66 3D iscreteT ime In terv al of aM ec hatronic Serv oS ystem within thegeneral working region, the effectivenessofthe proposed method can be alsoverified indirectly in the articulated mechatronic servosystem. 3.2.5Relation between Reference Input Time Interval and TransientVelocityFluctuation (1) Tr ansien tV elo cit yF luctuation of the Mec hatronic Servo System In the industrial field,the controller of amechatronic servosystem whichcan restrain the velocityfluctuation is designed. In the mechatronic servosystem whichcan restrain completelythe steady-state velocityfluctuation,the hold circuit h r between the reference input generatorand position control part uses one-orderhold circuit. The referenceinput time interval ∆T is settobeequal to the sampling time interval ∆t p of theposition loop (refer to 3.2.2). In this part, since the transientvelocityfluctuation occurred even when re- strainingthe steady-state velocityfluctuation,its analysis is carried out as be- low. As the control strategy,the transientvelocityfluctuation when ∆T = ∆t p in 3.2.2(1)isadoptedinthe restraining the steady-state velocityfluctuation. In thecontinuoussystem, the mathematicalmodel of the velocitycontrol part, motorpartand mechanismpartisexpressed as dv( t ) dt = − K v v ( t )+K v u v ( t ) . (3.17) If k is the stageofthe referenceinput time interval ∆T ,any momentcan be expressed by ( k∆T + t p )(0 ≤ t p <∆T ). The position command value u p is u p ( k∆T + t p )=v re f ( k +1) ∆T by the 0th order hold when the objective trajectory r ( t )=v ref t is sampled by the reference input time interval ∆T . Therefore, the ve lo cit yc ommandv alue u v ( k∆T + t p )isexpressed by u v ( k∆T + t p )=( v ref ( k +1) ∆T − p ( k∆T ))K p . (3.18) When equation (3.18) is putintoequation(3.17),byainverse Laplace transform (refer to appendix A.1), themotion velocity v ( k∆T + t p )isexpressed as v ( k∆ T + t p )=  1 − e − K v t p  ( v ref ( k +1 ) ∆T − p ( k∆ T )) K p + v ( k∆T ) e − K v t p , (0 ≤ t p <∆T ) . (3.19) Therefore, the analyticalsolution can be easily solved. This equation (3.19) is describingthe damping of velocitycommandvaluechanged stepwise within time constant1/K v . From thevelocityofequation (3.19), in the zero infinite state (objective trajectory r ( t )=v ref t is continuous) of the reference input time interval, the difference of velocityas 3.2R elation be twe en Reference Input Time In terv al and Ve lo cit yF luctuation 67 v r ( t )=v ref  1+ 1 p s 1 − p s 2  p s 2 e p s 1 t − p s 1 e p s 2 t   (3.20) p s 1 = − K v +  K 2 v − 4 K v K p 2 p s 2 = − K v −  K 2 v − 4 K v K p 2 is obtained with ∆T and usingthe maximumand maximumofmaximal error (the first referenceinput time interval ( k =1)ofthe smallestdamping), the maximal transientvelocityfluctuation e t v is defined as e t v = v ( t t max ) − v r ( t t max )(3.21) = v ref  ∆T K p  1 − e − K v t t max  −  1+ 1 p s 1 − p s 2  p s 2 e p s 1 t t max − p s 1 e p s 2 t t max   . (3.22) However, t t max is calculated by ∆T e − K v t t max + 1 p s 1 − p s 2  e p s 2 t t max − e p s 1 t t max  =0. (3.23) (2)Graph of the Relationship Equationofthe TransientVelocity Fluctuation In theanalyticalsolution equation (3.22), since using many parameters is difficult, the relation between frequently adopted parameters and the transient velocityfluctuation is graphed. When K v =100[1/s]isfixed, Fig. 3.5 illustrated the reference input time interval ∆T [s] when using K p =1, 5, 10,2 0[1/s]a nd the division e t v /v re f [%] of the transientvelocityfluctuation forthe objective velocity. By usingthis figure, the relationship between the reference input time interval and the tran- sien tv elo cit yfl uctuation can be kno wn. 3.2.6Experimental Verificationofthe TransientVelocity Fluctuation In order to verify the transientvelocityfluctuation within thereference input time interval analyzed in the last part, an experimentwas carried outusing DEC-1(refer to experimentdevice E.1). The experimental con- ditions are ∆T = ∆t p =40[ms], K p =5[1/s] and the objectivevelocity v ref =10 . 