The present invention proposes a kind of mechanical arm actuator failures fault-tolerant control system and its method based on double-layer structure, belongs to automatic control technology field with layered structure control optimization thought.To reduce calculation amount, real-time is improved, discrete system model under actuator failures is established using taylor series expansion；Designing FDD unit active process failure is topic, and the fault message estimated introduces fault model, realizes Active Fault Tolerant；Consider uncertain factor existing for real system, is compensated using feedback compensation mechanism；Mechanical arm fault-tolerant controller is made of trajectory planning layer and tracing control layer, according to every layer of different control target, separately designs controller, more targeted to problem.The faults-tolerant control of this double-layer structure can handle existing system constraints well, have strong robustness, can effectively solve complicated machinery arm actuator perseverance deviation fault problem, ensure the stability and control performance of whole system.
Description
Technical field
The present invention relates to a kind of mechanical arm actuator failures fault-tolerant control system and its method based on double-layer structure, belongs to
Automatic control technology field.
Background technique
With scientific and technological progress, more and more applies mechanical arm to complete production task in field of industrial production, it is controlled
Performance requirement is being continuously improved, it is necessary to assure the reliability and accuracy of its actuator, sensor and other elements.Especially navigate
The fields such as empty space flight, navigation, specific work environments propose tightened up specification to the operational safety of its control system.But it controls
System be easy to cause equipment attrition or in the process of running by external interference, and its mechanics actuator has complex nonlinear
Feature is chronically at working condition and easily breaks down situation.Faults-tolerant control strategy can be good at eliminating actuator failures band
The adverse effect come, but general fault tolerant control method does not account for the Dynamic Constraints that system itself has, and is extremely difficult to
The unification of stability and rapidity.Mechanical arm in actual application its system Control constraints in system construct and driven nature
Can, realize that quickly and accurately system control is also and its important in system restriction.
Moreover, real system is easy to be influenced by uncertain factors such as unmodeled state, unknown parameter and external interferences, no
Determine that the control problem of system has become in modern scientist one and important probes into direction.In practical applications, mechanical arm system is deposited
It is that a typical close coupling, nonlinearity are not known modeling is inaccurate and the uncertain factors such as external interference
Complication system, therefore, in mechanical arm control system design it should also be taken into account that the dynamics of uncertain factor and system complex
Characteristic influences its Control platform bring, this brings difficult and inconvenient to the faults-tolerant control of mechanical arm.
It is complicated to solve the design of uncertain manipulator system controller, fault diagnosis and tolerant system close coupling, height are non-thread
Property technical problem, a kind of actuator perseverance deviation fault that can meet system restriction demand present in actual moving process is provided
Faults-tolerant control is imperative.
Summary of the invention
To overcome the design of uncertain manipulator system controller complicated, fault diagnosis and tolerant system close coupling, height are non-
Linear technical problem, meets system constraints present in actual moving process, and the present invention provides a kind of based on the double-deck knot
The mechanical arm actuator failures fault-tolerant control system and its method of structure.
The object of the present invention is achieved like this:
A kind of mechanical arm actuator failures fault-tolerant control system based on double-layer structure of the present invention, the system include:
The discrete fault model of mechanical arm actuator, is established using taylor series expansion；
Fault diagnosis (FDD) unit is actively diagnosed and is estimated fault message to failure based on Adaptive Observer,
And the fault message of estimation is introduced into the discrete fault model of mechanical arm actuator, realize Active Fault Tolerant；
Mechanical arm fault-tolerant controller includes trajectory planning layer and tracing control layer, interactive information between two layers, according to every layer
Different control targets, separately designs controller, wherein the trajectory planning layer planned course planning control device cooks up one
Item meets the optimal reference locus of system constraints；The tracing control layer is to improve computational efficiency, is set using short-cut method
Count tracking of the contrail tracker realization to reference locus；
It predicts fault model, in track planning layer, is realized using MPC algorithm to optimal rail in failure mechanical arm prediction time domain
Obtained planned trajectory is passed to tracing control layer by the planning of mark；
Predict sliding formwork fault model, in tracing control layer, sliding formwork control be introduced into during Model Predictive Control designs, using with
Track error vector structure forecast sliding formwork fault model, solving optimization problem obtain control Lu, make each joint of failure mechanical arm system
Still quickly reach target position；
Feedback compensation mechanism compensation system, compensates uncertain factor existing for real system.
