CN103901776B - A kind of industry mechanical arm anti-interference robust adaptive PID control method - Google Patents

Abstract

The present invention relates to a kind of industry mechanical arm anti-interference robust adaptive PID control method, it is characterized in that: robust adaptive PID controller includes PID control item, Self Adaptive Control item, robust control item, the input of PID control item and robust control item is the Position And Velocity error of mechanical hand, the estimated value that input is the uncertain kinetic parameter of mechanical hand of Self Adaptive Control item, PID control item, Self Adaptive Control item, robust control item output through accumulator superposition, it is achieved robust adaptive PID control.

Description

A kind of industry mechanical arm anti-interference robust adaptive PID control method

Technical field

The present invention relates to a kind of industry mechanical arm anti-interference robust adaptive PID control method.

Background technology

Mechanical hand can reduce production cost in modern industry produces, and strengthens homework precision, improves production efficiency, therefore Obtain increasingly being widely applied.But, owing to arm-and-hand system self has strong coupling, nonlinearity and time variation Etc. feature, the control of mechanical hand is caused to face the biggest difficulty.Additionally, the working environment of mechanical hand often exists outside the unknown Boundary's disturbance, and mechanical hand own dynamics there is also uncertain factor, this will cause arm-and-hand system to go out in operation process Existing unstable situation.At present the simplest in industrial machinery hand control and effective method is that linear PD controls, but Showing in Practical Project, using linear PD to control to frequently can lead to drive mechanism has the biggest initial torque to export, in view of reality Drive mechanism excessive initial torque can not be provided, and the maximum moment that mechanical hand itself can bear also is limited, This will make to improve systematic function further by increase PD control gain and be restricted.

Summary of the invention

Present invention aim at providing a kind of industry mechanical arm anti-interference robust adaptive PID control method, it is possible to effectively Improve control accuracy and dynamic property, the enhancing system robustness of industrial machinery hand system.

Realize the object of the invention technical scheme:

A kind of industry mechanical arm anti-interference robust adaptive PID control method, it is characterised in that: robust adaptive PID is controlled Device processed includes that PID control item, Self Adaptive Control item, robust control item, PID control item are machinery with the input of robust control item The Position And Velocity error of hands, the estimated value that input is the uncertain kinetic parameter of mechanical hand of Self Adaptive Control item, PID controls Item, Self Adaptive Control item, robust control item output through accumulator superposition, it is achieved robust adaptive PID control.

The Position And Velocity error of mechanical hand obtains by the following method,

Measurement apparatus records the position of mechanical hand output, velocity amplitude, and comparator is defeated with expectation by aforementioned location, velocity amplitude The position, the velocity amplitude that enter compare acquisition error amount.

The estimated value of the uncertain kinetic parameter of mechanical hand obtains by the following method,

The Position And Velocity error input adaptive controller of mechanical hand, obtains the expectancy rate of uncertain kinetic parameter, The estimated value of uncertain kinetic parameter is obtained again through integrator.

Robust adaptive PID controller when disturbing signal supremum is known designs especially by following method,

1) mathematical description of controlled device:

For an arm-and-hand system with N number of cradle head, its kinetics can be by following second order linear differential side Journey describes:

$M\left(q\right)\stackrel{\·\·}{q}+C(q,\stackrel{\·}{q})\stackrel{\·}{q}+G\left(q\right)+u=\mathrm{\τ}---\left(1\right)$

In formula (1),

q∈RⁿManipulator joint angular displacement vector；

M(q)∈R^n×nThe inertial matrix of mechanical hand；

The centrifugal force of mechanical hand and Ge Shi moment battle array；

G(q)∈RⁿThe gravity item of mechanical hand；

τ∈RⁿThe external control moment of mechanical hand；

u∈RⁿVarious external disturbance items suffered by mechanical hand；

2) dynamics of controlled device:

1. M (q) is positive definite symmetric matrices；

②For skew symmetric matrix；

3. there is a parameter vector depending on robot parameter so that M (q),G (q) meets such as lower linear Relation:

$M\left(q\right)\mathrm{\α}+C(q,\stackrel{\·}{q})\mathrm{\β}+G\left(q\right)=\mathrm{\Ψ}(q,\stackrel{\·}{q},\mathrm{\α},\mathrm{\β})P---\left(2\right)$

