CN101807878B - Servo system control method based on relay feedback - Google Patents

Abstract

The invention relates to a servo system control method based on relay feedback, belonging to the technical field of motion control. The method comprises the following steps of: controlling a servo system for the first time by using a relay with an initial amplitude value to acquire a rotation rate after initial motion time; acquiring a relay amplitude value corresponding to the upper limit and the lower limit of the rotation rate according to the motion information of the first time, and respectively carrying out motion control on the servo system for the second time and the third time under the amplitude value through the relay in a time delay mode to acquire a stable response amplitude and a stable response cycle; identifying system model parameters and a dry friction magnitude according to the motion information of the second time and the third time; and carrying out optimization of control parameters and feedforward compensation of dry friction based on the identified parameters. The method of the invention can be used for quickly optimizing controller parameters and realizing effective compensation of friction, thereby improving the control accuracy of the servo system.

Description

Servo system control method based on relay feedback

Technical field

What the present invention relates to is the method in a kind of movement control technology field, specifically is a kind of servo system control method based on relay feedback.

Background technology

Servo system has been widely used in modern industry, and its closed loop controlling structure can obtain accurate position and speed control.Cascade PID control method is adopted in traditional servo system control, and its parameter testing has two class basic skills: one, direct debugging method, as ZN method and improvement ZN method; Two, based on the method for model, as width of cloth phase nargin method and POLE PLACEMENT USING method etc.In method based on model, at first will comprise external interference and be approximated to linear model in interior system, according to this model debugging control parameter, the method is effective under the not high situation of required precision then.But when required precision improves, just need compensate interference.

It is very strong non-linear that frictional force is that servo system topmost external interference, particularly dry friction partly have, and the performance of servo system is had very big influence.The model that static friction adds viscous friction can react the characteristic of frictional force to a certain extent, carries out the raising that Friction Compensation can realize the certain precision of servo system according to this.In order to realize the high performance control of servo system, key issue is how to determine the parameter of system model and frictional force model.At a certain specific equipment, the parameter of its frictional force model can record by repeatedly testing, but this method requires a great deal of time and manpower, and all needs to repeat this process for different equipment or operating mode, has brought very big trouble to actual production.Identification system model and frictional force model parameter have important use value to improving the servo system performance apace.

Through existing literature search is found, Chinese patent application number is 200810018783.0, name is called " the transmission inertia identification method of AC servo ", and this technology discloses utilizes servo system acceleration and deceleration motion identification load inertia, but has ignored other characterisitic parameters of system.

Find by retrieval again, Chinese patent application number is 200910051179.2, name is called " based on the AC servo automatic setting method of relay feedback ", and this technology is approximately single order with the speed ring of servo system and adds delay model, and utilizes relay feedback to come the parameter of this model of identification.But it is approximate in linear model that it will have nonlinear frictional force, can't carry out Friction Compensation.

Also find by retrieval, Si-Lu Chen etc. are at document " Friction Modeling and Compensation ofServomechanical Systems With Dual Relay Feedback Approach (based on the servo system friction force modeling and the compensation method of two relay feedback methods) " (IEEE Transactions on Control Systems Technology, 2009) use parallel relay feedback to come identification frictional force model in, obtained good effect.But the method selects that to the parameter of identification algorithm certain requirement is arranged, and is unfavorable to practical application.

Summary of the invention

The objective of the invention is to overcome the prior art above shortcomings, a kind of servo system control method based on relay feedback is provided.The present invention controls the method that servo system is moved twice by Intelligence Selection two group relay parameters and with this parameter, realized the off-line identification of servo system dry friction and model parameter, and, has the effectively advantage of compensation of the selection of relay parameter intelligent, Control Parameter rapid Optimum and dry friction based on this realization Control Parameter optimization and Friction Compensation.