A kind of method of the mechanical arm actuator failures fault-tolerant control system based on double-layer structure of the present invention comprising following
Step:
Step 1: establishing discrete system model under actuator failures: for the event of mechanical arm actuator perseverance deviation shown in formula (1)
The kinetic model of barrier establishes the state space equation formula (2) of mechanical arm actuator perseverance deviation fault, using Taylor series expansion
Formula carries out sliding-model control to formula (2), obtains formula (3),
Mechanical arm input constraint
τmin≤τ≤τmax
Wherein, q ∈ R2×1It is joint position vector,It is velocity vector,It is vector acceleration, M (q)
∈R2×2It is the symmetrical inertial matrix of positive definite,It is Coriolis and centrifugation torque vector, G (q) ∈ R2It is that gravity draws
The torque vector risen, τ ∈ R2For each joint control torque vector of mechanical arm, it is assumed that each joint control torque is relatively independent.For unknown permanent deviation fault function item, For failure function, T is failure hair
The raw time.Assuming that failure f norm-bounded, i.e., | | f | |≤ρ, ρ are constant.ω is system uncertain factor.τmax, τminIt is respectively
The upper bound of input torque and lower bound.
The kinetic model of permanent deviation fault occurs for mechanical arm actuator:
Mechanical arm input constraint
τmin≤τ≤τmax
Wherein,It is system mode vector, y is system output,
Wherein,
C=[Ιn On],
X (k) indicates that k-th of sampling instant quantity of state, y (k) indicate the output quantity of k-th of sampling instant, and τ (k) indicates kth
The control input quantity of a sampling instant；
Theory deduction is carried out based on Model Predictive Control and is obtained by formula (3) as prediction fault model in track planning layer
Optimal control codes acquire the predicted state value for making performance indicator optimal in prediction time domain according to optimal control codes as tracking control
The desired value of preparative layer.
In tracing control layer, sliding formwork control is introduced into Model Predictive Control design, is constructed using tracking error vector pre-
It surveys sliding formwork fault model formula (4), solving optimization problem obtains control Lu, reaches each joint of failure mechanical arm system still quickly
Target position.
Enable tracking error vector e (k)=x (k)-xr(k), wherein x (k) is current time system state amount, xr(k+1) it is
Desired value, xrIt (k) is subsequent time desired value.
DefinitionThen tracking error dynamical equation is
Defining sliding formwork function is
S (k)=He (k)
Wherein, H ∈ Rm×2nFor parameter to be designed.
Since sliding mode is unrelated with systematic uncertainty and interference, then predict that sliding formwork fault model is
Step 2: fault diagnosis (FDD) unit designs: designing following Failure Observer such as formula (5), thus estimate failure letter
Breath,
Wherein,Indicate the estimated value of x (k),Indicate the estimated value of y (k),It indicates ffault matrix f (k)
Estimated value, L indicates the observer gain matrix of appropriate dimension, selects suitable gain matrix L design error failure estimation observer
Obtain fault message estimated value
Step 3: feedback compensation mechanism Compensation System Design: by obtained current time actual value with and last time it is pre-
Measured value is made comparisons, and prediction error is obtained, and carries out feedback compensation by predicted value of the errors value to future time instance later, can be very
Good compensates systematic uncertainty；
Step 4: double-layer structure fault controller: using hierarchy optimization control thought, trajectory planning layer considers target
The conditions such as position, system restriction, design meet the optimal trajectory of system condition, and tracing control layer is realized to the accurate of optimal trajectory
Tracking.
Further, using the trajectory planning controller on Model Predictive Control Algorithm design upper layer.
The target position according to the physical constraint condition of system itself and artificially required designs one for tracing control layer
The optimal reference locus of position and speed comprising each joint of mechanical arm.
