CN107121977A - Mechanical arm actuator failures fault-tolerant control system and its method based on double-decker - Google Patents
Mechanical arm actuator failures fault-tolerant control system and its method based on double-decker Download PDFInfo
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- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
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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-decker, belongs to automatic control technology field with hierarchy control optimization thought.To reduce amount of calculation, real-time is improved, discrete system model under actuator failures is set up using taylor series expansion；It is topic to design FDD unit active process failure, and the fault message estimated introduces fault model, realizes Active Fault Tolerant；Consider the uncertain factor that real system is present, compensated using feedback compensation mechanism；Mechanical arm fault-tolerant controller is made up of trajectory planning layer and tracing control layer, according to every layer of different control targe, separately designs controller, more targeted to problem.The faults-tolerant control of this double-decker can handle the system constraints of presence well, with strong robustness, can effectively solve the problems, such as the permanent deviation fault of complicated machinery arm actuator, 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 based on double-decker and its method, belong to
Automatic control technology field.
Background technology
With scientific and technological progress, in field of industrial production, more and more application mechanical arm completes production task, and it is controlled
Performance requirement is being improved constantly, it is necessary to assure the reliability and accuracy of its actuator, sensor and other elements.Particularly navigate
The fields such as empty space flight, navigation, specific work environments propose tightened up specification to the operation safety of its control system.But control
System easily causes equipment attrition or by external interference in the process of running, 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 harmful effect come, but general fault tolerant control method does not account for the Dynamic Constraints that system has in itself, is extremely difficult to
The unification of stability and rapidity.Mechanical arm its system Control constraints in actual application are constructed and driven nature in system
Can, realize that quickly and accurately system control is also and its important in the case of system restriction.
Moreover, real system is easily influenceed by the uncertain factors such as state, unknown parameter and external interference are not modeled, no
Determine that the control problem of system has turned into modern scientist one and important probed into direction.In actual applications, mechanical arm system is deposited
It is that a typical close coupling, nonlinearity are not known modeling is inaccurate and the uncertain factor such as external interference
Complication system, therefore, when mechanical arm control system is designed it should also be taken into account that the dynamics of uncertain factor and system complex
The influence that characteristic is brought to its Control platform, this brings difficult and inconvenience to the faults-tolerant control of mechanical arm.
Solve the design of uncertain manipulator system controller complicated, fault diagnosis and tolerant system close coupling, height non-thread
Property the technical barrier permanent deviation fault of actuator that meets system restriction demand present in actual moving process there is provided a kind of
Faults-tolerant control is imperative.
The content of the invention
It is fault diagnosis and tolerant system close coupling, highly non-to overcome the design of uncertain manipulator system controller complicated
Linear technical barrier, meets system constraints present in actual moving process, and the present invention provides a kind of based on 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-decker of the present invention, the system includes：
The discrete fault model of mechanical arm actuator, is set up using taylor series expansion；
Fault diagnosis (FDD) unit, it is based on Adaptive Observer and failure is actively diagnosed and fault message is estimated, 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 interactive information between trajectory planning layer and tracing control layer, two layers, according to every layer of difference
Control targe, separately design controller, wherein, trajectory planning layer planned course planning control device, cook up one it is full
The optimal reference locus of pedal system constraints；The tracing control layer designs rail to improve computational efficiency using short-cut method
Mark tracking control unit realizes the tracking to reference locus；
Fault model is predicted, in track planning layer, is realized using MPC algorithm and predicts failure mechanical arm optimal trajectory in time domain
Planning, tracing control layer is passed to by obtained planned trajectory；
Sliding formwork fault model is predicted, in tracing control layer, sliding formwork control is introduced into Model Predictive Control design, missed using tracking
Difference vector structure forecast sliding formwork fault model, solving-optimizing problem obtains controlling Lu, makes each joint of failure mechanical arm system still
It is quick to reach target location；
Feedback compensation mechanism compensation system, is compensated to the uncertain factor that real system is present.