The present invention is achieved by the following technical solutions, the present invention includes following steps:

Step 1, it is the Torque Control pattern that servo system is set, and sets the speed of service upper limit ω of servo system _u, servo system movement velocity lower limit ω _l, time-delay d, the initial magnitude h of relay ₀And initial motion time t ₀

Step 2 is at initial motion time t ₀In, utilize initial magnitude to be h ₀Relay servo system is carried out the motion control first time, obtain servo system in the first time motion control rotational speed omega of the finish time ₀

Step 3 makes the servo system fine motion for pulse command of servo system, and in the time-delay d of relay, utilizing for the second time, amplitude is h _uRelay servo system is carried out the motion control second time, make servo system obtain stable vibration, and write down the response amplitude a in this vibration _uWith response cycle t _u

Described second time amplitude h _u, specifically:

$h_u=\frac{{4\mathrm{\&omega;}}_u{\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="HDA0000020174970000011.png,HDA0000020174970000012.png"\; state="\{\{state\}\}">t</figure-callout>}}_0}{{5\mathrm{\&omega;}}_0\mathrm{<figure-callout\; id="0"\; label="d\; h"\; filenames="HDA0000020174970000011.png,HDA0000020174970000012.png"\; state="\{\{state\}\}">d</figure-callout>}}{h}_{}{}_0,$

Wherein: ω _uBe the speed of service upper limit, h ₀Be initial magnitude, t ₀Be the initial motion time, d is the time-delay of relay, ω ₀It is the rotating speed of the finish time of motion control for the first time.

Step 4 makes the servo system fine motion for pulse command of servo system, and in the time-delay d of relay, utilizing for the third time, amplitude is h _lRelay servo system is carried out motion control for the third time, make servo system obtain stable vibration, and write down the response amplitude a in this vibration _lWith response cycle t _l

The described h of amplitude for the third time _l, specifically:

$h_l=\frac{{4\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="0"\; label="l\; t"\; filenames="HDA0000020174970000011.png,HDA0000020174970000012.png"\; state="\{\{state\}\}">l</figure-callout>}}{t}_{}{}_0}{{5\mathrm{\&omega;}}_0\mathrm{<figure-callout\; id="0"\; label="d\; h"\; filenames="HDA0000020174970000011.png,HDA0000020174970000012.png"\; state="\{\{state\}\}">d</figure-callout>}}{h}_{}{}_0,$

Wherein: ω _lBe the movement velocity lower limit, h ₀Be initial magnitude, t ₀Be the initial motion time, d is the time-delay of relay, ω ₀It is the rotating speed of the finish time of motion control for the first time.

Step 5, use the speed responsive of the approximate servo system of first order modeling, and use static friction to add the frictional force interference that viscous friction power model is similar to servo system, thereby obtain the model parameter of servo system, that is: timeconstant, static gain k and stiction f.

Described timeconstant, specifically:

$\mathrm{\&tau;}=\frac{{2\mathrm{kh}}_u\sin \left({\mathrm{d\&omega;}}_u\right)}{{\mathrm{\&pi;a}}_u{\mathrm{\&omega;}}_u}+\frac{{2\mathrm{kh}}_l\sin \left({\mathrm{d\&omega;}}_l\right)}{{\mathrm{\&pi;a}}_l{\mathrm{\&omega;}}_l},$

Wherein:

K is a static gain, ω _uBe the speed of service upper limit, ω _lBe the movement velocity lower limit, d is the time-delay of relay, h _uBe the amplitude second time, h _lBe amplitude for the third time, a _uBe the response amplitude that motion control for the second time obtains, t _uBe the response cycle that motion control for the second time obtains, a _lBe the response amplitude that motion control for the third time obtains, t _lIt is the response cycle that motion control for the third time obtains.

Described static gain k, specifically:

$k=-\frac{\mathrm{\&pi;}}{4}\frac{a_u-a_l}{h_u\cos \left({\mathrm{d\&omega;}}_u\right)-h_l\cos \left({\mathrm{d\&omega;}}_l\right)},$

Wherein:

a _uBe the response amplitude that motion control for the second time obtains, a _lBe the response amplitude that motion control for the third time obtains, d is the time-delay of relay, h _uBe the amplitude second time, h _lBe amplitude for the third time, t _uBe the response cycle that motion control for the second time obtains, t _lIt is the response cycle that motion control for the third time obtains.