Under Model Predictive Control frame, structural behavior target function formula (6), finding out in control time domain ensures that system exports
Thus optimal control amount calculates the optimal reference locus of mechanical arm subsequent time.
ey(k+j)=y (k)-y (k | k-j) j=1,2 ..., P
yopt(k+j)=yp(k+j)+ey(k+j) j=1,2 ..., P
τmin≤τ(k+j-1|k)≤τmaxJ=1 ..., M
τ (k+j-1 | k)=τ (k+M-1 | k) M < j≤P
Wherein, etching system actual value when y (k) is k, and y (k | k-j) it is last time to k moment predicted value, ey(k+j) it is
Predict output error, ypIt (k+j) is model prediction output, yopt(k+j) be mechanical arm correction output, τ (k+j-1 | k) be to
Optimal control variable, qsetIt is joint target position vector, P and M are prediction time domain and control time domain, Q respectivelyj, RjIt is certainly respectively
The error weighting coefficient and torque weighting coefficient of definition, Qj> 0, Rj> 0.
Further, using the contrail tracker of prediction sliding mode control algorithm design lower layer.
Structural behavior target function formula (7), finding out ensures that system exports optimal control Lu in control time domain, and will calculate
One-component τ (k | k) act on mechanical arm:
ex(k)=x (k)-xr(k)
S (k)=Hex(k)
es(k+i)=s (k)-s (k | k-i) i=1,2 ..., P
Wherein, x (k) is k moment system state amount, xrIt (k) is that constrained forecast planning control device passes to track following control
Device processed is in the subsequent time expectation to be tracked, exIt (k) is tracking error vector, s (k) is sliding formwork function, indicates that k moment sliding formwork is pre-
Measured value, and s (k | k-i) it is last time to k moment algorithm based on sliding mode prediction value, esIt (k+i) is prediction error, spIt (k+i) is that prediction sliding formwork is defeated
Out,It is that mechanical arm correction exports, and τ (k+i-1 | k) it is control variable to be optimized, P and M are prediction time domain and control respectively
Time domain processed；Qi, RiIt is customized error weighting coefficient and torque weighting coefficient, Q respectivelyi> 0, Ri> 0.
Compared with prior art, the medicine have the advantages that
The present invention has certain autokinetic movement ability while guaranteeing that mechanical arm has enough power performance；This hair
It is bright that system actuators perseverance deviation fault is detected by Adaptive Observer, Fault Estimation information is obtained instead of fault-signal
Realize Active Fault Tolerant；Effectively overcome that mechanical arm is difficult to Accurate Model and internal dynamic is unstable using feedback compensation mechanism
Characteristic makes system have strong robustness, improves tracking accuracy；Mechanical arm fault-tolerant controller includes trajectory planning layer and tracking
Control layer, every layer, according to different control targets, is based respectively on distinct methods design controller, and interactive information between two layers is total
Same-action can satisfy system various requirement, preferably processing input torque constraint condition and inhibition systematic uncertainty, real
The faults-tolerant control object procedure of existing complication system is well arranged.
Detailed description of the invention
Fig. 1 is the structure chart of double-layer structure faults-tolerant control of the present invention；
Fig. 2 is the failure true value and estimated value comparison diagram of double-layer structure faults-tolerant control of the present invention；
Fig. 3 is 1 desired locations of failure system joint and geometric locus figure of double-layer structure faults-tolerant control of the present invention；
Fig. 4 is 2 desired locations of failure system joint and geometric locus figure of double-layer structure faults-tolerant control of the present invention；
Fig. 5 is the failure system joint control input torque figure of double-layer structure faults-tolerant control of the present invention.
Specific embodiment
For the more intuitive understanding present invention, the detailed description of the invention is provided in conjunction with attached drawing.
As shown in Figure 1, utilizing Thailand the present invention is based on the mechanical arm actuator failures fault-tolerant control system of double-layer structure
It strangles series expansion and establishes the discrete fault model of mechanical arm actuator under actuator perseverance deviation fault, to reduce calculation amount, improve
Computational efficiency improves real-time.