5[rad/s](100[rpm]). The velocityresponse between 0.4 second from the beginning of control is showninFig. 3.6(a). Figure 3.6(b) shows the ve- locityfluctuation.Here, the horizontal axis is the time t [s], the upperpartof the ve rticala xis is the ve lo cit y v ( t )[rad/s] and the bo ttom part is the ve lo cit y 68 3D iscreteT ime In terv al of aM ec hatronic Serv oS ystem 0 1 0 20 30 4 0 5 0 0 0 . 02 0 . 0 4 0 . 06 0 . 0 8 0 .1 ∆ T e / v v ref K p 1 0 5 1 [ % ] [ s ] = 20 [ 1 /s] Fig. 3.5. Relation between velocityfluctuation e s v and reference input time interval ∆T ( K v =100[1/s]) [ s ] [ r a d /s] s imu l a t ion e x per iment 0 2 4 6 8 1 0 0 0 .1 0 . 2 0 . 3 0 .4 t v (a) Velocityresponse [ s ] [ r a d /s] 0 0 . 2 0 .4 0 . 6 0 .8 1 1.2 1.4 0 0 .1 0 . 2 0 . 3 0 .4 t e v (b) Velocityfluctuation Fig. 3.6. Experimental results using DEC-1 and simulation results using 2nd order mo del fluctuation e t v ( t )[rad/s]. The solid line denotes the exp erimen tal result, and the dotted line is the simulation results analyzed strictly by using Neuman seriesfor differential equation of (3.17) within 1[ms]. The characteristics of thetransientvelocityfluctuation between the experimentand the simulation are very close.Ineachreference input time interval ∆T =40[ms],the velocity fluctuation occurred and then decreased slowly.Inthe experiment, the size of theinitialmaximal velocityfluctuation of theinitialstageis1.10[rad/s]. By usingFig. 3.5 for visualizing the equation (3.22), with K v =100[1/s], ∆T =40[ms] and K p =5[1/s], the velocityfluctuation to objective velocity 3.3 Relationship between Reference Input Time Interval and Locus Irregularity 69 can be as e t v /v ref = 11. 0[%]. Therefore, the theoretical value of the transient velocity fluctuation is e t v = 0 . 110 × 10. 5 = 1 . 16[rad/s]. It is almost the same as the experimental result. Based on the above, the effectiveness of the analysis results can be verified. 3.3Relationship between Reference Input Time Interval andLocus Irregularity The reference input time interval and the velocityfluctuation in thedigital controller wasintroducedinthe section3.2. However, in the contourcontrol, this fluctuation mayoccur on the surface of the product andthis surface canbe changed as roughexpressed as locus irregularity. This locus irregularitymay occur in eachreference input time interval when the servosystem propertyof eachaxis in the mechanism is not consistent. The generation mechanism of this locus irregularityand itsquantitativeanalysisare expected. The analytical solutionoflocus irregularitygenerated in eachreference input time interval is given in equation (3.29). By usingthe theoretical analysissolution of thelocus irregularity, the predic- tion of movementprecisionofthe robotormachine tool as well as the design arrangementofthe mechatronic servosystem of the required locus precision are po ssible. 3.3.1Locus Irregularity in the Reference Input Time Interval (1) Mathematical Model of the Orthogonal Two-AxisMechatronic Servo System Foranalyzing the relation between the reference input time interval of a mechatronic servosystem and locus irregularity, firstly,the mathematical model of theorthogonal two-axis mechatronic servosystem is constructed, and then its response in eachreference input time interval is calculated. The relationship between the reference input time interval and the locus irregu- larityisanalyzedquantitatively.Next, its analysis result is expanded into the jointcoordinatesand space coordinates. The general locusirregularityofthe mechatronic system is discussed. As the reasonofdeteriorationofthe controlperformance, the effect of coor- dinate transform and mechanism