A kind of method of the mechanical arm actuator failures fault-tolerant control system based on double-decker of the present invention, it includes following
Step：
Step 1: setting up discrete system model under actuator failures：For the permanent deviation fault of mechanical arm actuator shown in formula (1)
Kinetic model, sets up the state space equation formula (2) of the permanent deviation fault of mechanical arm actuator, using taylor series expansion pair
Formula (2) carries out sliding-model control, obtains formula (3),
Mechanical arm input constraint
τmin≤τ≤τmax
Wherein,It is that joint position is vectorial (velocity vector, vector acceleration), M (q) ∈ R2×2It is that positive definite is symmetrically used to
Property matrix,It is Coriolis and centrifugation torque vector, G (q) ∈ R2It is torque vector caused by gravity, 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
Failure function, For failure function, T is time of failure.Assuming that failure f norm-boundeds,
I.e. | | f | |≤ρ, ρ are constant.ω is system uncertain factor.τmax, τminIt is the upper bound and the lower bound of input torque respectively.
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,
P(x1)=M-1(q)。
Wherein,
X (k) represents k-th of sampling instant quantity of state, and y (k) represents the output quantity of k-th of sampling instant, and τ (k) represents to adopt for k-th
The control input amount at sample moment；
In track planning layer, using formula (3) as prediction fault model, theory deduction is carried out based on Model Predictive Control and obtained
Optimal control codes, try to achieve according to optimal control codes and cause the optimal predicted state value of performance indications to be controlled as tracking in prediction time domain
The desired value of preparative layer.
In tracing control layer, sliding formwork control is introduced into Model Predictive Control design, it is pre- using tracking error vector construction
Sliding formwork fault model formula (4) is surveyed, solving-optimizing problem obtains controlling Lu, each joint of failure mechanical arm system is still quickly reached
Target location.
Make tracking error vector e (k)=x (k)-xr(k), wherein, x (k) be current time system state amount, xr(k+1) it is
Desired value, xr(k) it 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.
Because sliding mode is unrelated with systematic uncertainty and interference, then predict that sliding formwork fault model is
Step 2: fault diagnosis (FDD) unit is designed：Following Failure Observer such as formula (5) is designed, fault message is thus estimated,
Wherein,X (k) estimate is represented,Y (k) estimate is represented,Represent ffault matrix f (k) estimation
Value, L represents the observer gain matrix of appropriate dimension, selects suitable gain matrix L design error failures estimation observer to obtain event
Hinder information estimate
Step 3: feedback compensation mechanism Compensation System Design：By obtained current time actual value and and last time predicted value
Make comparisons, obtain predicated error, feedback compensation is carried out to the predicted value of future time instance by errors value afterwards, can be well
Systematic uncertainty is compensated；
Step 4: double-decker fault controller：With hierarchy optimization control thought, trajectory planning layer considers target position
Put, the condition such as system restriction, design meets the optimal trajectory of system condition, tracing control layer realize to optimal trajectory it is accurate with
Track.
Further, the trajectory planning controller on upper strata is designed using Model Predictive Control Algorithm.
It is that tracing control layer designs one according to the physical constraint condition of system itself and the target location artificially required
The optimal reference locus of position and speed comprising each joint of mechanical arm.
Under Model Predictive Control framework, structural behavior target function formula (6), obtaining in control time domain ensures that system is exported
Optimal controlled quentity controlled variable, thus 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, y (k | k-j) is last time to k moment predicted values, ey(k+j) it is prediction
Output error, yp(k+j) it is model prediction output, yopt(k+j) be mechanical arm correction output, τ (k+j-1 | k) is to be optimized
Control variable, qsetIt is joint target location vector, P and M are prediction time domain and control time domain, Q respectivelyi, Ri(Qi＞ 0, Ri＞ 0)
It is customized error weight coefficient and torque weight coefficient respectively.
Further, the contrail tracker of lower floor is designed using prediction sliding mode control algorithm.