Mechanical arm fault-tolerant controller includes trajectory planning layer and tracing control layer, interactive information between two layers, according to every layer
Different control targets, separately designs controller, more targeted to problem, wherein trajectory planning layer is based on MPC control synthesis
The advantages of quality height and the ability of good processing constraint, planned course planning control device cooks up one and meets system restriction
The optimal reference locus of condition.It is input parameter with the status information of target position, constraint condition and mechanical arm current time, if
Corresponding performance index function is counted, system constraints are met.Tracing control layer is to improve computational efficiency, is set using short-cut method
Count tracking of the contrail tracker realization to reference locus.
Fault diagnosis (FDD) unit based on design of Adaptive Observer discrete system, to be based on Adaptive Observer pair
Failure is actively diagnosed and is estimated fault message, and Fault Estimation information is substituted into the discrete fault model of mechanical arm, is realized actively
It is fault-tolerant.
Prediction fault model and prediction sliding formwork fault model are separately designed according to layered optimization scheme.In track planning layer,
Predict that fault model realizes the planning to optimal trajectory in failure mechanical arm prediction time domain, the planning that will be obtained using MPC algorithm
Track passes to tracing control layer；
In tracing control layer, tracing control layer does not consider the external demands such as target position and constraint condition, using as far as possible
Make easy-to-use control strategy, sliding formwork control is introduced into during Model Predictive Control designs by prediction sliding formwork fault model, using with
Track error vector structure forecast sliding formwork fault model, based on the excellent control performance and strong robustness of prediction sliding formwork control, design
Contrail tracker realizes the quick and precisely tracking to planned trajectory, and solving optimization problem obtains control Lu, keeps failure mechanical
Each joint of arm system still quickly reaches target position.
Consider uncertain factor existing for real system, using feedback compensation mechanism compensation system compensation system it is uncertain because
The influence of element improves system strong robustness.
The faults-tolerant control of this double-layer structure can handle existing system constraints well, have strong robustness, energy
It effectively solves the problems, such as complicated machinery arm actuator perseverance deviation fault, ensures the stability and control performance of whole system.
The present invention is based on the keyword processing methods and process of the mechanical arm actuator failures fault-tolerant control system of double-layer structure
It is as follows:
Step 1: establishing system failure model:
One kind has the two joint mechanical arm system of uncertain factor, when system actuators perseverance deviation fault, according to
Mono- Euler establishing equation mechanical arm faulty power model of Lagrange
Mechanical arm input constraint
τmin≤τ≤τmax
Wherein, q ∈ R2×1It is joint position vector,It is velocity vector,It is vector acceleration, M (q)
∈R2×2It is the symmetrical inertial matrix of positive definite,It is Coriolis and centrifugation torque vector, G (q) ∈ R2It is that gravity draws
The torque vector risen, τ ∈ R2For each joint control torque vector of mechanical arm, it is assumed that each joint control torque is relatively independent.For unknown permanent deviation fault function item, For failure function, T is failure hair
The raw time.Assuming that failure f norm-bounded, i.e., | | f | |≤ρ, ρ are constant.ω is system uncertain factor.τmax, τminIt is respectively
The upper bound of input torque and lower bound.
In order to reduce mechanical arm close coupling, nonlinearity bring difficulty, for the perseverance of mechanical arm actuator shown in formula (2)
The state space equation of deviation fault, is carried out discrete by the way of Taylor series expansion, obtains formula (3), keeps model quasi-
Really description mechanical arm dynamic characteristic, and can be reduced calculation amount, fast implement control algolithm.Formula (3) is prediction fault model.
The state space equation of permanent deviation fault occurs for mechanical arm system actuator
Mechanical arm input constraint
τmin≤τ≤τmax
Wherein,It is system mode vector, y is system output,P(x1)=M-1(q),For unknown permanent deviation fault letter
It is several, For failure function, T is time of failure.
Wherein,
C=[Ιn On],
X (k) indicates that k-th of sampling instant quantity of state, y (k) indicate the output quantity of k-th of sampling instant, and τ (k) indicates kth
The control input quantity of a sampling instant.For the accuracy for guaranteeing prediction model, enhance the robustness of control system, controller is incited somebody to action
The real-time system status information arrived introduces mechanical arm state-space model, reduces the influence of model mismatch.