Described stiction f, specifically:

$f=\frac{a_l{h}_u\cos \left({\mathrm{d\&omega;}}_u\right)-a_u{h}_l\cos \left({\mathrm{d\&omega;}}_l\right)}{a_u-a_l},$

Wherein:

a _uBe the response amplitude that motion control for the second time obtains, a _lBe the response amplitude that motion control for the third time obtains, d is the time-delay of relay, h _uBe the amplitude second time, h _lBe amplitude for the third time, t _uBe the response cycle that motion control for the second time obtains, t _lIt is the response cycle that motion control for the third time obtains.

Step 6 according to the model parameter of identification, is utilized existing P ID parameter designing principles such as POLE PLACEMENT USING method or width of cloth phase nargin method to optimize pid control parameter, and increase feedforward term in controller, utilizes the dry friction identified parameters to carry out Friction Compensation.

Described Friction Compensation, specifically:

$u=k_{p}e+k_i\&Integral;\mathrm{edt}+k_d\stackrel{\&CenterDot;}{e}+\mathrm{fsign}\left({\stackrel{\&CenterDot;}{x}}_d\right),$

Wherein: u is a controlled quentity controlled variable, e=x _d-x,

k _p, k _i, k _dBe respectively proportionality constant, integral constant and derivative constant, x _d,

Be respectively instruction displacement and command speed, x,

Be respectively output displacement and output speed,

Be frictional force feedforward compensation item, f is a stiction,

The is-symbol function is promptly worked as

The time, When

The time,

Compared with prior art, the invention has the beneficial effects as follows: the present invention only needs the user that nonlinear coulomb friction size in model parameter that the velocity of rotation scope of servo system in its actual production can pick out system apace and the frictional force is provided, for the Control Parameter of servo system is selected and the compensation of frictional force provides foundation, the final control precision that improves servo system promptly has the effectively advantage of compensation of the selection of relay parameter intelligent, Control Parameter rapid Optimum and dry friction.

Description of drawings

Fig. 1 is the vibratory response figure of embodiment motion control for the first time;

Wherein: (a) be the input curve of embodiment motion control for the first time; (b) be the response curve of embodiment motion control for the first time.

Fig. 2 is the vibratory response figure of embodiment motion control for the second time;

Wherein: (a) be the input curve of embodiment motion control for the second time; (b) be the response curve of embodiment motion control for the second time.

Fig. 3 is the vibratory response figure of embodiment motion control for the third time;

Wherein: (a) be the input curve of embodiment motion control for the third time; (b) be the response curve of embodiment motion control for the third time.

Fig. 4 is displacement curve and the rate curve of embodiment;

Wherein: (a) be the displacement curve of embodiment; (b) be the rate curve of embodiment.

Fig. 5 is the displacement tracking curve that prior art (zerofriction force compensation) obtains.

Fig. 6 is the displacement tracking curve that embodiment method (Friction Compensation is arranged) obtains.

Embodiment

Below in conjunction with accompanying drawing method of the present invention is further described: present embodiment is being to implement under the prerequisite with the technical solution of the present invention, provided detailed execution mode and concrete operating process, but protection scope of the present invention is not limited to following embodiment.

Embodiment

The servo system of present embodiment is peace river SGMAH-A5AAA41 AC servo motor and supporting servo controller SGDM-A5ADA, and present embodiment may further comprise the steps:

Step 1: it is the Torque Control pattern that servo system is set, and sets the speed of service upper limit ω of servo system _uThe movement velocity lower limit ω of=3000rpm, servo system _l=600rpm, time-delay d=25ms, the initial magnitude h of relay ₀=5000 and initial motion time t ₀=10ms.

Step 2 is at initial motion time t ₀In=the 10ms, utilize initial magnitude to be h ₀=5000 relay carries out the motion control first time to servo system, obtains servo system in the first time motion control rotational speed omega of the finish time ₀=500rpm.

The input curve that obtains in this motion control is shown in Fig. 1 (a), and response curve is shown in Fig. 1 (b).

