On foot the robot gets used to design of ambiguous servo controller oneself

Experimental result makes clear, better land settled this control program rotate speed gives span to be mixed greatly the problem changes when gain of object be accusinged, the rash club sex that improved control system and trends answer character.

Keyword: Walk robot; Servo control; Get used to faintness to control Pan Junmin(Department Of Information And Control Engineering of 　 of And of 　 of The Design Of Adaptive Fuzzy Servo Controller For Quadruped RobotPan Qielu oneself, shanghai Jiaotong University. Shanghai, 200030, p.

R.

China) 　 　 Abstract: This Paper Presents A New Adaptive Fuzzy Control Scheme And Its Application To Speed Servo Control For A Quadruped Robot.

The Scheme Solves Two Problems Successfully Which Are The Large Range Of Speed Set Points And The Time-variant Gain Of The Controlled Object.

Experiment Study Shows That The New Scheme Improves Dynamic Characteristic And Robustness Of The Control System Efficiently.

Key Words: Foreword of Quadruped Robot; Servo Control; Adaptive Fuzzy Control1 (Introduction) 　 walks technology of robot servo control is to decide the robot walks one of crucial technologies of function.

The JTUWM- Ⅲ that develops in Shanghai traffic university 4 sufficient walk in robot joint servo, be accused nonlinear to seeming complex system, its gain follows 4 sufficient robots to the attitude of the leg changes and be changed.

Additional, because rotate speed gives span big, the PID adjuster of reason tradition is satisfied hard on foot the servo of the robot controls a demand.

In last few years, ambiguous control, develop from adaptive control very fast, successful application was obtained in a lot of complex industry procedures, will ambiguous control and be united in wedlock from adaptive control photograph, hopeful obtains better control result to the control object that changes when nonlinear, parameter [1] .

In electric drive control, because sampling cycle is short (a few millisecond arrive between a few millisecond) , demand of algorithmic to control real time sex is high, restricted thereby get used to faintness to control the application in this one domain oneself [2] .

The article puts forward reference of model of type of a kind of increment to get used to ambiguous controller oneself, apply at walking in control of robot speed servo.

This controller gives next mixing to be accused in different rotate speed when changing when object gain, all can obtain good control result, the rash club sex that improved control system effectively thereby and trends answer character.

Brief introduction of system of 2 servo control (　 of Description Of The Servo Control System) walks system of control of servo of speed of robot weak key links is main by 8098 sheet piece joint of electric machinery of servo of circuit of enlarge of power of machine, PWM, dc, robot and measure fast generation set is become, if pursue,1 is shown.

In the graph, ns is given for rotate speed, n is actual measurement rotate speed, vs is voltage of direct current source, u controls a quantity to output signal for PWM, vd is voltage of armature of dc servo electric machinery.

Graph Fig of block diagram of system of control of rotate speed of 1 electric machinery.

1　 of Schematic Diagram Of The Motor Speed Control System because the Tm of Electromechanical time constant of servo electric machinery is ambitious at T1 of electromagnetism time constant, reason broad sense is accused object transfer function but described as [3] : (The Ifz in 1) type is equivalent load current.

K is nonlinear gain.

τ is the output that measures U from control to armature voltage Vd build the time defer between.

K ′ is constant coefficient.

3 control program is designed (Designing The Control Scheme)3.

1 controller structure (structure of controller of servo of speed of 　 of The Controller Structure) is shown 2 times like the graph.

See by the graph, controller basically includes faintness to control algorithm and reference of increment type model to get used to algorithm oneself two parts, give respectively below the introduction.

Graph Fig of graph of construction of system of control of servo of person of 2 disperse career.

2Discrete Model Of The Speed Control System3.

2 faintness control algorithm (ambiguous control of 　 of Fuzzy Control Algorithm) is substantially a kind nonlinear control, reason to a few nonlinear the control result that object be accusinged often can have obtained.

The condition is given to because nonlinear and what bring to control function is adverse,fall in different rotate speed to overcome influence, save computational time, the ambiguous controller that the article used self-regulated to make correction factor [4] .