Structural behavior target function formula (7), obtaining ensures that system exports optimal control Lu in control time domain, and will calculate
One-component τ (k | k) act on mechanical arm：
E (k)=x (k)-xr(k)
S (k)=He (k)
es(k+j)=s (k)-s (k | k-j) j=1,2 ..., P
Wherein, x (k) is k moment system state amounts, xr(k) it is that constrained forecast planning control device passes to contrail tracker
In the subsequent time expectation to be tracked, e (k) is tracking error vector, and s (k) is sliding formwork function, represents k moment algorithm based on sliding mode prediction values,
S (k | k-j) is last time to k moment algorithm based on sliding mode prediction values, es(k+j) it is predicated error, sp(k+j) it is prediction sliding formwork output,It is that mechanical arm correction is exported, and τ (k+j-1 | k) it is control variable to be optimized, when P and M are prediction time domain and control respectively
Domain；Qi, Ri(Qi＞ 0, Ri＞ 0) it is customized error weight coefficient and torque weight coefficient respectively.
Compared with prior art, present invention has the advantages that：
The present invention is while ensureing that mechanical arm has enough power performance, with certain autokinetic movement ability；The present invention is logical
Cross Adaptive Observer to detect the permanent deviation fault of system actuators, obtain Fault Estimation information and realized instead of fault-signal
Active Fault Tolerant；Mechanical arm, which is effectively overcomed, using feedback compensation mechanism is difficult to Accurate Model and the unstable spy of internal dynamic
Property, make system that there is strong robustness, improve tracking accuracy；Mechanical arm fault-tolerant controller includes trajectory planning layer and tracking control
Preparative layer, every layer, according to different control targes, is based respectively on interactive information between distinct methods design controller, two layers, jointly
Effect, disclosure satisfy that system various requirement, preferably handles input torque constraints and suppression system is uncertain, realize
The faults-tolerant control object procedure of complication system is well arranged.
Brief description of the drawings
Fig. 1 is the structure chart of double-decker faults-tolerant control of the present invention；
Fig. 2 is the failure actual value and estimate comparison diagram of double-decker faults-tolerant control of the present invention；
Fig. 3 is the desired locations of failure system joint 1 and geometric locus figure of double-decker faults-tolerant control of the present invention；
Fig. 4 is the desired locations of failure system joint 2 and geometric locus figure of double-decker faults-tolerant control of the present invention；
Fig. 5 is the failure system joint control input torque figure of double-decker faults-tolerant control of the present invention.
Embodiment
Understand the present invention to be more directly perceived, the detailed description of the invention is provided with reference to accompanying drawing.
As shown in figure 1, the mechanical arm actuator failures fault-tolerant control system of the invention based on double-decker, it utilizes Taylor
Series expansion sets up the discrete fault model of mechanical arm actuator under the permanent deviation fault of actuator, to reduce amount of calculation, improves meter
Efficiency is calculated, real-time is improved.
Mechanical arm fault-tolerant controller includes interactive information between trajectory planning layer and tracing control layer, two layers, according to every layer
Different control targes, separately designs controller, more targeted to problem, wherein, trajectory planning layer controls to integrate based on MPC
The advantage of the ability of the high and good processing constraint of quality, planned course planning control device cooks up one and meets system restriction
The optimal reference locus of condition.Using the status information of target location, constraints and mechanical arm current time as input parameter, if
Corresponding performance index function is counted, system constraints are met.Tracing control layer is set to improve computational efficiency 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, with based on Adaptive Observer pair
Failure is actively diagnosed and estimates 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 that optimal trajectory in time domain is predicted failure mechanical arm using MPC algorithm, by obtained planning
Track passes to tracing control layer；
In tracing control layer, tracing control layer does not consider the external demands such as target location and constraints, using making letter as far as possible
Sliding formwork control is introduced into Model Predictive Control design by the control strategy of easy row, prediction sliding formwork fault model, is missed using tracking
Difference vector structure forecast sliding formwork fault model, based on the excellent control performance and strong robustness of prediction sliding formwork control, planned course
Tracking control unit, realizes the quick and precisely tracking to planned trajectory, and solving-optimizing problem obtains controlling Lu, makes failure mechanical arm system
Each joint of uniting still quickly reaches target location..