dynamics, the calculationtime in the digital controller, the resolution of the encoder or D/A converter, coggingtorqueas well as stick-slip should be considered. Generally,when amechatronic sys- tem is structured with multiple axes. But it is better to separately consider the problem of generation in eachaxis of servosystem and the problem of generation of multi-axis structure(referto1.1.2 item 6). The reference input generators and position control partsare always adoptedwith adigitalcontroller.Since the position control part is simply 70 3D iscreteT ime In terv al of aM ec hatronic Serv oS ystem usedfor computation,its computation cycle is carried out within the narrow sampling time interval. But the reference input generatorperforms compli- cated computation, suchasinverse kinematics computation,etc. Therefore, its computation cycle is longer than the sampling time interval. According to this width of reference input time interval, the velocityfluctuation occurs at one axis and thelocus irregularityoccurswhen combiningtwo suchaxes. Therefore, the problem of the locus irregularityisfirstly solved in the orthogo- naltwo-axis mechatronic system with x axisand y axis, andthen the problem of locusirregularityofthe general mechatronic system with coordinate trans- form is solv ed. With the general motion condition, the mo del of x axisa nd y axisi nt he orthogonal two-axis mechatronic servosystem can be constructed with a1st order system respectively (refer to the item 2.2.3) dp x ( t ) dt = − K px p x ( t )+K px u x ( t )(3.24a ) dp y ( t ) dt = − K py p y ( t )+K py u y ( t )(3.24b ) where p x ( t ), p y ( t )are positions in time t , dp x ( t ) /dt, dp y ( t ) /dt arevelocities, u x ( t ), u y ( t )are servosystem input of eachaxis, K px , K py have the meanings of K p 1 in the lowspeed 1st order model equation (2.23) of item 2.2.3 at x axis and y axis Fo ra mec hatronic system, in order to mak et he steady-state errorv alues of eachaxis similar at the initial arrangementtime of device, the position loop gain of the controller of eachaxis in servosystem should be regulated. Ac- cording to the motion conditiona nd wo rking load basedo nt he arrangemen t, the propertyofthe servosystem will be changed slightly. Thereare existing the regulation erroratthe initial self-arrangement. Therefore, these summed errors accum ulate the difference of po sition lo op gain K px of equation( 3.24a ), (3.24 b )and K py expressthe propertyofthe mechatronic servosystem with the 1st order system. The difference of K px and K py is ther easonf or the generation of lo cusi rregularit y. (2) Response of aMechatronic Servo SysteminEachReference Input Time Interval Thelocus irregularity, as theanalysisobject, occurred in the rough reference input time interval, occurred in the transientstate with changeable input, cannotbefound in the steady state.Generally,inthe transientstate, there have been other kindsoflocus deterioration except thislocus irregularity. Comparing with the transientstate, the locus precision of contour control in the steady state can be improved. However, the locus irregularityineach referenceinput time interval in this section is themain reasonofdominant rest cont ourc on trol pe rformance deterioration in thes teady state. Wherein, the 3.3 Relationship between Reference Input Time Interval and Locus Irregularity 71 steady state analysis as the discussion point is performed. In the steady state, the response features with the reference input time interval is the transient response. The aim of this analysis is to understand the quantitative relation between the reference input time interval and the steady state of locus irregularity. Therefore, the drawn objective locus of the mechatronic system is a straight line (the objective operation velocity of each axis is constant) and the input of the model of a