In formula (2),For known joint variable function regression matrix, it is mechanical hand generalized coordinates And the known function matrix of all-order derivative；P∈R^mFor describing the unknown Stationary Parameter vector of mechanical hand mass property；

3) robot robust self-adaptive PID controller design when disturbing signal supremum is known:

The arm-and-hand system described for formula (1), when disturbing signal supremum is known, robust adaptive PID controller Design as follows:

$\mathrm{\τ}=-K_{P}e-K_D\stackrel{\·}{e}-K_I\left({\∫}_0^t\mathrm{edt}\right)+\mathrm{\Ψ}(q,\stackrel{\·}{q},{\stackrel{\·}{q}}_k,{\stackrel{\·\·}{q}}_k)\hat{P}+V---\left(3\right)$

$V={\left[\begin{array}{ccc}{v}_1,& ...& v_n\end{array}\right]}^T---\left(4\right)$

$v_i=-(b_1+b_2|\left|e\right||+b_3|\left|\stackrel{\·}{e}\right||+b_4|\left|{\∫}_0^t\mathrm{edt}\right|\left|\right)\mathrm{sgn}\left(x_i\right)---\left(5\right)$

For the estimated value of P, takeExpectancy rate be:

$\stackrel{\·}{\hat{P}}=-{\mathrm{\Φ\Ψ}}^T(q,\stackrel{\·}{q},{\stackrel{\·}{q}}_k,{\stackrel{\·\·}{q}}_k)x---\left(6\right)$

Taking control gain matrix is:

K_P=diag [k_P1,...,k_Pn] (7)

K_D=diag [k_D1,...,k_Dn] (8)

K_I=diag [k_I1,...,k_In] (9)

Wherein, e=q-q_dFor manipulator joint turning error,For manipulator joint angular velocity error, q_dFor Desired joint angles；γ is constant, and γ ＞ 0；b₁, b₂, b₃And b₄All For the constant more than zero；Matrix Φ ∈ R^m×mFor positive definite symmetrical matrix, k_Pi, k_Di, k_IiIt is normal number, and k_Di=k_Ii, i=1, 2,...,n。

The arm-and-hand system described for formula (1), when supremum the unknown of disturbing signal, robust adaptive PID controls Device design is as follows:

$\mathrm{\τ}=-K_{P}e-K_D\stackrel{\·}{e}-K_I\left({\∫}_0^t\mathrm{edt}\right)+\mathrm{\Ψ}(q,\stackrel{\·}{q},{\stackrel{\·}{q}}_k,{\stackrel{\·\·}{q}}_k)\hat{P}+V---\left(10\right)$

$V=-\frac{{\left(\hat{b}\mathrm{\ξ}\right)}^2}{\left(\hat{b}\mathrm{\ξ}\right)\left|\right|x\left|\right|+{\mathrm{\ϵ}}^2}\·x---\left(11\right)$

$\stackrel{\·}{\hat{b}}={\mathrm{\λ}}_1\mathrm{\ξ}\left|\right|x\left|\right|---\left(12\right)$

$\stackrel{\·}{\mathrm{\ϵ}}=-{\mathrm{\λ}}_2\mathrm{\ϵ},\mathrm{\ϵ}\left(0\right)=0---\left(13\right)$

Wherein, b=b₁+b₂+b₃,For the estimated value of b, $\mathrm{\ξ}=\max (1,|\left|e\right||,|\left|\stackrel{\·}{e}\right||,|\left|{\∫}_0^t\mathrm{edt}\right|\left|\right),$ λ₁, λ₂ For arbitrary normal number.

The invention have the benefit that

Controller of the present invention is made up of PID control item, Self Adaptive Control item, robust control item, and adaptive algorithm is used for The uncertain kinetic part of arm-and-hand system estimated by line, robust control item and PID control item be then used for eliminating bounded external disturbance, ART network error and mechanical hand track following error, and the supremum for bounded external disturbance is known and unknown two The situation of kind has separately designed controller；When the initial joint position of mechanical hand and velocity error are bigger, PID/feedback control item plays master Act on, to avoid excessive initial joint moment to export；When the initial joint position of mechanical hand and velocity error are less, adaptive Control item is answered to play a major role, the dynamic property good to ensure arm-and-hand system.Compared with prior art, the present invention can increase The external disturbance that big arm-and-hand system is allowed, improves the dynamic property of arm-and-hand system Trajectory Tracking Control and at finite time Interior tracing control precision.The present invention is applicable to have the most non-linear, the strong coupling and rigid mechanical hand system of time variation Control under bounded environmental perturbation, and the Control platform of system can be effectively improved.

