Transcript Torque Sensorless Control in Multidegree-of

運動控制概論
題目：Torque Sensorless Control in
Multidegree-of-Freedom Manipulator
作者：Toshiyuki Murakami,
Fangming Yu, and Kouhei Ohnishi
出處：IEEE TRANSACTIONS ON INDUSTRIAL
ELECTRONICS, VOL. 40, NO. 2, APRIL 1993
P259~P265
報告人：控晶四乙─黃筌園
指導老師：王明賢 老師
Abstract-The paper describes a torque sensorless control in a
multidegree-of-freedom manipulator. In the proposed method,
two disturbance observers are applied to each joint. One is
used to realize the robust motion controller. The other is used
to obtain a sensorless torque controller. First, a robust
acceleration controller based on the disturbance observer is
shown. To obtain the sensorless torque control, it is necessary
to calculate reaction torque when the mechanical system
performs a force task. Second, we explain the calculation
method of the reaction torque. Then the proposed method is
expanded to workspace force control in the multidegree-offreedom manipulator. Finally,several experimental results are
shown to confirm thevalidity of the proposed sensorless force
controller.
摘要
I. INTRODUCTION
II. OBSERVER-BASMEDO TIONC ONTROLLER
III. SENSORLESS FORCECO NTROLLER IN
WORKSPACE
IV. EXPERIME
V. CONCLUSIONS
VI. REFERENC
I.INTRODUCTION
The paper deals with an advanced torque control technique
to realize sensorless torque control in the multidegree-offreedom manipulator. If the generated torque is known, it will
bring some sophisticated abilities to the manipulator. For
example, impedance control is one of the important
applications. From the viewpoint of motion control, any
motion control is attained precisely if the generated torque is
well controlled. To realize the precise torque control, it is
necessary to detect the transient generated torque by more
than one torque sensor. This makes the structure of the drive
system complicated. In addition, the sensor output is affected
by unknown disturbances such as temperature variation.
Since torque sensor is not convenient from a mechanical and
an economic viewpoint, it is strongly desirable to realize the
torque control without the torque sensor [6].
In this paper, a sensorless torque control is achieved by
applying a disturbance observer at each joint, thus estimating
the disturbance torques imposed on the manipulator [l], [3], [4].
First, the estimated disturbance torque is directly fed back to
realize the acceleration controller whose input is the
acceleration reference. The motion system based on the
acceleration controller generates the desired acceleration
without any disturbance effect. Second, the reaction torque is
calculated from the estimated disturbance torque and the
identified dynamic model of manipulator. By the feedback of the
calculated reaction torque, the sensorless torque control is
realized. The proposed algorithm is very simple and easy to
apply to the control system. In this paper, the algorithm is
extended to the workspace force control of a multidegree-offreedom manipulator.
The paper consists of five sections. In Section 11, the
disturbance observer is explained. The acceleration controller
is also introduced. Sections I11 and IV present the sensorless
force controller in the multidegree-of-freedom manipulator and
several experimental results. The conclusions are summarized in
Section V.
II. OBSERVER-BASMEDO TIONC ONTROLL
A. Robust Motion Controller Based on Disturbance Observer
Fig. 1 shows a model of an electrical motor and manipulator.
Here, Ktni and Jni are the nominal torque coefficient and inertia,
respectively. The system reference is the torque current
Reference
. Tdisi is the total disturbance torque imposed on
the system, which is defined in (1). Here, the lower suffix i
denotes the joint number in the multidegree-of-freedom
Manipulator.
On the right-hand side of (0, the first term is the interactive torque,
including the coupling inertia torque, gravitation, and so on.
The second term is the reaction torque when the mechanical system
does force task. The third and fourth terms are the viscosity and
Coulomb friction,respectively. The fifth term is the self-inertia variation
torque. The last term models the torque pulsation due to the flux
distribution variation of the motor. As shown in (l), Tdisi includes not
only the general load torque, but also the parameter variations. From
Fig. 1 and (l), we obtain (2a), which is the joint motion equation of the
manipulator:
Equation (2b) means that the disturbance torque Tdisi can
be calculated from the angular acceleration of motor qi
and the current reference In general, it is difficult to
detect the angular acceleration directly by an industrialgrade
sensor. So we obtain the acceleration by differentiating
the angular velocity. Then, a low-pass (LP) filter is inserted to
reduce the noise included in the velocity signal.
