A HIGH PERFORMANCE TRACKING CONTROL METHOD BASED ON ADISTURBANCE OBSERVER WITH PARAMETER ADAPTATION

Dong Jin HyunDepartment of Mechanical EngineeringMassachusetts Institute of Technology

Cambridge, Massachusetts, USA 02139Email: mecjin@mit.edu

Jungsu ChoiDepartment of Mechanical Engineering

Sogang UniversitySeoul, Korea 121-742

Email: zz1zzy@sogang.ac.kr

Kyoungchul KongDepartment of Mechanical Engineering

Sogang UniversitySeoul, Korea 121-742

Email: kckong@sogang.ac.kr

ABSTRACTA disturbance observer (DOB) is a useful control algorithm

for systems with uncertain dynamics, such as nonlinearity andtime-varying dynamics. The DOB, however, is designed basedon a nominal model, and its stability is sensitive to the magni-tude of discrepancy between a controlled system and its nominalmodel. Therefore, to increase the stability margin of the DOB, itrequires an accurate model identification, which is often difficultfor nonlinear or uncertain systems. In this paper, the parame-ters of the nominal model are continuously updated by a param-eter adaptation algorithm (PAA) to keep the model discrepancysmall, such that the DOB is able to show its desired performancewithout losing stability robustness even in the presence of non-linearity and/or time-varying dynamics. In the integration of theDOB and the PAA, however, there exists a complicated signal in-teraction. In this paper, such interaction problem is solved froma practical point of view; signal filtering. The proposed methodshows improved performance for an electric motor system, andis verified by experimental results in this paper.

INTRODUCTIONSince the concept of a disturbance observer (DOB) was first

introduced in [1], the DOB has been refined by many controlengineers [2], [3], [4], [5] and applied in various applicationssuch as robotic manipulators [6] and hard disc drives [7]. TheDOBs estimate a disturbance injected to a system by compar-ing an output simulated by a nominal model with the measuredactual output, and the observed disturbance is fedback into thesystem for the rejection of the disturbance. Moreover, they alsoattenuate the discrepancy between the nominal model and the ac-tual system by treating it as an external disturbance. Although

the DOB is not a tracking control method that reduces track-ing error, it makes the controlled system behaves as its nomi-nal model, which allows model-based control methods to showtheir ideal performance along with the DOB [8]. For example,zero-phase tracking control [9] was utilized with the DOB forthe control of an automotive engine that exhibits a large modeluncertainty [10], and sliding mode control was applied with theDOB in [11] for tracking control of a nonlinear plant.

Given a nominal model, the performance of the DOB andits stability robustness are related to the magnitude of model dis-crepancy. It is a well-known condition that the Q filter of theDOB should be designed such that its magnitude is small at fre-quency domains where the magnitude of the model discrepancyis large. To satisfy this condition, however, there is a trade-offbetween performance and stability robustness, in particular, forsystems with large nonlinearity and uncertain dynamics. There-fore, the structure (e.g. the order of a transfer function) and pa-rameters of the nominal model should be selected and identifiedas accurate as possible, which is often difficult in practice.

Many researchers have sought solutions to obtain the desiredperformance of the DOB in practice from the viewpoint of thenominal model. Kong et al. proposed an algorithm to adjust thenominal model parameters for improved robustness [12]. A non-linear nominal model was used in [13] to enhance the stiffness ofa robot manipulator. Although the DOB with a nonlinear nomi-nal model, often called a nonlinear DOB, fulfills its performanceobjectives, the closed-loop dynamics of the DOB becomes non-linear, and thus it is difficult for linear feedback and feedforwardcontrol methods to show the desired performance along with thenonlinear DOB.