Consider the uncertain factor that real system is present, 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-decker can handle the system constraints of presence well, with strong robustness, energy
The permanent deviation fault of complicated machinery arm actuator is effectively solved the problems, such as, the stability and control performance of whole system is ensured.
The keyword processing method and process of mechanical arm actuator failures fault-tolerant control system of the invention based on double-decker
It is as follows：
Step 1: setting up system failure model：
One class has the two joint mechanical arm system of uncertain factor, during system actuators perseverance deviation fault, according to Lagrange
One Euler establishing equation mechanical arm faulty power models
Mechanical arm input constraint
τmin≤τ≤τmax
Wherein,It is that joint position is vectorial (velocity vector, vector acceleration), M (q) ∈ R2×2It is that positive definite is symmetrically used to
Property matrix,It is Coriolis and centrifugation torque vector, G (q) ∈ R2It is torque vector caused by gravity, 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
Failure function, For failure function, T is time of failure.Assuming that failure f norm-boundeds,
I.e. | | f | |≤ρ, ρ are constant.ω is system uncertain factor.τmax, τminIt is the upper bound and the lower bound of input torque respectively.
It is permanent for mechanical arm actuator shown in formula (2) for the difficulty for reducing mechanical arm close coupling, nonlinearity is brought
The state space equation of deviation fault, is carried out discrete by the way of Taylor series expansion, obtains formula (3), makes model accurate
Really description mechanical arm dynamic characteristic, can reduce amount of calculation, quickly realize control algolithm again.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)。
Wherein,
X (k) represents k-th of sampling instant quantity of state, and y (k) represents the output quantity of k-th of sampling instant, and τ (k) represents to adopt for k-th
The control input amount at sample moment.To ensure the accuracy of forecast model, strengthen the robustness of control system, controller will be obtained
Real-time system status information introduces mechanical arm state-space model, reduces the influence of model mismatch.
In track planning layer, using formula (3) as prediction fault model, theory deduction is carried out based on Model Predictive Control and obtained
Optimal control codes, try to achieve according to optimal control codes and cause the optimal predicted state value of performance indications to be controlled as tracking in prediction time domain
The desired value of preparative layer.
In tracing control layer, sliding formwork control is introduced into Model Predictive Control design, it is pre- using tracking error vector construction
Sliding formwork fault model is surveyed, solving-optimizing problem obtains controlling Lu, each joint of failure mechanical arm system is still quickly reached target
Position.
It is current time system state amount, x to remember x (k)r(k+1) it is desired value, xr(k) it is subsequent time desired value.Order with
Track error vector e (k)=x (k)-xr(k), and define
Then tracking error dynamical equation is
Defining sliding formwork function is
S (k)=He (k)
Wherein, H ∈ Rm×2nFor parameter to be designed.
Because sliding mode is unrelated with systematic uncertainty and interference, then predict that sliding formwork fault model is
Step 2: fault diagnosis (FDD) unit is designed：
The need for based on faults-tolerant control, Adaptive Observer good combination property, the good suppression system uncertain factor of energy are utilized
The advantages of, following Failure Observer such as formula (5) is designed, fault message is thus estimated.
Wherein,X (k) estimate is represented,Y (k) estimate is represented,Represent ffault matrix f (k) estimation
Value, L represents the observer gain matrix of appropriate dimension.Suitable gain matrix L is selected to enter based on observer error dynamics equation
Row theory deduction obtains fault message estimate
Step 3: feedback compensation mechanism：
For the prediction fault model of trajectory planning layer, the system actual value y (k) and last time at current k moment are detected first
Error between predicted value y (k | k-P), errors are added with the prediction sliding formwork value y (k+P) at k+P moment and obtain the k+P moment
Closed low predictions output valve
Wherein, ey(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, calculate obtain k moment sliding formwork function currency s (k) first
Deviation between last time predicted value s (k | k-P), passes through prediction sliding formwork value s (k of the gained deviation to the k+P moment afterwards
+ P) carry out feedback compensation, then the closed-loop corrected prediction sliding formwork output at k+P moment
Wherein, es(k)=s (k)-s (k | k-P).hiFor correction coefficient, in general 0 ＜ hi＜ 1.