The total calculation process of the disturbance torque is shown
in (3a) and Fig. 2(a). In general, it is difficult to implement the
ideal differentiator, so a pseudodifferentiator is used to obtain
the angular acceleration as shown in the second part of (3a). In
Fig. 2(a), the torque
is the sum of
and Icmpi, which is the
compensated current to cancel out the disturbance effect.
Then the total system becomes robust against the disturbance
effect including the parameter variations:
In the disturbance observer shown in Fig. 2(a), the filter design
relates to the approximation of the disturbance effect. When the
filter element is first order, the disturbance effect is
approximated by the step change function,as shown in Fig. 3.
Therefore, the disturbance effect is estimated more precisely if
the order of the filter is higher. Then, the higher the order is, the
more the calculation of the observer becomes complicated. In
case the sampling ratio of the control system is small and the
time delay of the filter is negligibly small, the disturbance
effect is well estimated by the first-order system. So we use the
first-order filter to simplify the calculation of the disturbance
observer. In Fig. 3, we assume a discrete-time system. In the real
implementation, the sampling ratio is negligibly small (1 ms), so
that we introduce a continuous-time discussion in the filter
representation and the latter analyses.
Fig. 2(a) is transformed into the hatched block in Fig.2(b) by
using (3b). Here, Gsi(s) is the sensitivity function of the system
against the disturbance torque. The smaller Gsi(s) is, the more
robust the system becomes. That is to say, the robustness of the
total system is evaluated by the sensitivity function Gsi(s) [l], [3],
[8]. In the observer-based
system, the robustness and the robust stability of the system
relate to the selection of g. The larger g is, the more robust the
system becomes. On the other hand, the smaller g is, the more
the stability margin of the system increases. This means that
there exists a tradeoff in the selection of g. In general, it is
possible to select g large enough so that the disturbance effect
is well suppressed, that is, Gsi(s) = 0. When the gain Jni/Krni is
inserted to determine the current reference , Fig. 2(b) is the
acceleration controller whose input is the acceleration
reference. Then the desired acceleration is generated without
any disturbance.
In the manipulator based on this joint acceleration controller, highperformance motion control is expected by the feedback of the state
variables of the manipulator.
In force control applications, it is necessary to feed back the reaction
force in the outer loop. As mentioned before, the observer-based
manipulator is robust against the disturbance torque, including the
reaction torque, so that the manipulator will apply the infinite force to
the environment which the manipulator contacts in case the reaction
force is not fed back. From this point of view, the force sensor is
essential to realize the force control in the observer-based system. Of
course, in the conventional force controller, the force feedback is
important to obtain the high-performance force control. As described
previously,this makes the structure of the manipulator system
complicated. To improve this matter, the paper proposes the force
control strategy without using the force sensor.
In the next section, the calculation method for the reaction torque is
shown.
B. Calculation of Reaction Torque
In this section, we explain the calculation method of the
reaction torque by using the output of the disturbance
imposed on the manipulator is defined in (1) and is estimated
by the disturbance observer. If the total disturbance effect is
known, the reaction torque can be calculated as follows:
Here, we assume that the nominal values Jni and Ktni are well
adjusted, that is, these values are almost equal to the real
values Ji, Kti. In fact, it is possible to know the values of Ji and Kti
in advance by implementing several motion tests. Under this
assumption, (4a) is rewritten as follows:
ln (4b), Tinti is the interactive torque imposed on each joint. Here,we
introduce, the serial multilink manipulator, which has one electrical
motor at each joint. In this case,the theoretical equation of Tinti is
derived from the Euler-Lagrange equation. Using the Euler-Lagrange
equation, the end-effector equations of motion are given
bY
where t(q,q) and u(q) are the kinetic energy and the potential
energy respectively. is the joint torque and I (q) is the joint
inertia matrix. We assume that is the sum of the input torque
Kt
, the reaction torque Text, and the friction effect f(q). From
(5), we obtain (6), which are the motion equations of the
manipulator. Here,Kt is a diagonal matrix whose elements are
the torque coefficients of each joint:
In (6), the joint inertia matrix z ( q ) changes according to the
configuration of the manipulator, and the matrix of torque
coefficient Kt changes due to the variation of flux distribution of
the rotor. These effects are represented by (7), and it is
substituted into (6). As a result, we obtain (8), which is the
vector formulation of (1) and (2). Here, Ktn and In are the
diagonal matrices whose (i, i ) elements are the nominal torque
coefficient and the nominal inertia of the ith joint, respectively.