When a system exhibits nonlinear dynamics but can be as-sumed to be piecewise linear, a linear time-varying (LTV) nom-

1 Copyright © 2013 by ASME

Proceedings of the ASME 2013 Dynamic Systems and Control Conference DSCC2013

October 21-23, 2013, Palo Alto, California, USA

DSCC2013-3814

inal model can be used for the nominal model in the DOB. Theadvantage of the DOB with a LTV nominal model is that thenominal model can still be regarded as a linear system, whichmake it possible to use linear model-based control algorithms(e.g. ZPETC) along with the DOB. Using such advantage of theDOB, an adaptive scheme outside of the DOB closed loop wasused in feedforward compensation for robust control [14] andestimation/tuning of the control gain based on the disturbanceerror given from the DOB was proposed in [15]. In this paper, anadaptive disturbance observer (ADOB) that adaptively updatesthe parameters of a LTV nominal model in the DOB and a feed-forward controller is proposed for the control of systems with un-certain dynamics and/or nonlinearity. A recursive least squares(RLS) method, one of parameter adaptation algorithms (PAAs),is applied to update the parameters of LTV nominal model. Thesimilar concept is shown in [16]; the inertias of a two-link robotwere identified by a PAA, while the robot was controlled by a2-DoFs controller with a DOB. In this paper, the ADOB with anarbitrary LTV nominal plant is proposed. The implementationof the ADOB is challenging due to possible interactions betweenthe DOB and the PAA. Both schemes respond to a model discrep-ancy in different approaches; i.e., the DOB is to cancel the modeldiscrepancy with high-gain control, while the PAA is to updatethe model parameters. Therefore, it is difficult to integrate bothcontrol schemes in one controller. In this paper, such problemsare avoided by smoothing adaptation considering the stability ofthe ADOB. Tracking control experiments with an electric motorsystem show that the ADOB maintains the tracking performancewhile the parameters of the motor system change.

PRELIMINARY STUDYA disturbance observer

ZOH

Figure 1: Block diagram of a typical motion control system witha disturbance observer and feedforward control

Figure 1 shows the block diagram of a typical motion track-ing control system with a conventional DOB for a discrete-timesingle input, single output (SISO) plant, Gp(z), where z, u, u∗, d,d, y, yd , r, and Ts are one step advance operator, a control input,a treated control input by the DOB, an external disturbance, anestimated disturbance, a system output, a desired output, a feed-forward signal, and a sampling time respectively. In the blockdiagram, G−1

n (z) is a filter to estimate the actual input exerted

into the controlled plant Gp(z) from the output y; thus, the out-put of G−1

n (z) can be assumed to be u∗+ d, if Gn(z) accuratelyrepresents Gp(z). Therefore, the disturbance can be estimated bysubtracting u∗ from the output of G−1

n (z). Subsequently, the esti-mated disturbance is negatively fedback into the control input ufor rejection of the actual disturbance. Notice that the Q filter hasbeen introduced in order to avoid anti-casuality problem inducedwhen taking the inverse of Gn(z).

It is in general impossible to represent the whole dynam-ics of a system by a transfer function, i.e., the nominal model.Therefore, the estimated disturbance by the DOB is subjected toan error due to the modeling uncertainty. Suppose that the ac-tual dynamics of the plant, Gp(z), is subjected to a multiplicativemodel uncertainty, i.e.,

Gp(z) = Gn(z)(1+∆(z)) (1)

where Gn(z) is an unitarily stable function, ∆(z) is a stable trans-fer function. Notice that the nominal model, Gn(z), and its in-verse G−1

n (z) are all stable by definition, and the model uncer-tainty does not introduce instability to the system. It is, however,arguable that many open-loop systems are unstable, which can-not be represented as in (1). In such cases, a stabilizing controllermay be applied to the system, and the stabilized closed-loop sys-tem can be regarded as a nominal model for the DOB. Then, theclosed-loop transfer function by the DOB is

Y (z) = Gu(z)U(z)+Gd(z)D(z) (2)

where U(z) and D(z) are respectively the z-transforms of u(k)and d(k), and

Gu(z) =Gn(z) [1+∆(z)]

1+Q(z)∆(z)(3)

Gd(z) =Gn(z) [1+∆(z)] [1−Q(z)]

1+Q(z)∆(z)(4)

Based on the derived closed-loop transfer functions, the follow-ing specifications for the performance of the DOB should be con-sidered in the design of the Q filter.