Can good compensation system uncertainty, lifting system control performance using feedback compensation mechanism.
Step 4: double-decker fault controller
With double-decker optimal control thought, whole fault-tolerant control system is made up of trajectory planning layer and tracing control layer, root
According to every layer of different control targe, controller is separately designed.
1. trajectory planning controller
Upper strata trajectory planning controller is designed using Model Predictive Control Algorithm, according to the physical constraint condition of system itself and people
It is required that target location, be tracing control layer design one comprising each joint of mechanical arm position and speed optimal reference rail
Mark.
Under Model Predictive Control framework, structural behavior target function formula (6), obtaining in control time domain ensures that system is exported
Optimal controlled quentity controlled variable, thus 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, y (k | k-P) is last time to k moment predicted values, ey(k+j) it is prediction
Output error, yp(k+j) it is model prediction output, yopt(k+j) be mechanical arm correction output, τ (k+j-1 | k) is to be optimized
Control variable, qsetIt is joint target location vector, P and M are prediction time domain and control time domain, Q respectivelyi, Ri(Qi＞ 0, Ri＞ 0)
It is customized error weight coefficient and torque weight coefficient respectively.
Due to there is system input constraint, performance index function optimization problem formula (6) is deformed into chemical conversion standard by formula
The quadratic programming problem formula containing constraints, the formula, which can be solved, to be obtained controlling to ensure that system exports optimal numerical value in time domain
Solution, is derived from causing the predicted state value x of best performanceopt(k) reference locus to be tracked as subsequent time.In order to protect
System control performance requirement is demonstrate,proved, still using Rolling optimal strategy, 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 location.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 torque can be directly obtained,
But this method requires accurate system model, and disturbance can not be compensated, and system easily dissipates.Based on prediction sliding formwork control
The good robustness of system, using prediction sliding mode control algorithm design lower floor contrail tracker, suppression system uncertain factor,
Realize the tracking to the optimal reference locus in upper strata so that reality output and reference locus deviation are minimum.
Structural behavior target function formula (7), obtaining ensures that system exports optimal control Lu in control time domain, and will calculate
One-component τ (k | k) act on mechanical arm.
E (k)=x (k)-xr(k)
S (k)=He (k)
es(k+j)=s (k)-s (k | k-j) j=1,2 ..., P
Wherein, x (k) is k moment system state amounts, xr(k) it is that constrained forecast planning control device passes to contrail tracker
In the subsequent time expectation to be tracked, e (k) is tracking error vector, and s (k) is sliding formwork function, represents k moment algorithm based on sliding mode prediction values,
S (k | k-j) is last time to k moment algorithm based on sliding mode prediction values, es(k+j) it is predicated error, sp(k+j) it is prediction sliding formwork output,It is that mechanical arm correction is exported, and τ (k+j-1 | k) it is control variable to be optimized, when P and M are prediction time domain and control respectively
Domain；Qi, Ri(Qi＞ 0, Ri＞ 0) it is customized error weight coefficient and torque weight coefficient respectively.
In the case where not considering constraint, according toSolving-optimizing problem (7) obtains predicting the control of sliding formwork control
Lu
U=- (ΩTQΩ+R)-1ΩTQΦ
According to the thought of rolling optimization, the one-component for only choosing current time optimal control U is the optimal control at current time
The mechanical arm system that amount τ (k) processed=[I 0 ... 0] U is acted on after failure as actual control input.In subsequent time, prediction
Time domain pushes forward simultaneously, and using the measured value that newly obtains as primary condition, re-optimization calculates and obtains τ (k+1), real
Existing rolling optimization.This mode can effective adaptive system latest development, reduce the requirement to system model precision, make control
System can keep actual optimal.