Theory deduction is carried out based on Model Predictive Control and is obtained by formula (3) as prediction fault model in track planning layer
Optimal control codes acquire the predicted state value for making performance indicator optimal in prediction time domain according to optimal control codes as tracking control
The desired value of preparative layer.
In tracing control layer, sliding formwork control is introduced into Model Predictive Control design, is constructed using tracking error vector pre-
Sliding formwork fault model is surveyed, solving optimization problem obtains control Lu, each joint of failure mechanical arm system is made still quickly to reach target
Position.
Remember that x (k) is current time system state amount, xrIt (k+1) is desired value, xrIt (k) is subsequent time desired value.Enable with
Track error vector e (k)=x (k)-xr(k), it and defines
Then tracking error dynamical equation is
Defining sliding formwork function is
S (k)=He (k)
Wherein, H ∈ Rm×2nFor parameter to be designed.
Since sliding mode is unrelated with systematic uncertainty and interference, then predict that sliding formwork fault model is
Step 2: fault diagnosis (FDD) unit designs:
Needs based on faults-tolerant control using Adaptive Observer good combination property, can inhibit system uncertain well
The advantages that factor, designs following Failure Observer such as formula (5), thus estimates fault message.
Wherein,Indicate the estimated value of x (k),Indicate the estimated value of y (k),It indicates ffault matrix f (k)
Estimated value, L indicates the observer gain matrix of appropriate dimension.Suitable gain matrix L is selected to be based on observer error dynamics
Equation carries out theory deduction and obtains fault message estimated value
Step 3: feedback compensation mechanism:
For the prediction fault model of trajectory planning layer, system actual value y (k) and the past at current k moment are detected first
Error between moment predicted value y (k | k-P), errors are added to obtain k+ with the prediction sliding formwork value y (k+P) at k+P moment
The closed low predictions output valve at P moment
Wherein, e2(k)=y (k)-y (k | k-P), σiFor correction coefficient, in general 0 < σi< 1.
For the prediction sliding formwork fault model of tracing control layer, k moment sliding formwork function current value s (k) is calculated first
Deviation between last time predicted value s (k | k-P), later by gained deviation to the prediction sliding formwork value s (k at k+P moment
+ P) carry out feedback compensation, then the closed-loop corrected prediction sliding formwork output at k+P moment
Wherein, e1(k)=s (k)-s (k | k-P).hiFor correction coefficient, in general 0 < hi< 1.
Using feedback compensation mechanism energy, compensation system is uncertain well, lifting system control performance.
Step 4: double-layer structure fault controller
With double-layer structure optimal control thought, entire fault-tolerant control system is by trajectory planning layer and tracing control layer group
At separately designing controller according to every layer of different control target.
1. trajectory planning controller
Trajectory planning controller in upper layer is designed using Model Predictive Control Algorithm, according to the physical constraint condition of system itself
The target position required with people designs the optimal ginseng of a position and speed comprising each joint of mechanical arm for tracing control layer
Examine track.
Under Model Predictive Control frame, structural behavior target function formula (6), finding out in control time domain ensures that system exports
Thus optimal control amount calculates the optimal reference locus of mechanical arm subsequent time.
ey(k+j)=y (k)-y (k | k-j) j=1,2 ..., P
yopt(k+j)=yp(k+j)+ey(k+j) j=1,2 ..., P
τmin≤τ(k+j-1|k)≤τmaxJ=1 ..., M
τ (k+j-1 | k)=τ (k+M-1 | k) M < j≤P
Wherein, etching system actual value when y (k) is k, and y (k | k-j) it is last time to k moment predicted value, ey(k+j) it is
Predict output error, ypIt (k+j) is model prediction output, yopt(k+j) be mechanical arm correction output, τ (k+j-1 | k) be to
Optimal control variable, qsetIt is joint target position vector, P and M are prediction time domain and control time domain, Q respectivelyj, RjIt is certainly respectively
The error weighting coefficient and torque weighting coefficient of definition, Qj> 0, Rj> 0.