1. Disturbance rejection : Notice in (3) that if Q(e jωTs) =1 + j0, Gd(z) becomes zero, which is the desired perfor-mance of the DOB. Therefore, the Q filter should be de-signed such that Q(e jωTs) is close to 1+ 0 j at frequencieswhere disturbance exist. Moreover, if Q(e jωTs) = 1 + 0 j,Gu(z) is equal to Gn(z), which implies that the DOB rejectsthe model uncertainty and the system follows the nominalmodel of the actual plant.

2. Stability Condition: According to the small gain theorem onwhich the existing robust stability conditions [17], [18], [19]

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are mainly based, a sufficient condition for the stability ofthe DOB is

‖Q(z)∆(z)‖∞ < 1. (5)

This condition indicates that the magnitude of the Q filterhas to be small at frequencies where the model uncertaintyis large. Since the DOB is not effective if the magnitudeof the Q filter is small, the DOB requires a good nominalmodel that accurately represents the actual dynamics of thecontrolled system, such that the Q filter can have the maxi-mum bandwidth.

A parameter adaptation algorithm (PAA)Recall that the DOB-controlled system behaves as a nominal

model assumed in the design of the DOB, but the model discrep-ancy sets a challenge in the design of the Q filter. In nonlinearor time-varying systems, however, it is difficult to obtain a linearnominal model that describes the behavior of the system for theentire time, and thus, a large uncertainty is often unavoidable,which can lead to instability of the DOB. This paper is moti-vated from the effort to minimize the model discrepancy evenin the presence of time-varying dynamics or nonlinearities, suchthat the DOB can maintain its desired performance for the entiretime.

When controlling nonlinear or time-varying systems with alinear nominal model, it is necessary to update the parametersof a nominal model so that the model discrepancy is maintainedminimal. A parameter adaptation algorithm(PAA) based on re-cursive least squares (RLS) is appropriate for this purpose. ThePAA updates the model parameters on-line from a regressor vec-tor constructed by the input and output signal sequences. Assum-ing that the structure of the nominal model is determined, thenominal model Gn(z) can be represented as an autoregressive-moving-average (ARMA) model in

Gn(z−1) =z−dB(z−1)

A(z−1)(6)

where

A(z−1) = 1+a1z−1 + · · ·+anz−n (7)B(z−1) = b0 +b1z−1 + · · ·+bmz−m (8)

then, the nominal-based estimated output y(k) at the k-th se-quence is

y(k) = θT (k−1)φ(k−1) (9)

where the estimated model parameter vector θ ∈ℜn+m+1 is

θ(k−1) =[a1 . . . an b0 . . . bm

](10)

and the known regressor vector is

φ(k−1) =

y(k−1)...

y(k−n)u(k)

...u(k−m)

∈ℜ

n+m+1 (11)

The RLS method estimates the unknown model parameters basedon the measured and estimated outputs, i.e., y(k) and y(k), by

θ(k) = θ(k−1)+F(k)φ(k−1) [y(k)− y(k)] (12)

where

F(k+1) (13)

= 1λ1

[F(k)−λ2

F(k)φ(k)φT (k)F(k)λ1(k)+λ2(k)φT (k)F(k)φ(k)

]The RLS method can be divided into the following settings bychanging the hyper parameters, λ1(k) and λ2(k), i.e.

1. Typical recursive least squares, if λ1(k) = 1 and λ2(k) = 1.2. Least squares method with a forgetting factor, if 0< λ1(k)<

1 and λ2(k) = 0.3. Constant gain method, if λ1(k) = 1 and λ2(k) = 0.

Note that the forgetting factor, λ1(k), prevents the magnitude ofF(k) from converging to zero and the RLS method from even-tually stopping the parameter update. It should, also, be notedthat the constant gain can be applied for preventing F(k) fromblowing up when φ(k) is not persistently exciting.

AN ADAPTIVE DISTURBANCE OBSERVER (ADOB)Structure of ADOB

An ADOB is a DOB with a continuously updated nominalmodel, simultaneously returning the estimated parameters to acontroller. Figure. 2 shows the block diagram of the ADOB.Note that washout filters, H(z), are added to input path to theRLS block to make the RLS algorithm insensitive to measure-ment noise and unexpected disturbance. Also, a lowpass filter,L(z), is introduced to the output path from the RLS block to re-move the fast change of the estimated parameters returned fromthe RLS block.