Accompanying drawing explanation

Fig. 1 is the theory diagram of industry mechanical arm of the present invention anti-interference robust adaptive PID control method；

Fig. 2 is the structure chart of robust adaptive PID controller of the present invention；

Fig. 3-Fig. 8 be disturbing signal supremum known time the present invention and existing PD control method the contrast of control effect emulation Figure；

The present invention and the control effect emulation pair of existing PD control method when Fig. 9-Figure 14 is disturbing signal supremum the unknown Than figure.

Detailed description of the invention

As shown in Figure 1, it is achieved the device of industry mechanical arm of the present invention anti-interference robust adaptive PID control method includes surveying Amount device, comparator, robust adaptive PID controller 3, manipulator driving device 4, actuator 5, mechanical hand 6, self-adaptive controlled Device 7 processed, integrator 8.External interference 107 obtains interference measure 108 by measurement apparatus, and is applied on mechanical hand 6, it is desirable to Input 101 obtains the measured value 102(position of expectation input, velocity amplitude by measurement apparatus), and with output valve 109 by measuring The outputting measurement value 110(position of device gained, velocity amplitude) compare, obtain between input measurement value and outputting measurement value Error 103, is input to error 103 obtain in adaptive controller 7 expectancy rate 104 of uncertain kinetic parameter, and passes through Integrator 8 obtains the estimated value 105 of uncertain kinetic parameter, now by error 103 and uncertain Chemical kinetic parameter estimation Value 105 input robust adaptive PID controller 3, obtains control moment 106 by robust adaptive PID controller 3, controls power Square 106 is input to manipulator driving device 4 and controls mechanical hand 6 by actuator 5 and fulfil assignment task, outside inhibiting simultaneously Boundary's disturbed one 07.For obtaining relatively accurate measured value 102 and 110, measurement system needs addition wave filter carry out filtering interfering and make an uproar Sound.

As in figure 2 it is shown, robot robust self-adaptive PID controller includes PID control item 9, Self Adaptive Control item 10, robust Control item 11, the input of PID control item 9 and robust control item 11 is the Position And Velocity error 103 of mechanical hand, self-adaptive controlled The estimated value 105 that input is uncertain kinetic parameter of item 10 processed, above three control item is made through the superposition of accumulator 12 Control with rear formation robust adaptive PID.

For the supremum of Bounded Perturbations signal suffered by mechanical hand whether it is known that to separately design two kinds of robot robust adaptive Answer PID controller.The mathematical description of both controllers is as follows:

1. the mathematical description of controlled device:

For an arm-and-hand system with N number of cradle head, its kinetics can be by following second order linear differential side Journey describes:

$M\left(q\right)\stackrel{\·\·}{q}+C(q,\stackrel{\·}{q})\stackrel{\·}{q}+G\left(q\right)+u=\mathrm{\τ}---\left(1\right)$

(1) in formula,

q∈RⁿManipulator joint angular displacement vector；

M(q)∈R^n×nThe inertial matrix of mechanical hand；

The centrifugal force of mechanical hand and Ge Shi moment battle array；

G(q)∈RⁿThe gravity item of mechanical hand；

τ∈RⁿThe external control moment of mechanical hand；

u∈RⁿVarious external disturbance items suffered by mechanical hand.

2. the dynamics of controlled device:

1. M (q) is positive definite symmetric matrices；

②For skew symmetric matrix；

3. there is a parameter vector depending on robot parameter so that M (q),G (q) is satisfied such as to roll off the production line Sexual relationship:

$M\left(q\right)\mathrm{\α}+C(q,\stackrel{\·}{q})\mathrm{\β}+G\left(q\right)=\mathrm{\Ψ}(q,\stackrel{\·}{q},\mathrm{\α},\mathrm{\β})P---\left(2\right)$

In formula (2),For known joint variable function regression matrix, it is mechanical hand generalized coordinates And the known function matrix of all-order derivative；P∈R^mFor describing the unknown Stationary Parameter vector of mechanical hand mass property.