Step 3 makes the servo system fine motion for pulse command of servo system, and in the time-delay d=25ms of relay, utilizing for the second time, amplitude is h _uRelay servo system is carried out the motion control second time, make servo system obtain stable vibration, and write down the response amplitude a in this vibration _u=2900rpm and response cycle t _u=90ms.

Described second time amplitude h _u, specifically:

$h_u=\frac{{4\mathrm{\&omega;}}_u{\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="HDA0000020174970000011.png,HDA0000020174970000012.png"\; state="\{\{state\}\}">t</figure-callout>}}_0}{{5\mathrm{\&omega;}}_0\mathrm{<figure-callout\; id="0"\; label="d\; h"\; filenames="HDA0000020174970000011.png,HDA0000020174970000012.png"\; state="\{\{state\}\}">d</figure-callout>}}{h}_{}{}_0=\frac{4*3000*10}{5*500*25}*5000=9600.$

The input curve that obtains in this motion control is shown in Fig. 2 (a), and response curve is shown in Fig. 2 (b).

Step 4 makes the servo system fine motion for pulse command of servo system, and in the time-delay d=25ms of relay, utilizing for the third time, amplitude is h _lRelay servo system is carried out motion control for the third time, make servo system obtain stable vibration, and write down the response amplitude a in this vibration _l=486rpm and response cycle t _l=76ms.

The described h of amplitude for the third time _l, specifically:

$h_l=\frac{{4\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="0"\; label="l\; t"\; filenames="HDA0000020174970000011.png,HDA0000020174970000012.png"\; state="\{\{state\}\}">l</figure-callout>}}{t}_{}{}_0}{5{\mathrm{\&omega;}}_0\mathrm{<figure-callout\; id="0"\; label="d\; h"\; filenames="HDA0000020174970000011.png,HDA0000020174970000012.png"\; state="\{\{state\}\}">d</figure-callout>}}{h}_{}{}_0=\frac{4*600*10}{5*500*25}*5000=1920.$

The input curve that obtains in this motion control is shown in Fig. 3 (a), and response curve is shown in Fig. 3 (b).

Step 5, use the speed responsive of the approximate servo system of first order modeling, and use static friction to add the frictional force interference that viscous friction power model is similar to servo system, thereby obtain the model parameter of servo system, that is: timeconstant, static gain k and stiction f.

The response frequency ω of motion control for the second time in the present embodiment _u, specifically:

${\mathrm{\&omega;}}_u=\frac{2\mathrm{\&pi;}}{t_u}=\frac{2\mathrm{\&pi;}}{90}=0.069813\mathrm{rad}/\mathrm{ms}.$

The response frequency ω of motion control for the third time in the present embodiment _l, specifically:

${\mathrm{\&omega;}}_l=\frac{2\mathrm{\&pi;}}{4_l}=\frac{2\mathrm{\&pi;}}{76}=0.082673\mathrm{rad}/\mathrm{ms}.$

Described static gain k, specifically:

$k=-\frac{\mathrm{\&pi;}}{4}\frac{a_u-a_l}{h_u\cos \left({\mathrm{d\&omega;}}_u\right)-h_l\cos \left({\mathrm{d\&omega;}}_l\right)}$

$=-\frac{\mathrm{\&pi;}}{4}\frac{2900-486}{9600*\cos (25*0.069813)-1920*\cos (25*0.082673)}.$

$=2.517$

Described timeconstant, specifically:

$\mathrm{\&tau;}=\frac{{2\mathrm{kh}}_u\sin \left({\mathrm{d\&omega;}}_u\right)}{{\mathrm{\&pi;a}}_u{\mathrm{\&omega;}}_u}+\frac{{2\mathrm{kh}}_l\sin \left(d{\mathrm{\&omega;}}_l\right)}{{\mathrm{\&pi;a}}_l{\mathrm{\&omega;}}_l}$

$=\frac{2*k}{\mathrm{\&pi;}}(\frac{9600*\sin (10*0.069813)}{2900*0.069813}+\frac{1920*\sin (10*0.096813)}{486*0.096813}).$