mechatronic servo system as the equation (3.24a )(3.24b ) is constructed. The objective working velocity of each axis is v x , v y , respectively. The input u x ( t ), u y ( t ) of each axis of the servo system calculated in each reference input time interval ∆T is expressed by the step-wise function of ∆T amplitude as u x ( t ) = v x ∆T U ( t ) + v x ∆T U ( t − ∆T ) + v x ∆T U ( t − 2 ∆T ) + v x ∆T U ( t − 3 ∆T ) + ··· (3.25a ) u y ( t ) = v y ∆T U ( t ) + v y ∆T U ( t − ∆T ) + v y ∆T U ( t − 2 ∆T ) + v y ∆T U ( t − 3 ∆T ) + ··· (3.25b ) where U ( t ) is the unit step function. For analyzing the locus irregularity generated with a rough reference input time interval, the above equation (3.24a ) ∼ (3.25b ) are one of the main point of this analysis and their solutions can be easily obtained by the existed analysis method. Here, a Laplace transform (refer to the appendix A.1) is carried out in equation (3.25a ), (3.25b ), and put them into the equation (3.24a ), (3.24b ) which have been also transformed by a Laplace transform. Then the response in each ∆T can be solved. If performing an inverse Laplace transform (refer to appendix A.1), the response in one reference input time interval ∆T with big enough stage m of ∆T is as p x ( m∆T + t ) = v x ∆T  m − e − K px t 1 − e − K px ∆T  , (0 ≤ t<∆T ) . (3.26 a ) p y ( m∆T + t )=v y ∆T  m − e − K py t 1 − e − K py ∆T  , (0 ≤ t<∆T ) . (3.26 b ) Forthis purpose,since the input of the mechatronic servosystem and the servosystem can be clearly expressed by the equations (3.24 a ), (3.24 b )and (3.25 a ), (3.25 b ), the response in eachreference input time interval ∆T in the steady state can be clearly worked out. Theseresponse equations (3.26 a ), (3.26 b )ineach ∆T is adoptedfor thelocus irregularityanalysisinthe next part. (3) Theoretical Solution of the Locus Irregularity Fr om ther esp onse equation (3.26 a )a nd (3.26 b )i ne ac hr eference input time interval ∆T ,the time t is eliminated, and then the response locus of the 72 3D iscreteT ime In terv al of aM ec hatronic Serv oS ystem x y L o c us i rregu l a r i ty Objec t i v elo c us y =(v y /v x ) x P m a x =(x ( m ∆ T + t m ) , y ( m ∆ T + t m )) P min =(x ( m ∆ T + 0 ) , y ( m ∆ T + 0 )) P m a x P min Fig. 3.7. Locus irregularity in mechatronic servosystem mechatronic system is obtained. The errorbetween the locus of this mecha- tronic system and the objectivelocus is the locus error .This locus erroris determinedbythe normalvector distance from the objectivelocus to the lo- cus of theservosystem. By the error of maximum value and minimum value of locus error in one reference input time interval, the locus irregularityis defined. In Fig. 3.7, theresponse among manyreference input time intervals of an orthogonal two-axis mechatronic servosystem is shown. In Fig. 3.7,the horizontal axisisthe x axis, verticalaxis is the y axisand the dotted broken line is the objectivelocus y =(v y /v x ) x .Atthe moment ( m∆T + t ), the normal ve ctor distance from ob jectiv el oc us y =(v y /v x ) x to locus coordinate ( x ( m∆T + t ) ,y( m∆T + t )) is e ( t )= | v y x ( m∆T + t ) − v x y ( m∆T + t ) |  v 2 x + v 2 y . (3.27) When we put p x , p y of equation (3.26 a ), (3.26 b )i nt o x and y ,t he lo cus error e ( t )isas e ( t )= v x v y ∆T  v 2 x + v 2 y     e − K px t 1 − e − K px ∆T − e − K py t 1 − e − K py ∆T     . (3.28) As shown in Fig. 3.7,ifthe locus is minimal position P min at t =0andthe maximalposition P max as de( t ) /dt =0,the locus irregularity e m is as below by the error of maximalvalueand minimal value of the locus error e ( t )and using equation (3.28). e m = | e ( t m ) − e (0)| 3.3 Relationship between Reference Input Time Interval and Locus Irregularity 73 = v x v y ∆T  v 2 x + v 2 y     e − K px t m − 1 1 − e − K px ∆T − e − K py t m − 1 1 − e − K py ∆T     (3.29) where t m is as be lo ww ith de( t ) /dt =0 t m = 1 K px − K py log K px  1 − e − K py ∆T  K py (1 − e − K px ∆T ) . (3.30) This equation (3.29) is the analyticals olution of lo cusi rregularit yo ccur- ringi ne ac hr eference input time in terv al ∆T .F rome quation (3.29), if the po sition lo op gain K px of the x axisand K py of the y axisare the same, e m is zero. In general, it is difficult to make the position loop gain K px and K py of theservosystem in the mechatronic servosystem absolutely the same, i.e., ( K px = K py ). As thereason, the generation of locus irregularityaccording to the equation(3.29) in eachreference input time interval ∆T can be found fromthe above equation. (4)Expansion to the ArticulatedRobot Thediscussion on the analysis of locus irregularityoccurred in the orthogonal two-axis mechatronic servosystem, carried out at 3.3.1(3), is expanded to the articulated robot. The articulated robot with two axesisconstructed with two rigid links andt wo join ts,a si llustrated in Fig. 2.11o fs ection 2.3.E ac h jointhas aservomotor andisconstructed by aposition control system.Its eac hj oin ta ngle is cont rolled to follow the ob jectiv ea ngle. The mathematicalm od el of eac ha xis in the articulated rob ot sho wn in Fig. 2.11isexpressed as the following 1st order system with the same discus- sion with equation (3.24 a )a nd (3.24 b ). dθ 1 ( t ) dt = − K p 1 θ 1 ( t )+K p 1 u 1 ( t )(3.31a ) dθ 2 ( t ) dt = − K p 2 θ 2 ( t )+K p 2 u 2 ( t )(3.31b ) where dθ 1 ( t ) /dt, dθ 2 ( t ) /dt aret he angle ve lo cities, K p 1 , K p 2 ha ve the meanings of K p 1 in the lowspeed 1st order model equation (2.23) of item 2.2.3 for each joint. u 1 ( t ), u 2 ( t )are input of eachaxis. Fordiscussingthe locus irregularityonthe working coordinates(x, y )for this articulated robot, the relation with the locus irregularityinthe joint coordinates(θ 1 ,θ 2 )isworkedout. The transformation fromjointcoordinates ( θ 1 ,θ 2 )toworking coordinates(x, y )isexpressed as (refer to section 2.3) x = l 1 cos( θ 1 )+l 2 cos( θ 1 + θ 2 )(3.32a ) y = l 1 sin(θ 1 )+l 2 sin(θ 1 + θ 2 ) . (3.32 b ) The transformationbetween two coordinates is anonlineartransform. It adopts thelinear transformation within the small part. The relation between 74 3D iscreteT ime In terv al of aM ec hatronic Serv oS ystem theslightchange(dθ 1 ,dθ 2 )near ( θ 0 1 ,θ 0 2 )inthe jointcoordinatesand the slight change ( dx, dy)inthe working coordinatesisexpressed by aone-order approx- imation of aTaylor expansion as  dx dy  = J  dθ 1 dθ 2  (3.33) where J is the Jacobian matrix J =  − l 1 sin(θ 0 1 ) − l 2 sin(θ 0 1 + θ 0 2 ) − l 2 sin(θ 0 1 + θ 0 2 ) l 1 cos( θ 0 1 )+l 2 cos( θ 0 1 + θ 0 2 ) l 2 cos( θ 0 1 + θ 0 2 )  . (3.34) Moreover, by using the same Jacobianmatrix J ,two coordinates for velocity can be expressed as ⎛ ⎜ ⎝ dx dt dy dt ⎞ ⎟ ⎠ = J ⎛ ⎜ ⎝ dθ 1 dt dθ 2 dt ⎞ ⎟ ⎠ . (3.35) With the commonmotion condition, in the jointcoordinatesofthe artic- ulatedrobot, themodel (3.31 a ), (3.31 b )can be approximatedbythe model (3.24 a ), (3.24 b )ofanorthogonal two-axis mechatronic servosystem (refer to section 2.3). In an articulated robot with the discussion of 3.3.1(1) ∼ (3) by using (3.24 a ), (3.24 b ), the locus irregularitycan be expressed approximately by the relation equation (3.29). (5)Expansion to the Three-AxisMechatronic Servo System The discussion in 3.3.1(4)isthe locus irregularitydiscussion on the plate of two axes. In this part, the locus irregularitydiscussion is expanded to three axes. In the expansion from two axesdiscussion to three axes, the z axisis added with the x axisand the y axisinthe mechatronic servosystem model (3.24 a ), (3.24 b ) dp z ( t ) dt = − K pz p z ( t )+K pz u z ( t )(3.36) where p z ( t )isthe position of the z axis, dp z ( t ) /dt is velocity, u z ( t )isthe input of servosystem, K pz hast he meaningo f K p 1 in the lo ws pe ed 1st order mo del (2.23) of item 2.2.3 in the z axis. Thei nput u z ( t )ofservosystem of the z axis is as u z ( t )=v z ∆T U ( t )+v z ∆T U ( t − ∆T ) + v z ∆T U ( t − 2 ∆T )+v z ∆T U ( t − 3 ∆T )+···. (3.37) If calculating the response of the z axisafterenoughstagenumber m is put into equation (3.36), as similar as equation (3.26 a ), (3.26 b ), it can be obtained that 3.3 Relationship between Reference Input Time Interval and Locus Irregularity 75 p z ( m∆T + t ) = v z ∆T  m − e − K pz t 1 − e − K pz ∆T  , (0 ≤ t<∆T )(3.38) where v z is the objectivevelocityofthe z axis. In theorthogonal plate with an objective locus, the locus error e 3 ( t )isthe distance with the space coordinates(p x ( m∆T + t ) ,p y ( m∆T + t ) ,p z ( m∆T + t )) of the servosystem calculated according to the (3.26 a ), (3.26 b ), (3.38) about the objectivespace coordinates. By using the locus erroratthe moment of t =0and de 3 ( t ) /dt =0,the locus irregularitycan be calculated by e m 3 = | e 3 ( t m 3 ) − e 3 (0)| (3.39) where t m 3 is the momentof de 3 ( t ) /dt =0. Based on the above,the locus irregularitydiscussion about two axescan be expanded into the three axes. 3.3.2Experimental Verificationofthe Lo cus Irregularity Generated in the Reference Input Time Interval (1) ExperimentalResult of Locus Irregularity Forverifying the theoretical analysis results of equation (3.29) of locus irreg- ularityineachreference input time interval derived in item 3.3.1, the experi- mental work wascarriedout using DEC-1 (refer to experimentdeviceE.1). In amechatronic system, since it is difficult to makethe gain of theservosystem of eachaxis exactly consistent, the locus irregularityoccursineachreference input time interval. This experimentimitates the actual situation. The DC servomotor is rotatedtwo cycles by changingthe conditions of onemotor. Thefirst rotation is themotion of the x axisand second rotation is themotion of the y axis. Combining the motion resultsoftwo rotations, theexperiment of an orthogonal two-axis mechatronic servosystem wascarriedout. The in- consistencyofposition loop gain of theservosystem wasrealized by changing thesetting of position loop gain K p in the computer for experiment. The control conditions are reference input time interval ∆T =0. 1[s], ob- jective velocity v x = v y =6[rad/s], sampling time interval ∆t p =0. 01[s], x axis(K p =1 0[1/s]= K px )f or thefi rst rotation, y axis(K p =1 1[1/s]= K py ) fort he second rotation.T hesec on trol conditions ares elected if the torque limitation(currentlimitation) of the servodriver neednot be considered in the exp erimen t. The experimental results are shown in Fig. 3.8 and Fig. 3.9.Fig. 3.8 il- lustrates the objectivelocus andthe resultsofthe locus in the experimentof the orthogonal two-axis mechatronic servosystem. The horizontal axis is the x axisposition [rad]. Thevertical axis is the y axisposition [rad]. In Fig. 3.8, forchecking the locus irregularitythatoccurred in experiment, the calculated locus error is given in Fig. 3.9.The horizontal axisisthe motion distance [rad] combiningthe x axisand the y axis. Thevertical axis is locus error [rad]. The [...]... software servo system is shown in figure 4.1 The software servo system is briefly classified into the servo controller, motor and mechanism part The position and velocity of motor are controlled by the servo controller The control system of the servo controller is always constructed with the position loop and the velocity loop in the industrial field The positioning precision of a software servo system is... (4 .6) according to its contour control performance From contour control performance required in a software servo system, encoder resolution is determined properly M Nakamura et al.: Mechatronic Servo System Control, LNCIS 300, pp 79– 96, 2004 Springer-Verlag Berlin Heidelberg 2004 80 4 Quantization Error of a Mechatronic