Therefore, while the nominal model is updated automati-cally, the design parameters of the ADOB are Q(z), H(z), andL(z). The criteria for the design of these parameters are as fol-lows.

1. Q(z): The objective of Q(z) is to reject the effect of the in-accessible disturbance and model discrepancy. In general, it

3 Copyright © 2013 by ASME

ZOH

Figure 2: Block diagram of the proposed ADOB

is a lowpass filter such that the action of the DOB is effec-tive in a low frequency domain where the unexpected effectgiven from the model discrepancy is small.

2. H(z): H(z) is introduced to enhance the reliability of thePAA, i.e., RLS method, in this paper. H(z) is to regulatethe disturbance as much as possible to be 0+ 0 j. Since thefiltered output to the RLS block is not affected by the distur-bance, the RLS method is allowed to find the true parame-ters.

3. L(z): The objective of L(z) is to decrease the rate of param-eter adaptation. If the change of the model parameters islarge, it may result in an unexpected transient response evenif the parameters are converging to the true values. L(z) re-duces highly dynamic parametric effects given from contin-uous parameter update.

The RLS method as the PAA in the ADOB is to update theparameters of G−1

n (z) based on the input and output of a system.The updated Gn(z) represents the actual dynamics more accu-rately, if the PAA is effective. Thus the updated parameters fromthe PAA can be used for the update of the nominal model in theDOB.

In addition to the performance of the DOB, its stability isan important issue. The closed-loop characteristic equation ofthe ADOB is the same as that of the DOB explicitly. Throughthe action of the PAA outside of the closed-loop of the DOB, themodel uncertainty ∆(z) is minimized to maintain the stability ofthe DOB in the ADOB. However, there exists the parameter tran-sient dynamics by the update of the nominal parameters. If L(z)on the output path of the PAA removes high frequency parametervariation, the effect of the parameter adaptation for the stabilityof the ADOB may be reduced to be ignorable.

In summary, a few problems arise in this method as follows.

1. How to guarantee the stability in the transient of adaptationwhen the parameters of Gn(z) vary too fast, and

2. How to deal with the input and output of the PAA affected byexternal disturbances and noises. As explained, the PAA as-sumed that U(Z) = G−1

n (z)Y (z) and does not consider noisein the adaptation process. Therefore, it is difficult to guaran-tee that the PAA identifies the true parameters of the system

properly in the presence of noise. Moreover,3. there may be an interaction between the DOB and the PAA.

H(z): a washout filter for the PAARecall the output, y, is resulted from a disturbance, d, as

well as a treated control input u∗. Assuming that the disturbanceis additive to the treated control input, the output is

Y (z) = Gp(z) [U∗(z)+D(z)] (14)

The disturbance is unavoidable and it can be evaluated as the lim-itation of the PAA. To prevent the disturbance from deterioratingthe reliability of the PAA, a washout filter H(z) is applied to theboth side of (14). The filtered ones are obtained as

H(z)Y (z) = Gp(z)H(z)U∗(z)+Gp(z)H(z)D(z) (15)

If any information on the disturbance can be obtained in thefrequency domain, H(z) can be designed such that the termGp(z)H(z)D(z) in (15) is small. For example, if the disturbanceis concentrated at high frequency domain, H(z) can be designedsuch that Gp(z)H(z)D(z) is small. Conversely, if the disturbancehas significantly low frequency components such as a DC in-put, H(z) should be designed as a high pass filter. Based onthe assumption that the disturbance does not influence the fil-tered output for the PAA, the RLS method is allowed to find thetrue parameters even in the presence of the disturbance. Namely,the objective of H(z) is to enhance the reliability of the PAA.In general, however, it is difficult to obtain information on thedisturbance. Therefore, H(z) provides an additional degree offreedom to deal with the stability of the ADOB, its design is notstraightforward unless information on the disturbance is known.