$=142.1779\mathrm{ms}$

Described stiction f, specifically:

$f=\frac{a_l{h}_u\cos \left({\mathrm{d\&omega;}}_u\right)-a_u{h}_l\cos \left(d{\mathrm{\&omega;}}_l\right)}{a_u-a_l}$

$=\frac{486*9600*\cos (10*0.069813)-2900*1920*\cos (10*0.096813)}{2900-486}.$

$=762.1798$

Step 6 according to the model parameter of identification, is used the PD controller in position ring, and the closed-loop pole that adopts the POLE PLACEMENT USING method that control system is set is compound radical-30, and increases feedforward term in controller, utilizes the dry friction identified parameters to carry out Friction Compensation.

Under PD control, the transfer function of closed-loop system is:

$G\left(s\right)=\frac{(k_p+k_{d}s)\frac{k}{(\mathrm{\&tau;s}+1)}}{1+(k_p+k_{d}s)\frac{k}{(\mathrm{\&tau;s}+1)}}=\frac{(k_p+k_{d}s)k}{{\mathrm{\&tau;s}}^2+(1+k_{d}k)s+k_{p}k}.$

Timeconstant is changed into standard unit, i.e. τ=0.1422s.Obtain by characteristic equation and characteristic root:

kk _p/τ＝-30*(-30)

-(1+k _dk)/τ＝-30-30

Thereby controlled parameter k _p=50.8, k _d=2.99.

The controlled quentity controlled variable that finally obtains system is:

$u=50.8*e+2.99*\stackrel{\&CenterDot;}{e}+762.1798*\mathrm{sign}\left({\stackrel{\&CenterDot;}{x}}_d\right)$

Wherein: e=x _d-x,

x _d, Be respectively instruction displacement and command speed, x,

Be respectively output displacement and output speed, Be frictional force feedforward compensation item,

The is-symbol function is promptly worked as

The time,

When

The time,

The displacement curve of the platform command curve of present embodiment is shown in Fig. 4 (a), and rate curve is shown in Fig. 4 (b).

Adopt art methods, response curve when using above-mentioned PD control (zerofriction force compensation) as shown in Figure 5, as can be seen from Figure 5: because the influence of dry friction, the displacement tracking error has tangible deviation with the change of velocity attitude, and maximum tracking error about 0.0062 changes, and the mean square of error value is 9.7 * 10 ^-5Change; Under identical PD controller, the response curve that obtains when using embodiment method (increasing the feedforward compensation of dry friction) as shown in Figure 6, as can be seen from Figure 6: maximum tracking error about 0.004 changes, and the mean square of error value is 2.1 * 10 ^-5Change, compare with Fig. 5, maximum tracking error has reduced by 30%, and the mean square of error value has reduced by 70%, thereby has proved that fully the present embodiment method has improved the control precision to servo system greatly.

Claims (1)

1. the servo system control method based on relay feedback is characterized in that, may further comprise the steps:

Step 1, it is the Torque Control pattern that servo system is set, and sets the speed of service upper limit ω of servo system _u, servo system movement velocity lower limit ω _l, time-delay d, the initial magnitude h of relay ₀And initial motion time t ₀

Step 2 is at initial motion time t ₀In, utilize initial magnitude to be h ₀Relay servo system is carried out the motion control first time, obtain servo system in the first time motion control rotational speed omega of the finish time ₀

Step 3 makes the servo system fine motion for pulse command of servo system, and in the time-delay d of relay, utilizing for the second time, amplitude is h _uRelay servo system is carried out the motion control second time, make servo system obtain stable vibration, and write down the response amplitude a in this vibration _uWith response cycle t _u

Step 4 makes the servo system fine motion for pulse command of servo system, and in the time-delay d of relay, utilizing for the third time, amplitude is h _lRelay servo system is carried out motion control for the third time, make servo system obtain stable vibration, and write down the response amplitude a in this vibration _lWith response cycle t _l