If system actuators occur permanent deviation fault and there is system uncertain factor, it is considered to system input constraint condition,
Fault-tolerant control system is built, effectiveness of the invention is verified.
Fig. 2 is that the joint of mechanical arm the 1st is held when showing 1.5s in the diagnostic result of actuator f1 failures and Fault Estimation, figure
Permanent deviation fault occurs for row device, now f1=3, failure size can effectively be estimated by showing the adaptive failure observer of design.
From the joint of mechanical arm output trajectory shown in Fig. 3-Fig. 4, it can be seen that using double-decker 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 location.When permanent deviation fault occurs for system actuators, the movement output track in the joint of mechanical arm the 1st
Occur acutely shake, then realize the tracking to target location again in a short time, as shown in Figure 3；The joint of mechanical arm the 2nd
The fluctuation of movement output track is little, as shown in figure 4, illustrating that the faults-tolerant control scheme can be compensated to failure well, meets
The performance requirement of fault-tolerant control system.
Fig. 5 shows that mechanical arm system quickly changes, tended towards stability quickly in startup stage, control input torque.In system
After breaking down, corresponding actions can be also made, and whole process is all in the range of input constraint., can according to emulation experiment figure
The mechanical arm faults-tolerant control based on Model Predictive Control and the fault-tolerant control of mechanical arm based on prediction sliding formwork control are combined to find out
Method processed is real in the case of may being broken down to processing actuator come the fault tolerant control method controlled based on double-decker designed
Now the control problem to mechanical arm system is feasible and effective, when solving control input restricted problem with good energy
Power, while also having good performance in terms of suppression system uncertainty, rapidity and stability.
Specific embodiment described above, structure and technology to the present invention are implemented to have made detailed analysis, but and are not used to
Limit the present invention.Do not departing within spirit of the invention and principle, it can further studied, enrich the content of the invention.Cause
This, the scope of the present invention should be defined by claim.
Claims (4)
1. a kind of mechanical arm actuator failures fault-tolerant control system based on double-decker, it is characterised in that the system includes：
The discrete fault model of mechanical arm actuator, is set up using taylor series expansion；
Fault diagnosis (FDD) unit, it is based on Adaptive Observer and failure is actively diagnosed and fault message is estimated, 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 interactive information between trajectory planning layer and tracing control layer, two layers, according to every layer of difference
Control targe, separately design controller, wherein, trajectory planning layer planned course planning control device, cook up one it is full
The optimal reference locus of pedal system constraints；The tracing control layer designs rail to improve computational efficiency using short-cut method
Mark tracking control unit realizes the tracking to reference locus；
Fault model is predicted, in track planning layer, is realized using MPC algorithm and predicts failure mechanical arm optimal trajectory in time domain
Planning, tracing control layer is passed to by obtained planned trajectory；
Sliding formwork fault model is predicted, in tracing control layer, sliding formwork control is introduced into Model Predictive Control design, missed using tracking
Difference vector structure forecast sliding formwork fault model, solving-optimizing problem obtains controlling Lu, makes each joint of failure mechanical arm system still
It is quick to reach target location；
Feedback compensation mechanism compensation system, is compensated to the uncertain factor that real system is present.