L(z): a lowpass filter for the parameters estimated bythe PAA

The stability condition of the ADOB follows the same con-dition for the DOB when the convergence rate of the parameterupdated by the PAA is fast enough compared to the change ofthe real parameters, i.e., if ∆(k + 1) ≤ ∆(k) is guaranteed, thestability of the ADOB is not able to deteriorate. In addition, themodel discrepancy that deteriorates the stability of the ADOBloop includes not only the model mismatch between Gp(z) andGn(z) but also dynamics of the rapidly changed model parame-ters. For example, Gn(z) at the (k+ 1)-th sequence memorizesthe input and output resulted from Gn(z) at the (k)-th sequence.If the change of the model parameters is large, it may result in anexpected transient response even if the parameters are converg-ing to their true values.

One way to decrease the rate of a parameter adaptation is theaddition of a lowpass filter, L(z), to the updated parameters, i.e.the output of the PAA as shown on Fig.2. Then, L(z) reduces the

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fast change of the nominal parameters by the PAA while pass-ing on the slow change. In other words, L(z) induces the sameeffect as the introduction of the variable parameter irrelevant tothe stability of the PAA and minimizes the transient dynamics ofthe parameters to prevent the change of the parameters from in-creasing, deteriorating the performance and spoiling the stabilityof the ADOB.

Feedback and Feedforward control with the ADOBIn addition to the ADOB, a feedback controller is necessary

to reduce a tracking error for trajectory-following control setting.The block diagram of overall control algorithm is that includes afeedforward F(z,k) and feedback controller C(z) shown in Fig.3.The feedback controller for a electric motor can be designed

Figure 3: Block diagram for a feedforward and PID controllerswith the ADOB

based on all possible Gn(z)’s, the expected nominal models, con-sist of time varying parameters because the nominal model ofelectric motors should not have unstable poles physically. Ifthe controlled plant has unstable poles, the careful considerationshould be required for the design of the PID controller accordingto the general PID design method. In this paper, the closed-looptransfer function with the PID controller should not possess anypoles outside of the unit circle on the z-plane. In another way,a model-based control such as linear quadratic regulator (LQR)can be implemented, but it is left for future research.

Subsequently, a feedforward controller F(z,k) is designedbased on Gn(z,k) constructed by the estimated parameter vec-tor θ(k), in order to reduce the delay because the constructionof the feedforward controller can be free from an anti-causalityproblem. The desired output sequence should be determined forthe feedforward action. Then, the feedforward controller can bedesigned for the motion-tracking control such that its transferfunction is

F(z,k) =[

C(z)Gn(z,k)1+C(z)Gn(z,k)

]−1

(16)

In this case, as long as the change of the parameters in F(z,k)and Gn(z,k) is slow enough, the output can be obtained to bethe same as the desired output yd(k). Note that a feedforwardcontroller includes Gn(z,k) updated by the PAA in the ADOB,

the feedforward controller is connected in series to the designedclosed-loop ADOB and the PID combination while Gn(z,k) inthe feedforward controller is updated together with the nominalmodel in the ADOB.

EXPERIMENTAL RESULTSExperimental setup

The proposed method was verified by experimental resultswith a three-link robot arm shown in Fig.4. Each link of the robot

Distal joint axis

Middle joint axis

Proximal joint axis

Figure 4: Experimental test bed; three-link robot arm

arm is driven by an 400W AC motor. The joints and motors areconnected by a belt. The belt introduces nonlinearity such as itsfriction and backlash while the motor has inherent nonlinearityin the current-torque relationship. Such nonlinearities are to berejected by the DOB in the experiment.