Step 5, use the speed responsive of the approximate servo system of first order modeling, and use static friction to add the frictional force interference that viscous friction power model is similar to servo system, thereby obtain the model parameter of servo system, that is: timeconstant, static gain k and stiction f;

Step 6 according to the model parameter of identification, is utilized POLE PLACEMENT USING method or width of cloth phase nargin method existing P ID parameter designing principle to optimize pid control parameter, and increase feedforward term in controller, utilizes the dry friction identified parameters to carry out Friction Compensation;

Described second time amplitude h _u, specifically:

$h_u=\frac{4{\mathrm{\&omega;}}_u{t}_0}{5{\mathrm{\&omega;}}_{0}d}{h}_0,$

Wherein: ω _uBe the speed of service upper limit, h ₀Be initial magnitude, t ₀Be the initial motion time, d is the time-delay of relay, ω ₀It is the rotating speed of the finish time of motion control for the first time;

The described h of amplitude for the third time _l, specifically:

$h_l=\frac{4{\mathrm{\&omega;}}_l{t}_0}{5{\mathrm{\&omega;}}_{0}d}{h}_0,$

Wherein: ω _lBe the movement velocity lower limit, h ₀Be initial magnitude, t ₀Be the initial motion time, d is the time-delay of relay, ω ₀It is the rotating speed of the finish time of motion control for the first time;

Described timeconstant, specifically:

$\mathrm{\&tau;}=\frac{{2\mathrm{kh}}_u\sin \left({\mathrm{d\&omega;}}_u\right)}{{\mathrm{\&pi;a}}_u{\mathrm{\&omega;}}_u}+\frac{2{\mathrm{kh}}_l\sin \left({\mathrm{d\&omega;}}_l\right)}{\mathrm{\&pi;}{a}_l{\mathrm{\&omega;}}_l},$

Wherein:

K is a static gain, ω _uBe the speed of service upper limit, ω _lBe the movement velocity lower limit, d is the time-delay of relay, h _uBe the amplitude second time, h _lBe amplitude for the third time, a _uBe the response amplitude that motion control for the second time obtains, t _uBe the response cycle that motion control for the second time obtains, a _lBe the response amplitude that motion control for the third time obtains, t _lIt is the response cycle that motion control for the third time obtains;

Described static gain k, specifically:

$k=-\frac{\mathrm{\&pi;}}{4}\frac{a_u-a_l}{h_u\cos \left({\mathrm{d\&omega;}}_u\right)-h_l\cos \left({\mathrm{d\&omega;}}_l\right)},$

Wherein: a _uBe the response amplitude that motion control for the second time obtains, a _lBe the response amplitude that motion control for the third time obtains, d is the time-delay of relay, h _uBe the amplitude second time, h _lBe amplitude for the third time, t _uBe the response cycle that motion control for the second time obtains, t _lIt is the response cycle that motion control for the third time obtains;

Described stiction f, specifically:

$f=\frac{a_l{h}_u\cos \left({\mathrm{d\&omega;}}_u\right)-a_u{h}_l\cos \left(d{\mathrm{\&omega;}}_l\right)}{a_u-a_l},$

Wherein:

a _uBe the response amplitude that motion control for the second time obtains, a _lBe the response amplitude that motion control for the third time obtains, d is the time-delay of relay, h _uBe the amplitude second time, h _lBe amplitude for the third time, t _uBe the response cycle that motion control for the second time obtains, t _lIt is the response cycle that motion control for the third time obtains;

Described Friction Compensation, specifically:

$u=k_{p}e+k_i\&Integral;\mathrm{edt}+k_d\stackrel{\&CenterDot;}{e}+\mathrm{fsign}\left({\stackrel{\&CenterDot;}{x}}_d\right),$

Wherein: u is a controlled quentity controlled variable, e=x _d-x,

k _p, k _i, k _dBe respectively proportionality constant, integral constant and derivative constant, x _d,

Be respectively instruction displacement and command speed, x, Be respectively output displacement and output speed, Be frictional force feedforward compensation item, f is a stiction,

The is-symbol function is promptly worked as

The time,

When

The time,

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