2. a kind of method of the mechanical arm actuator failures fault-tolerant control system based on double-decker, it comprises the following steps：
Step 1: setting up discrete system model under actuator failures：For the permanent deviation fault of mechanical arm actuator shown in formula (1)
Kinetic model, sets up the state space equation formula (2) of the permanent deviation fault of mechanical arm actuator, using taylor series expansion pair
Formula (2) carries out sliding-model control, obtains formula (3),
Mechanical arm input constraint
τmin≤τ≤τmax
Wherein,It is that joint position is vectorial (velocity vector, vector acceleration), M (q) ∈ R2×2It is that positive definite is symmetrically used to
Property matrix,It is Coriolis and centrifugation torque vector, G (q) ∈ R2It is torque vector caused by gravity, 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
Failure function, For failure function, T is time of failure.Assuming that failure f norm-boundeds,
I.e. | | f | |≤ρ, ρ are constant；ω is system uncertain factor.τmax, τminIt is the upper bound and the lower bound of input torque respectively；
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,
P(x1)=M-1(q)；
Wherein,
X (k) represents k-th of sampling instant quantity of state, and y (k) represents the output quantity of k-th of sampling instant, and τ (k) represents to adopt for k-th
The control input amount at sample moment；
In track planning layer, using formula (3) as prediction fault model, theory deduction is carried out based on Model Predictive Control and optimized
Controlled quentity controlled variable, tries to achieve according to optimal control codes and causes the optimal predicted state value of performance indications as tracing control layer in prediction time domain
Desired value；
In tracing control layer, sliding formwork control is introduced into Model Predictive Control design, slided using the vectorial structure forecast of tracking error
Mould fault model formula (4), solving-optimizing problem obtains controlling Lu, each joint of failure mechanical arm system is still quickly reached target
Position；
Make tracking error vector e (k)=x (k)-xr(k), wherein, x (k) be current time system state amount, xr(k+1) it is expectation
Value, xr(k) it 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；
Because sliding mode is unrelated with systematic uncertainty and interference, then predict that sliding formwork fault model is
Step 2: fault diagnosis (FDD) unit is designed：Following Failure Observer such as formula (5) is designed, fault message is thus estimated,
Wherein,X (k) estimate is represented,Y (k) estimate is represented,Represent ffault matrix f (k) estimation
Value, L represents the observer gain matrix of appropriate dimension, selects suitable gain matrix L design error failures estimation observer to obtain event
Hinder information estimate
Step 3: feedback compensation mechanism Compensation System Design：By obtained current time actual value and and last time predicted value
Make comparisons, obtain predicated error, feedback compensation is carried out to the predicted value of future time instance by errors value afterwards, can be well
Systematic uncertainty is compensated；
Step 4: double-decker fault controller：With hierarchy optimization control thought, trajectory planning layer considers target position
Put, the condition such as system restriction, 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, it is characterised in that
The trajectory planning controller on upper strata is designed using Model Predictive Control Algorithm, according to the physical constraint condition of system itself and
The target location artificially required, is the optimal ginseng that tracing control layer designs a position comprising each joint of mechanical arm and speed
Examine track；
Under Model Predictive Control framework, structural behavior target function formula (6), obtaining ensures that system output is optimal in control time domain
Controlled quentity controlled variable, 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, y (k | k-j) is last time to k moment predicted values, ey(k+j) it is that prediction is defeated
Go out error, yp(k+j) it 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 location vector, P and M are prediction time domain and control time domain, Q respectivelyi, Ri(Qi＞ 0, Ri＞ 0) point
It is not customized error weight coefficient and torque weight coefficient.
4. the method for mechanical arm actuator failures fault-tolerant control system according to claim 2, it is characterised in that
The contrail tracker of lower floor is designed using prediction sliding mode control algorithm,
Structural behavior target function formula (7), obtaining ensures that system exports optimal control Lu in control time domain, and by the of calculating
One-component τ (k | k) act on mechanical arm：
E (k)=x (k)-xr(k)
S (k)=He (k)
es(k+j)=s (k)-s (k | k-j) j=1,2 ..., P
Wherein, x (k) is k moment system state amounts, xr(k) it is that constrained forecast planning control device passes to contrail tracker and existed
The subsequent time expectation to be tracked, e (k) is tracking error vector, and s (k) is sliding formwork function, represents k moment algorithm based on sliding mode prediction values, s
(k | k-j) is last time to k moment algorithm based on sliding mode prediction values, es(k+j) it is predicated error, sp(k+j) it is prediction sliding formwork output,It is that mechanical arm correction is exported, and τ (k+j-1 | k) it is control variable to be optimized, when P and M are prediction time domain and control respectively
Domain；Qi, Ri(Qi＞ 0, Ri＞ 0) it is customized error weight coefficient and torque weight coefficient respectively.
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