Since there are system input constraints, performance index function optimization problem formula (6) is deformed into chemical conversion standard by formula
The quadratic programming problem formula containing constraint condition, which, which can solve to obtain in control time domain, ensures that system exports optimal numerical value
Solution, thus to obtain the predicted state value x for making best performanceopt(k) as the subsequent time reference locus to be tracked.In order to protect
System control performance requirement is demonstrate,proved, Rolling optimal strategy is still used, trajectory planning controller only exports the prediction of subsequent time
Value xopt(k+1) contrail tracker is passed to as its reference locus xr(k+1), two layers of collective effect realizes mechanical arm pair
The accurate tracking of target position.To next sampling instant, trajectory planning controller redesigns an optimal trajectory.
2. contrail tracker
If obtaining manipulator motion track and original state and actuator failures estimated information, system force can be directly found out
Square, but this method requires accurate system model, and can not compensate to disturbance, and system is easy diverging.It is slided based on prediction
Mould controls good robustness, designs lower layer's contrail tracker using prediction sliding mode control algorithm, inhibits system uncertain
Factor realizes the tracking to the optimal reference locus in upper layer, so that reality output and reference locus deviation are minimum.
Structural behavior target function formula (7), finding out ensures that system exports optimal control Lu in control time domain, and will calculate
One-component τ (k | k) act on mechanical arm.
ex(k)=x (k)-xr(k)
S (k)=Hex(k)
es(k+i)=s (k)-s (k | k-i) i=1,2 ..., P
Wherein, x (k) is k moment system state amount, xrIt (k) is that constrained forecast planning control device passes to track following control
Device processed is in the subsequent time expectation to be tracked, exIt (k) is tracking error vector, s (k) is sliding formwork function, indicates that k moment sliding formwork is pre-
Measured value, and s (k | k-i) it is last time to k moment algorithm based on sliding mode prediction value, esIt (k+i) is prediction error, spIt (k+i) is that prediction sliding formwork is defeated
Out,Mechanical arm correction output, τ (k+i-1 | k) is control variable to be optimized, P and M be respectively prediction time domain and
Control time domain；Qi, RiIt is customized error weighting coefficient and torque weighting coefficient, Q respectivelyi> 0, Ri> 0.
In the case where not considering constraint, according toSolving optimization problem obtains prediction sliding formwork control after (7) are arranged
The control Lu of system
U=- (ΩTQΩ+R)-1ΩTQΦ
According to the thought of rolling optimization, only choose current time optimal control U one-component be current time most
Mechanical arm system of excellent control amount τ (k)=[I 0 ... the 0] U as practical control input action after failure.In subsequent time,
Prediction time domain pushes forward simultaneously, and the measured value newly to obtain, as primary condition, τ (k+ is calculated in re-optimization
1) rolling optimization, is realized.This mode can effectively adapt to the latest development of system, reduce and want to system model precision
It asks, is able to maintain control actual optimal.
If permanent deviation fault occurs for system actuators and there are system uncertain factors, system input constraint condition is considered,
Fault-tolerant control system is constructed, effectiveness of the invention is verified.
Fig. 2 is the diagnostic result of actuator f1 failure and Fault Estimation, and the 1st joint of mechanical arm holds when showing 1.5s in figure
Permanent deviation fault occurs for row device, at this time f1=3, show that failure size can be effectively estimated in the adaptive failure observer of design.
From Fig. 3-joint of mechanical arm output trajectory shown in Fig. 4, it can be seen that using double-layer structure design of control method
Mechanical arm fault-tolerant control system shows preferable performance in terms of to systematic uncertainty, and mechanical arm can be made quick
Move to specified target position.When permanent deviation fault occurs for system actuators, the movement output track in the 1st joint of mechanical arm
Acutely shake occurs, then realizes the tracking to target position again in a short time, as shown in Figure 3；The 2nd joint of mechanical arm
The fluctuation of movement output track less, as shown in figure 4, illustrating that the faults-tolerant control scheme can well compensate failure, meets
The performance requirement of fault-tolerant control system.