3. robot robust self-adaptive PID controller design when disturbing signal supremum is known

The arm-and-hand system described for formula (1), when disturbing signal supremum is known, it is ensured that position of manipulator follow the tracks of with The robust adaptive PID controller design of speed Tracking Globally asymptotic is as follows:

$\mathrm{\τ}=-K_{P}e-K_D\stackrel{\·}{e}-K_I\left({\∫}_0^t\mathrm{edt}\right)+\mathrm{\Ψ}(q,\stackrel{\·}{q},{\stackrel{\·}{q}}_k,{\stackrel{\·\·}{q}}_k)\hat{P}+V---\left(3\right)$

$V={\left[\begin{array}{ccc}{v}_1,& ...& v_n\end{array}\right]}^T---\left(4\right)$

$v_i=-(b_1+b_2|\left|e\right||+b_3|\left|\stackrel{\·}{e}\right||+b_4|\left|{\∫}_0^t\mathrm{edt}\right|\left|\right)\mathrm{sgn}\left(x_i\right)---\left(5\right)$

For the estimated value of P, takeExpectancy rate be:

$\stackrel{\·}{\hat{P}}=-{\mathrm{\Φ\Ψ}}^T(q,\stackrel{\·}{q},{\stackrel{\·}{q}}_k,{\stackrel{\·\·}{q}}_k)x---\left(6\right)$

Taking control gain matrix is:

K_P=diag [k_P1,...,k_Pn] (7)

K_D=diag [k_D1,...,k_Dn] (8)

K_I=diag [k_I1,...,k_In] (9)

Wherein, e=q-q_dFor manipulator joint turning error,For manipulator joint angular velocity error, q_dFor Desired joint angles.γ is constant, and γ ＞ 0.b₁, b₂, b₃And b₄All For the constant more than zero.Matrix Φ ∈ R^m×mFor positive definite symmetrical matrix.k_Pi, k_Di, k_IiIt is normal number, and k_Di=k_Ii, i=1, 2,...,n。

4. the robot robust self-adaptive PID controller design during the unknown of disturbing signal supremum

The arm-and-hand system described for formula (1), when supremum the unknown of disturbing signal, use following controller and from Adaptating law, it is ensured that system Globally asymptotic:

$\mathrm{\τ}=-K_{P}e-K_D\stackrel{\·}{e}-K_I\left({\∫}_0^t\mathrm{edt}\right)+\mathrm{\Ψ}(q,\stackrel{\·}{q},{\stackrel{\·}{q}}_k,{\stackrel{\·\·}{q}}_k)\hat{P}+V---\left(10\right)$

$V=-\frac{{\left(\hat{b}\mathrm{\ξ}\right)}^2}{\left(\hat{b}\mathrm{\ξ}\right)\left|\right|x\left|\right|+{\mathrm{\ϵ}}^2}\·x---\left(11\right)$

$\stackrel{\·}{\hat{b}}={\mathrm{\λ}}_1\mathrm{\ξ}\left|\right|x\left|\right|---\left(12\right)$

$\stackrel{\·}{\mathrm{\ϵ}}=-{\mathrm{\λ}}_2\mathrm{\ϵ},\mathrm{\ϵ}\left(0\right)=0---\left(13\right)$

Wherein, b=b₁+b₂+b₃+b₄,For the estimated value of b, $\mathrm{\ξ}=\max (1,|\left|e\right||,|\left|\stackrel{\·}{e}\right||,|\left|{\∫}_0^t\mathrm{edt}\right|\left|\right),$ λ₁, λ₂ For arbitrary normal number, the definition of other parameters is with 3.

The stability of above two controller by choosing suitable Lyapunov function and can combine Barbalat lemma Demonstrate,prove.