Servo System 4.1.1 Encoder Resolution of the Software Servo System (1) Software Servo. .. Software Servo System Structure In a software servo system, the position controller and the velocity controller are constructed in software In addition, the current controller is also constructed in software In this section, concerning the control problem about position, the position controller and velocity controller are only taken into account by neglecting the current controller and power amplifier... interval and locus irregularity shown in Fig 3.10, the reference input time interval ∆T can be determined based on the required locus precision in the design process Fig 3.10 can be also adopted as the useful figure in the design process 4 Quantization Error of a Mechatronic Servo System The control circuit of a servo controller is a completely software servo system equipped by software (micro-computer) and. .. 76 3 Discrete Time Interval of a Mechatronic Servo System solid line is the experimental results and the dotted line is simulation results of the servo system using the 1st order system as (3.24a), (3.24b) From Fig 3.9, the steady-state error and occurred unevenness in each reference input time interval of the locus can be seen Since this steady-state error is different from... different compared with the ripple-type velocity in the velocity detector of an analogue servo system Since ripple-type velocity in Servo controller u + - Kp + - Difference operation Counter Motor and mechanism part 2 Kv Velocity signal 2 d y/dt 1 dy/dt s Position signal 1 s y Encoder Fig 4.1 Structure of software servo system ... software servo system, the precision of velocity feedback is deteriorated compared with an analogue servo system Hence, control performance is degraded due to a decrease of resolution of the velocity feedback signal because of difference computation, and ripple-type velocity fluctuation in the output of the the servo system is generated This velocity fluctuation is different compared with the ripple-type... generating a command in the power amplifier according to motor current, equivalent to torque, and the bit number of the A/D conversion for performing feedback In this chapter, encoder resolution and control performance of torque resolution and servo system is introduced 4.1 Encoder Resolution In the software servo system, a general velocity feedback signal is obtained according to the difference computation... Discrete Time Interval of a Mechatronic Servo System reference input time interval ∆T In addition, the deviationof Kpx andKpy can be easily found visually with their increment By using this graph, if the deviation of Kpx and Kpy of the mechatronic servo system is known, the occurrence of locus irregularity can be predicted in advance Concretely, the gains are Kpx = 20[1/s] and Kpy = 21[1/s](5% error), the... of the encoder installed in the servo motor, i.e., according to the measured position of the motor through dividing one rotation of the motor The position output of the servo motor is the accumulated pulse output of the encoder by a counter, and measured by putting data at each sampling time interval (refer to section 3.1) into the servo controller In an analogue servo system, the velocity signal can . Software ServoSystem (1)Software ServoSystemStructure In asoftware servosystem, the position controller and the velocitycontroller areconstructed in software. In addition, the current controller is. The 76 3D iscreteT ime In terv al of aM ec hatronic Serv oS ystem solid lineisthe experimentalresults and the dotted line is simulation results of the servosystem usingthe 1st order system as (3.24a ),. the resolution of velocity informationthen becomes lowand contourcontrol performance is degraded. In general, encoder resolution is determinedfromthe positioningprecisionin manycasesinindustry.However,