Correction factor α reachs according to deviation size computation.

Specific control algorithm is as follows: Δ U(k)= β [E(k)- α E(k-1) ] , (　 of 2) 　 (in 3) type, for solid constant, it is the absolute value of the speed deviation of correspondence of the place when S of α = α .

β is E(k) of rotate speed deviation and deviation change ratio [E(k)-e(k-1) ] quantify factor.

3.

3 from adaptive control algorithm (because 　 of Adaptive Control Algorithm) is accused object gain is change, this caused adverse effect with respect to the dynamic performance that gives control the system, serious when bring about a system to be not stabilized, because this is necessary,undertake gain is compensated.

Civil [5] model of gain of the make a present of before introducing a kind is referenced from adaptive control plan.

But this algorithm can not apply directly.

By type (1) is visible, electric machinery rotate speed measures U to concern with control not only, and concern with laden moment of force.

As a result of 4 sufficient laden moment of force cannot be measured in system of robot servo control on foot, reason cannot press type (1) builds referenced model.

We discuss the case with laden constant and changeless moment of force above all below, right now Ifz is constant.

Pure lag τ is contented in presumably type: 0<L<Ts of τ =(d-1)Ts+L; 　 .

(The D in 4) type is integral, ts is contented sweet farming theorematic sampling is periodic.

Should use 0 rank sampling maintains implement when, the Z transfer function of discrete system is: N(z)=H(z)u(z)+K ′ Ifz, (5) 　 　 (the 　 in 6) type (　 of 7) 　 (8) 　 　 (9) gets used to algorithmic influence oneself to eliminate constant and laden moment of force to be opposite, to type (5) both sides is multiplied together with (1-z-1) builds referenced model, can derive reference of increment type model gets used to a system oneself, if its structure pursues the place in 2 pane is shown.

The reference of increment type model of above introduction gets used to algorithm to be able to use oneself below description of a group of equation that need branch: Y(k)= [N(k)-n(k-1) ] + A1 [N(k-1)-n(k-2) ] , (Δ of 10)ym(k)=b0 Δ U(k-d)+b1 U(k-d-1) , (11) ε (K)=y(k)-ym(k) , (12) θ (K)=- γ ε (K)ym(k)+ θ (K-1); θ (0)=1.

0, (13)u(k)= θ (K) Δ U(k)+u(k-1) .

(14) type (in 13) , γ is get used to rate oneself.

Type (10) ～ (14) and type (2)(3) formed complete get used to faintness to control algorithm oneself.

By the graph 2 visible, the output θ action that gets used to link oneself at Δ U(k) , and rather than is direct action at U(k) , its purpose is to avoid pair of because of the change of θ objects be accusinged to cause bigger impact, (Because | U(k) Δ θ | >> | θ of Δ U(k) Δ | ) .

3.

4 what get used to algorithm oneself is perfect (The Amendment Of The Adaptive Algorithm)3.

4.

1 astringent condition (Convergence Conditions) 　 gets used to ambiguous control oneself in above in algorithm, according to the balance of average theory condition is analysed [6] , u(k) of Δ of command signal of referenced model input must be first-order and incentive signal at least, want to make sure incentive signal has certain amplitude, parameter θ ability is convergent at its true value.

Walk robot servo process is such: Above all You Jing stops to come quickly give rotate speed, maintain next in this one constant rotate speed runs, be about to arrive at the decelerate when target position, enter positional servo phase.

Apparent, quickening, decelerate phase, u(k) of Δ of referenced model command signal is amplitude is very big rank jump signal, the basis lasts incentive signal differentiate is theorematic [6] , rank jumping signal is first-order continuously incentive signal, reason satisfies convergent requirement.

But the division runs in constant speed, when laden moment of force keeps changeless, good case issues Yu Ling of Δ U(k) approach, if get used to operation oneself in proceed of this one phase, estimate θ of gain of the make a present of before bringing about to variance increases ceaselessly.