Moreover, the multi-link robots are in general time-varyingsystems, because the moment of inertia D(q), Coriolis C(q, q)and gravity G(q) effects are dependent on its motion q and pos-ture q as shown in

D(q)q+C(q, q)q+G(q) = B(q)u+ J(q)T Fext (17)

Where J(q) is the Jacobian and Fext is an external force. There-fore, a change of states for each joint affects the system param-eters of a nominal model as well, if an effective PAA updatesa nominal model along with motion of the robot arm. In ad-dition, when the three joints are in motions simultaneously, thechange of the system parameters become more drastic due to thecoupled dynamics such that D(q), C(q, q) and G(q) are not di-agonal matrices in general. Also, the AC motors are regardedas time-varying systems with respect to the whole life cycle dueto mechanical wearing, its environment (e.g. room temperature),and decrease of the magnetization of magnets in the motor. Ac-cordingly, when the motor is under a long-term operation, thechange of the system parameters is unavoidable. In this paper, amore conservative setting was assumed; Fig.5 shows a reference

5 Copyright © 2013 by ASME

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0 20 40 60 80 100−1

−0.5

0

0.5

Time (sec.)

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(a) 0~20 sec.

(b) 20~40 sec.

(c) 40~60 sec.

(d) 60~80 sec.

(e) 80~100 sec.

Distal joint axis

Middle joint axis

Proximal joint axis

Figure 5: Reference trajectories for three joints of the robot arm

trajectory of joint angles. When all of the three joints were op-erated to follow the reference trajectories, the behaviors of thethree-link robot arm were changed as drawn. In experiment, theinitial angle of each joint was defined as the forward outstretchedstate in (a) of Fig.5. The overall robot control system is lineartime-varying (LTV) and the objective of the controller with theADOB is to make this LTV robot arm system follow the refer-ence trajectory as pre-defined.

Design of controllerTo apply the ADOB to the robot arm, the feasible linear

structure of the each joint was assumed as shown in

Gn(z) =b1

z2 +a1z+a2(18)

From the feasible linear structure of the each joint, the initialnominal model can be obtained as

Gn0(z) =0.0003478

z2−1.835z+0.8353(19)

The initial nominal model was obtained by frequency domainanalysis method. This model identification method is a processto identify the model parameters of a plant based on the inputand output signals obtained from the pre-experiment.

In order to verify the performance of the ADOB, the mea-sured tracking trajectory with the ADOB was compared withone with the DOB. First, a controller with the DOB was imple-mented on the robot arm to make it track the reference trajectory.Then, after adding the PAA to the DOB as proposed, the trackingperformance with the ADOB was evaluated through comparisonwith the performance with the DOB.

Recall that the Q(z) should be designed prior to the designand the implementation of the DOB. In this experiment, the Q(z)was chosen to be

Q(z) =0.1266

z2−1.288z+0.4149(20)

which corresponds to a lowpass filter with the cutoff frequency of70 Hz. The bandwidth of the Q(z) is much larger than frequen-cies of the desired path, i.e., the operational range of the DOBincludes the designed desired trajectories. The DOB with (20)is verified to satisfy the stability condition through preliminarytest on the LTI robot arm system, which is modeled as an initialnominal model.

Subsequently, the gains of the PID is selected based on theinitial nominal model with consideration of gain margin andphase margin. The matched pole-zero method was used to ob-tain the discrete PID controller as

C(z) =2025z−2000

z(21)

The feedforward controller is automatically determined by(16). Hereby, the model-based controller design with the DOBis competed and also the tracking performance was tested on theLTI robot arm system which is modeled as Gn0(z). Fig.6 showstracking error eDOB at each robot arm joint while following thepre-determined trajectories.

PAA in the ADOBIn order to design the ADOB, the PAA with the L(z) and

H(z) are simply added to the designed DOB. L(z) reduces thefast change of the nominal model parameters by the PAA whilepassing on the slow change. Therefore, L(z) is set as

L(z) =7.999×10−8z+7.997×10−8

z2−1.999z+0.9994(22)

Recall that the links and the motors are connected by a belt, andthe belt introduces large nonlinearity due to its friction and back-lash. Therefore, the information about disturbance to the robotsystem on the present setup has low frequency components, then,the H(z) is set as

H(z) =0.999z−0.999

z−0.999(23)

6 Copyright © 2013 by ASME

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2nd m

oto

r (r

ad.)