Fig. 5 shows that mechanical arm system controls input torque and quickly change, tend towards stability quickly in startup stage.In system
After breaking down, corresponding actions can be also made, and whole process is all within the scope of input constraint.It, can according to emulation experiment figure
The faults-tolerant control of the mechanical arm based on Model Predictive Control is combined and based on the fault-tolerant control of mechanical arm for predicting sliding formwork control to find out
Method processed is real in the case of may breaking down come the fault tolerant control method based on double-layer structure control designed to processing actuator
Be to the control problem of mechanical arm system now it is feasible and effective, solve the problems, such as control input constraint when have good energy
Power, while also having good performance in terms of inhibiting systematic uncertainty, rapidity and stability.
Specific embodiment described above has made detailed analysis to structure of the invention and technology implementation, but not to
Limit the present invention.It is not departing within spirit of that invention and principle, it can further studied, enriching summary of the invention.Cause
This, the scope of the present invention should be subject to the claims.
Claims (4)
1. a kind of mechanical arm actuator failures fault-tolerant control system based on double-layer structure, which is characterized in that the system includes:
The discrete fault model of mechanical arm actuator, is established using taylor series expansion；
Fault diagnosis (FDD) unit is actively diagnosed and is estimated fault message to failure based on Adaptive Observer, and will
The fault message of estimation introduces the discrete fault model of mechanical arm actuator, realizes Active Fault Tolerant；
Mechanical arm fault-tolerant controller includes trajectory planning layer and tracing control layer, interactive information between two layers, according to every layer of difference
Control target, separately design controller, wherein the trajectory planning layer planned course planning control device, cook up one it is full
The optimal reference locus of pedal system constraint condition；The tracing control layer is to improve computational efficiency, designs rail using short-cut method
Mark tracking control unit realizes the tracking to reference locus；
It predicts fault model, in track planning layer, is realized using MPC algorithm to optimal trajectory in failure mechanical arm prediction time domain
Planning, passes to tracing control layer for obtained planned trajectory；
It predicts sliding formwork fault model, in tracing control layer, sliding formwork control is introduced into Model Predictive Control design, is missed using tracking
Difference vector structure forecast sliding formwork fault model, solving optimization problem obtain control Lu, make each joint of failure mechanical arm system still
Quickly reach target position；
Feedback compensation mechanism compensation system, compensates uncertain factor existing for real system.
2. a kind of method of the mechanical arm actuator failures fault-tolerant control system based on double-layer structure comprising following steps:
Step 1: establishing discrete system model under actuator failures: for mechanical arm actuator perseverance deviation fault shown in formula (1)
Kinetic model establishes the state space equation formula (2) of mechanical arm actuator perseverance deviation fault, using taylor series expansion pair
Formula (2) carries out sliding-model control, obtains formula (3),
Mechanical arm input constraint
τmin≤τ≤τmax
Wherein, q ∈ R2×1It is joint position vector,It is velocity vector,It is vector acceleration, M (q) ∈ R2×2
It is the symmetrical inertial matrix of positive definite,It is Coriolis and centrifugation torque vector, G (q) ∈ R2It is to be turned round caused by gravity
Square vector, τ ∈ R2For each joint control torque vector of mechanical arm, it is assumed that each joint control torque is relatively independent；
For unknown permanent deviation fault function item, For failure function, T is time of failure；Assuming that
Failure f norm-bounded, i.e., | | f | |≤ρ, ρ are constant；ω is system uncertain factor；τmax, τminIt is the upper of input torque respectively
Boundary and lower bound；
The kinetic model of permanent deviation fault occurs for mechanical arm actuator:
Mechanical arm input constraint
τmin≤τ≤τmax
Wherein,It is system mode vector, y is system output,
Wherein,
X (k) indicates that k-th of sampling instant quantity of state, y (k) indicate the output quantity of k-th of sampling instant, and τ (k) indicates to adopt for k-th
The control input quantity at sample moment；
Theory deduction is carried out based on Model Predictive Control and is optimized by formula (3) as prediction fault model in track planning layer