It is two kinds of mechanical hands designed by known and unknown two kinds of situations in the above-mentioned supremum for Bounded Perturbations signal In robust adaptive PID controller, gain matrix parameter K_P, K_D(K_D=K_I), Φ and normal number parameter lambda₁, λ₂Choose right The control effect of mechanical hand plays a key effect, it should suitably adjust taking of above-mentioned parameter according to the working environment that mechanical hand is concrete Value, to reach rapidity and the accuracy of mechanical hand tracking desired trajectory.Parameter K_P, K_D(K_D=K_I), Φ, λ₁, λ₂Choose also Unique, during reality is answered, can adopt and experimentally be controlled device parameter tuning, by design robot parameter Adjustment Tests And build test platform, substantially impact system responded according to each regulation parameter, choose suitable optimized amount (such as overshoot and Rise time etc.) and carry out repetition test, until system optimization amount reaches satisfied response, so that it is determined that suitably controller ginseng Number.

By emulation experiment, the Adaptive PD control device that the present invention and burnt Xiao Hong etc. propose is contrasted, further illustrates Beneficial effects of the present invention.Simulation result from Fig. 3-Figure 14 (simulation result include the position in each joint follow the tracks of with speed with Track, position tracking error input with the control in speed Tracking error, the uncertain Chemical kinetic parameter estimation of system and each joint) can To find out, for the manipulator control system under Bounded Perturbations signal function, select suitable situation in controller gain parameter Under, the Adaptive PD control device of the either proposition such as burnt Xiao Hong or the robust adaptive PID controller of the present invention can compensate Uncertain part in external interference and mechanical, hand-driven mechanics, it is achieved mechanical hand is under bounded environmental disturbances and kinetics system System exists Exact trajectory tracking control during uncertain factor.But the control effect of two kinds of controllers is different, with burnt Xiao Hong Comparing Deng the robot robust Adaptive PD control device proposed, the robust adaptive PID controller of the present invention ensure that mechanical hand The more preferable control performance of system.The position of mechanical hand is followed the tracks of and for speed Tracking, the robust adaptive PID control of the present invention Device processed can improve arm-and-hand system tracking accuracy in finite time, accelerates position of manipulator and follows the tracks of and speed Tracking Convergence rate and reduce system overshoot during track following.In the uncertain Chemical kinetic parameter estimation side of mechanical hand Face, the present invention can be obviously reduced the overshoot of estimates of parameters in parameter estimation procedure, and improve the ginseng in finite time Number estimated accuracy.In terms of controlling input, present invention also reduces the seismism of manipulator joint control moment, be more beneficial for Mechanical hand smoothly completes job task and the working life of prolonged mechanical hands.Additionally, compared with existing Adaptive PD control device, The present invention also increases the external interference that arm-and-hand system is allowed, therefore enhances the robustness of arm-and-hand system.

Claims (4)

1. an industry mechanical arm anti-interference robust adaptive PID control method, it is characterised in that: robust adaptive PID controls Device includes that PID control item, Self Adaptive Control item, robust control item, PID control item are mechanical hand with the input of robust control item Position And Velocity error, the input of Self Adaptive Control item is the estimated value of the uncertain kinetic parameter of mechanical hand, and PID controls Item, Self Adaptive Control item, robust control item output through accumulator superposition, it is achieved robust adaptive PID control；

Robust adaptive PID controller when disturbing signal supremum is known designs especially by following method,

1) mathematical description of controlled device:

For an arm-and-hand system with N number of cradle head, its kinetics can be retouched by following Second-order Non-linear Differential Equation State:

$M\left(q\right)\stackrel{\·\·}{q}+C(q,\stackrel{\·}{q})\stackrel{\·}{q}+G\left(q\right)+u=\mathrm{\τ}---\left(1\right)$

In formula (1),

q∈RⁿManipulator joint angular displacement vector；

M(q)∈R^n×nThe inertial matrix of mechanical hand；

The centrifugal force of mechanical hand and Ge Shi moment battle array；

G(q)∈RⁿThe gravity item of mechanical hand；

τ∈RⁿThe external control moment of mechanical hand；

u∈RⁿVarious external disturbance items suffered by mechanical hand；

2) dynamics of controlled device:

1. M (q) is positive definite symmetric matrices；

②For skew symmetric matrix；

3. there is a parameter vector depending on robot parameter so that M (q),G (q) meets lower linear such as and closes System:

$M\left(q\right){\stackrel{\·\·}{q}}_k+C(q,\stackrel{\·}{q}){\stackrel{\·}{q}}_k+G\left(q\right)=\mathrm{\Ψ}(q,\stackrel{\·}{q},{\stackrel{\·}{q}}_k,{\stackrel{\·\·}{q}}_k)P---\left(2\right)$