0 20 40 60 80 100−0.2

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3rd

moto

r (r

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Figure 6: Tracking errors with the DOB

Fig.7 shows the experimental result of the time-varyingmodel parameter estimated by the RLS based on the structureof the nominal model. As shown, the model parameters werechanged for the entire time. When the posture configurationof the three-link robot arm was largely changed at 20 sec., 40sec., 60 sec, and 80 sec., the model parameters updated by thePAA showed distinct converging trend lines. L(z) affected to thechange rate of the nominal parameters updated by the PAA, andthe adaptation was conducted slowly.

Tracking error with the ADOBThe tracking error eADOB as a performance index of the

ADOB is shown in Fig.8. Although the trend of Fig.8 is similarto the tacking error with the DOB shown in Fig.6, the quantityof eDOB is larger than the quantity of eADOB. In order to com-pare both quantities , the 2-norm of eDOB and eADOB is shownin Table.1. ‖eADOB‖2 of each joints of the robot arm was smallerthan ‖eDOB‖2 of each joint; in particular the proximal joint showssignificant discrepancy. When the shape of the three-link robot

Table 1: The 2-norm of tracking error of the DOB and the ADOB

Joint number ‖eDOB‖2 ‖eADOB‖2

Distal joint 0.2807 rad. 0.2783 rad.

Middle joint 0.3038 rad. 0.2420 rad.

Proximal joint 3.4851 rad. 1.8310 rad.

arm was changed, the moment of inertia of the proximal joint

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Figure 7: Updated parameters for each joint by the PAA

was affected more than the other two joints. This caused the sig-nificant change of model parameters of proximal joint, and themodel uncertainty was increased as well. The large model dis-crepancy continued, which made the DOB ineffective in practice.The ADOB, however, reduced the model uncertainty so that thetracking error was decreased.

7 Copyright © 2013 by ASME

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Figure 8: Tracking errors with the ADOB

DISCUSSIONS AND CONCLUSIONSRecall that H(z) and L(z) were designed considering the in-

formation on the disturbance and characteristics of the controlledsystem. In practice, however, it is difficult to obtain this informa-tion required for the design of H(z) and L(z). In this paper, sincethe theory on the design of the H(z) and L(z) is not proposed,the performance of the ADOB was verified by the experimen-tal result through setting of H(z) and L(z) in the ADOB by trialand error, which is the limitation of the proposed tracking controlwith the ADOB.

In this paper, the ADOB for motion control for an LTV elec-tric motor is proposed with the experiment. The PAA is intro-duced to the closed-loop of the conventional DOB with a fewtreatments such as the addition of the H(z) and the L(z). The pro-posed method should be designed with consideration of two ma-jor problems: 1) the effectiveness of the PAA and 2) handling thetransient dynamics of the updated parameters. Therefore, char-acteristics of the plant such as its disturbance and LTV behaviorshould be understood for the application of the ADOB. The de-sign of the ADOB based on the better understanding enables theQ(z) to have the large bandwidth and increases the adaptationspeed. The path tracking performance of the proposed methodwas verified by the experiments where the ADOB maintainedthe performance while the DOB lost the stability in the operatingtime.

The ADOB can be applied to various applications. For ex-ample, it has the potential use for the automotive engine and therobot manipulator. Generally, it is difficult to obtain the exactnominal model of the time varying automotive engine and robotmanipulators. If the model based control method is used forthem, model uncertainties must exist. The ADOB is expectedto handle these uncertainties and also show performances suchas robustness and small tracking errors from the uncertainties asalready shown through the experiment on the electric motor.

In the design of motion control algorithms, model-based ap-proach is expected to show better performance than PID con-trollers if the model accurately represents the actual plant. How-ever, a large amount of effort is put into obtaining an accuratemodel. Therefore, model-based design has been often accom-panied with application of robust control techniques that reducethe effect of model uncertainty like the DOB. As the conductedexperiments showed, there is definitely the limitation of modeluncertainty the robust control is capable of handling and thebarrier can be broken with the addition of the adaptive control.Conversely, the adaptive control should be vulnerable to exoge-nous disturbance and sensor noise, which might spoil the perfor-mance and the stability of the control system. Therefore, a robustcontrol can also complement the vulnerability of the adaptivecontrol. The proposed ADOB shows the performance throughthe experiment as a complimentary combination of both controlphilosophies for better model-based control.

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