A simple way is dead band introduces in getting used to algorithm oneself, algorithm is as follows: | N(k)-ns | When ≥ Ndead, continue to get used to algorithm oneself; | N(k)-ns | When <ndead, break down gets used to operation oneself; The Ndead in type is constant, when the spot is debugged, according to suiting oneself the effect tries to decide.

3.

4.

2 get used to rate to amend oneself (　 of Modifying The Adaptive Rate) is analysed by stability [6] know, get used to loop stability to consult amplitude of U(k) of Δ of model input signal is concerned together oneself.

When Δ U(k) amplitude increases, to keep stable, get used to rate to should be reduced accordingly oneself.

On the other hand, by astringent analysis [6] knowable, before the convergent rate direct ratio of θ of gain of make a present of the square at Δ U(k) amplitude, this is unreasonable apparently, a reasonable parameter adjusts a law to should input the amplitude of signal to have nothing to do with referenced model.

Be based on above two respects reason, be necessary to undertake correction to getting used to rate oneself.

By type (2) is knowable, u(k) of Δ of increment of output control quantity is approximate on quantitative class direct ratio at rotate speed deviation, we used reason below this kind gets used to rate to revise a method oneself: (In 15) type, γ 0 to get used to rate initial value oneself.

To avoid to eliminate 0 appearances, introduce invariable λ > 0.

Because the existence when sampling measures noise, when amplitude of reason Δ U(k) is lesser, make get used to rate direct ratio oneself the square at its amplitude is beneficial, because this λ shoulds not be too small.

3.

4.

The influence that 3 laden moment of force disturb and compensation (the reference of increment type model that puts forward before 　 of The Effect Of Load Interference And Its Compensation) gets used to a system oneself is to be based on laden moment of force to be worth what reach below this one premise for constant.

In fact, laden moment of force is constant change, and happen to be jumped substantially likely change, this can give the effect with get used to algorithm to cause certain oneself.

By the graph 2 visible, an integrator is included in getting used to link oneself, this is equivalent to low connect filter, can filter goes laden moment of force disturbs brought high frequency noise.

Because get used to rate to take a cost oneself lesser, the laden moment of force of reason little scope is fluctuant (assume for white noise) do not produce any effects to getting used to link to output θ oneself.

When laden moment of force increases by degrees continuously with minor rate or decreasing successively, analyse not hard, the deviate that gets used to output θ to will have fixed rate with true value oneself (deviation size decides) by rate of change of outside force rules.

But this won't bring adverse effect to control system, contrary, it is equivalent to giving control effect of the make a present of before the system increased laden moment of force, go up somehow can improve control performance.

Change when laden moment of force rate is older and when range is bigger also, for instance substantially jump change, can give get used to link to bring adverse effect oneself, θ value fluctuates substantially, serious when bring about a system to be not stabilized.

To overcome this one weakness, adopt the following algorithm: | Ym(k)-y(k) | ≤ η [| Ym(k) | + | Y(k) | ] when, continue to get used to algorithm oneself; | Ym(k)-y(k) | > η [| Ym(k) | + | Y(k) | ] when, break down gets used to algorithm oneself; In type, η is [0, 1] the constant on interval.

This algorithmic essence is the moment of force outside becoming disturbs bigger when, bigger error arises between Ym(k) and Y(k) , the computer thinks this sampling is bad value, give eliminate.

Adjust η is worth size, be equivalent to those who adjust good value and bad value delimiting dividing line is restricted namely.

η value is too little, often cause the change that gets used to link to cannot compensate gain of object be accusinged in time oneself; η value is too great, θ gets laden moment of force interference is serious, wave motion is bigger.

Reason η is worth should when the basis is debugged, actual condition tries to choose.

4 tests result (the article uses Experiment Results) 　 MCS98 assembly language wove servo controls a process, in JTUWM- Ⅲ model 4 sufficient undertook the experiment studies on the robot on foot.