Control amount acquires the predicted state value for making performance indicator optimal in prediction time domain as tracing control layer according to optimal control codes
Desired value；
In tracing control layer, sliding formwork control is introduced into Model Predictive Control design, it is sliding using tracking error vector structure forecast
Mould fault model formula (4), solving optimization problem obtain control Lu, each joint of failure mechanical arm system are made still quickly to reach target
Position；
Enable tracking error vector e (k)=x (k)-xr(k), wherein x (k) is current time system state amount, xrIt (k+1) is expectation
Value, xrIt (k) is subsequent time desired value；
DefinitionThen tracking error dynamical equation is
Defining sliding formwork function is
S (k)=He (k)
Wherein, H ∈ Rm×2nFor parameter to be designed；
Since sliding mode is unrelated with systematic uncertainty and interference, then predict that sliding formwork fault model is
Step 2: fault diagnosis (FDD) unit designs: following Failure Observer such as formula (5) is designed, thus estimates fault message,
Wherein,Indicate the estimated value of x (k),Indicate the estimated value of y (k),Indicate estimating for ffault matrix f (k)
Evaluation, L indicate the observer gain matrix of appropriate dimension, and suitable gain matrix L design error failure estimation observer is selected to obtain
Fault message estimated value
Step 3: feedback compensation mechanism Compensation System Design: obtained current time actual value and last time predicted value are made
Compare, obtain prediction error, feedback compensation is carried out by predicted value of the errors value to future time instance later, it can be right well
Systematic uncertainty compensates；
Step 4: double-layer structure fault controller: using hierarchy optimization control thought, trajectory planning layer considers target position
Set, system constraints, design meets the optimal trajectory of system condition, tracing control layer realize to optimal trajectory it is accurate with
Track.
3. the method for mechanical arm actuator failures fault-tolerant control system according to claim 2, which is characterized in that
Using the trajectory planning controller on Model Predictive Control Algorithm design upper layer, according to the physical constraint condition of system itself and
The target position artificially required designs the optimal ginseng of a position and speed comprising each joint of mechanical arm for tracing control layer
Examine track；
Under Model Predictive Control frame, structural behavior target function formula (6), finding out ensures that system output is optimal in control time domain
Control amount, thus calculate the optimal reference locus of mechanical arm subsequent time；
ey(k+j)=y (k)-y (k | k-j) j=1,2 ..., P
yopt(k+j)=yp(k+j)+ey(k+j) j=1,2 ..., P
τmin≤τ(k+j-1|k)≤τmaxJ=1 ..., M
τ (k+j-1 | k)=τ (k+M-1 | k) M < j≤P
Wherein, etching system actual value when y (k) is k, and y (k | k-j) it is last time to k moment predicted value, eyIt (k+j) is that prediction is defeated
Error out, ypIt (k+j) is model prediction output, yopt(k+j) be mechanical arm correction output, τ (k+j-1 | k) is control to be optimized
Variable processed, qsetIt is joint target position vector, P and M are prediction time domain and control time domain, Q respectivelyj, RjIt is customized respectively
Error weighting coefficient and torque weighting coefficient, Qj> 0, Rj> 0.
4. the method for mechanical arm actuator failures fault-tolerant control system according to claim 2, which is characterized in that
The contrail tracker of lower layer is designed using prediction sliding mode control algorithm,
Structural behavior target function formula (7), finding out in control time domain ensures that system exports optimal control Lu, and by the of calculating
One-component τ (k | k) act on mechanical arm:
ex(k)=x (k)-xr(k)
S (k)=Hex(k)
es(k+i)=s (k)-s (k | k-i) i=1,2 ..., P
Wherein, x (k) is k moment system state amount, xrIt (k) is that constrained forecast planning control device passes to contrail tracker and exists
The subsequent time expectation to be tracked, exIt (k) is tracking error vector, s (k) is sliding formwork function, indicates k moment algorithm based on sliding mode prediction value, s
(k | k-i) it is last time to k moment algorithm based on sliding mode prediction value, esIt (k+i) is prediction error, spIt (k+i) is prediction sliding formwork output,It is that mechanical arm correction exports, and τ (k+i-1 | k) it is control variable to be optimized, P and M are prediction time domain and control respectively
Time domain；Qi, RiIt is customized error weighting coefficient and torque weighting coefficient, Q respectivelyi> 0, Ri> 0.
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