In formula (2),For known joint variable function regression matrix, be mechanical hand generalized coordinates and The known function matrix of all-order derivative；P∈R^mFor describing the unknown Stationary Parameter vector of mechanical hand mass property；

3) robot robust self-adaptive PID controller design when disturbing signal supremum is known:

The arm-and-hand system described for formula (1), when disturbing signal supremum is known, robust adaptive PID controller design As follows:

$\mathrm{\τ}=-K_{P}e-K_D\stackrel{\·}{e}-K_I\left({\∫}_0^{t}edt\right)+\mathrm{\Ψ}(q,\stackrel{\·}{q},{\stackrel{\·}{q}}_k,{\stackrel{\·\·}{q}}_k)\hat{P}+V---\left(3\right)$

V=[v₁, … v_n]^T (4)

$v_i=-(b_1+b_2|\left|e\right||+b_3|\left|\stackrel{\·}{e}\right||+b_4|\left|{\∫}_0^{t}edt\right|\left|\right)sgn\left(x_i\right)---\left(5\right)$

For the estimated value of P, takeExpectancy rate be:

$\stackrel{\·}{\hat{P}}=-{\mathrm{\Φ\Ψ}}^T(q,\stackrel{\·}{q},{\stackrel{\·}{q}}_k,{\stackrel{\·\·}{q}}_k)x---\left(6\right)$

Taking control gain matrix is:

K_P=diag [k_P1, …, k_Pn] (7)

K_D=diag [k_D1, …, k_Dn] (8)

K_I=diag [k_I1, …, k_In] (9)

Wherein, e=q-q_dFor manipulator joint turning error,For manipulator joint angular velocity error, q_dFor expectation Joint angles；γ is constant, and γ ＞ 0；b₁, b₂, b₃And b₄It is Constant more than zero；Matrix Φ ∈ R^m×mFor positive definite symmetrical matrix, k_Pi, k_Di, k_IiIt is normal number, and k_Di=k_Ii, i=1,2 ..., n。

Industry mechanical arm the most according to claim 1 anti-interference robust adaptive PID control method, it is characterised in that: machine The Position And Velocity error of tool hands obtains by the following method,

Measurement apparatus records the position of mechanical hand output, velocity amplitude, the position that aforementioned location, velocity amplitude are inputted by comparator with expectation Put, velocity amplitude compares acquisition error amount.

Industry mechanical arm the most according to claim 2 anti-interference robust adaptive PID control method, it is characterised in that: machine The estimated value of the uncertain kinetic parameter of tool hands obtains by the following method,

The Position And Velocity error input adaptive controller of mechanical hand, obtains the expectancy rate of uncertain kinetic parameter, then warp Cross integrator and obtain the estimated value of uncertain kinetic parameter.

Industry mechanical arm the most according to claim 3 anti-interference robust adaptive PID control method, it is characterised in that:

The arm-and-hand system described for formula (1), when supremum the unknown of disturbing signal, robust adaptive PID controller sets Count as follows:

$\mathrm{\τ}=-K_{P}e-K_D\stackrel{\·}{e}-K_I\left({\∫}_0^{t}edt\right)+\mathrm{\Ψ}(q,\stackrel{\·}{q},{\stackrel{\·}{q}}_k,{\stackrel{\·\·}{q}}_k)\hat{P}+V---\left(10\right)$

$V=-\frac{{\left(\hat{b}\mathrm{\ξ}\right)}^2}{\left(\hat{b}\mathrm{\ξ}\right)\left|\right|x\left|\right|+{\mathrm{\ϵ}}^2}\·x---\left(11\right)$

$\stackrel{\·}{\hat{b}}={\mathrm{\λ}}_1\mathrm{\ξ}\left|\right|x\left|\right|---\left(12\right)$

$\stackrel{\·}{\mathrm{\ϵ}}=-{\mathrm{\λ}}_2\mathrm{\ϵ},\mathrm{\ϵ}\left(0\right)=0---\left(13\right)$

Wherein, b=b₁+b₂+b₃+b₄, For the estimated value of b,λ₁, λ₂For appointing The normal number of meaning.