Robot joint sheds servo electric machinery to be the R406T-11 that 3 foreign companies of Japanese produce electric machinery continuously.

Choice sampling cycle is 4ms.

To raise computational precision, operation of check the number of 3 byte float was used in the program.

Additional, measure noise to reduce, undertook to speed sampling signal digital filter wave is handled.

Get used to the effect oneself to highlight, increase to be accused in the experiment through changing Vs of power source voltage the span of object gain K.

Graph 3 gave out laden moment of force rank jump faze to move curve of below the circumstance one group of comparative experiments.

In the graph, the abscissa represents time, the unit is a second.

The A/D that Zun Zong reference axis shows rotate speed changes a value (decimal numeral) , rotate speed gives Ns=80.

Experimental process is as follows: Disconnect to get used to loop oneself above all, when power source voltage is 13V, adjust ambiguous controller parameter is gotten optimal rank jump answer a curve (graph 3(a)) .

Maintain ambiguous controller parameter next changeless, rise power source tension 24V, measure take rank jump answer a curve (graph 3(b)) .

Farther, close get used to loop oneself, below condition of parameter of likewise ambiguous controller, measure those who take condition of two kinds of voltage to fall respectively by similar move rank jump answer a curve (3(d)) of graph 3(c) , graph.

Still gave out to control the metabolic curve of θ of gain of the make a present of before the process is medium in 3(d) of graph 3(c) , graph, its are right ordinate axis expresses θ .

Additional, in above experiment process, when rotate speed stability is near set value hind, factitious ground increases the load with equal size pitching moment rank is jumped disturb, faintness suits in order to observe laden moment of force disturbs to dominate algorithmic result oneself below the circumstance.

Compare 3(b) of graph 3(a) , graph to see, using the condition that gets used to link oneself to fall, add by 13V when power source voltage to 24V when, ambiguous controller controls the effect to drop substantially, speed oscillation aggravate.

Used after getting used to link oneself, when Vs of power source voltage is 13V, see by graph 3(c) , θ of gain of make a present of maintains before in 1.

0 around; And rise when power source voltage to 24V when, see by graph 3(d) , θ by 1.

0 fall to 0.

40 the left and right sides, compensated the change of K of gain of object be accusinged accurately, achieve better control result thereby.

By the graph 3(c) , 3(d) still can be seen, because adopted a few perfect measure, overcame the adverse effect that laden moment of force disturbs to be brought to getting used to algorithm oneself effectively, change substantially in laden moment of force when, article algorithm still can work reliably.

Graph 3.

Get used to effect contrast to try test result Fig oneself.

3　 of Experiment Results With And With Out The Adaptive Algaritm pursues 4 it is power source voltage when be 24V, to what place in different rotate speed speed rank is jumped answer a curve, reference axis states method and graph 3(c) are identical.

See by the graph, because used nonlinear faintness to control strategy, better land overcame rotate speed to give span to give control the adverse effect that function brings greatly, give in different rotate speed below, should get used to ambiguous controller to all obtain good control result oneself.

Additional, for many times the experiment makes clear, if use groovy faintness to control algorithm, difference of fluctuant mean square is in rotate speed 6 ～ between 15 limits, and after using article algorithm, difference of this mean square maintains in 7 less than, effect improvement is marked.

Graph 4 different rotate speed give Fig of result of the test below the condition.

4Last word of Experiment Results With Different Speed Set Poins5 (the article is aimed at Conclusion) 　 on foot medium speed of control of robot speed servo gives span to be mixed greatly the problem that changes when gain of object be accusinged, designed reference of model of type of a kind of increment to get used to ambiguous controller oneself, a few specific problems that in carrying out a process to algorithm, encounter gave out practical settlement method.

Experimental result makes clear, this controller algorithm is simple, real time sex is good, the rash club sex that improved control system greatly and trends answer character.

In the other control domain such as process control, a lot of objects be accusinged but described as type (the form that 1) place shows, what the article puts forward apply to get used to faintness to dominate program oneself in these domains, be expected to achieve good control result.

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