From (1) and (8), Tnf is defined as follows:
• Using (4) and (9), the reaction torque Text is calculated.Here,
Tint and f(4) are the inverse dynamics swith respect to the
disturbance torque. The total CalCUlation process of the
reaction torque is summarized in Fig. 4(a). In the actual
application, (3a) is expanded into the calculation of the
reaction torque.olution.
Then the calculation ofFig. 4(a) is Performed as follOws:
• Equation (10) shows the observer structure of each joint to
calculate the reaction torque. In this paper, the observer
shown in (10) is called the torque estimator. In this calculation
process, it is necessary and important to know the gravity and
the friction effect as precisely as possible.In fact, they are the
main disturbance effects and have highly nonlinear
characteristics. Excepting the gravity term, all parameters of
(9) are calculated from the motion
• equations of the manipulator. Fortunately, in the observerbased system, the gravity and the friction effects are
measured precisely by implementing the constant angular
velocity motion tests. In the next section, the measurement
method of the gravity and the friction effects is shown.
C. Measurement of Gravity and Friction Effect
The gravity and the friction effects can be measured in
advance by using the estimated disturbance torque of the
disturbance observer. Under the constant angular velocity
motion test, the estimated disturbance torque is given by
In the two-link manipulator of Fig. 5(a), which uses joint2
and joint3, (11) is rewritten as follows:
All parameters A2, A3, f2(q2), f 3 ( q 3 ) in (12) with respect to
each velocity are determined by repeating the constant angular
velocity motion tests. The calculation of Fig. 4(a) is performed by
using these measured parameters.
III. SENSORLESS FORCECO NTROLLER IN WORKSPACE
As mentioned in the former part, the robust acceleration
controller is realized by the feedback of the estimated
disturbance torque. In addition, we can obtain the
reaction torque from the torque estimator shown in (10).
In this part, the sensorless force controller is constructed
based on the joint acceleration controller and the torque
estimator in the workspace.
IV. EXPERIME
In this part, several experimental results are shown to confirm the validity of
the proposed sensorless force controller.
A. Experimental System
Fig. 5(a) shows the tested direct drive manipulator which has three degreesOf-freedom. In this system, one direct drive motor is attached to each joint,
and the force sensor is mounted at the tip of manipulator. The force sensor is
used to compare the estimated reaction force with the real reaction force.
The specifications of the DD motor are summarized in Table I. The signal flow
Diagram of the control system is illustrated in Fig. 5(b). The sampling period of
the controller is 1 ms, and all calculations are performed by DSP (digital signal
processor: pPD77230). In the experiments, joint2 and joint3 are used to
implement the workspace force control. First, the results of the constant
angular velocity motion test are done to measure the gravity and the friction
effects. Second,the sensorless force control based on the proposed method
are implemented by the DD manipulator.
B. Constant Angular Velocity Motion Test
To measure the friction and the gravity effects, two observers
are constructed in each joint. One is used to realize the robust
motion controller. The other is used to measure the friction and
the gravity effects. Especially the latter observer is called the
dynamics identification observer. First, to measure the gravity
effect, the constant angular velocity motion tests are
implemented. In this case, the dynamics identification observer
has the same structure of the general disturbance observer. The
tested motions are illustrated in Fig. 6(a). In Fig. 6(a), joint3
moves from 0 [radl to 27r [radl with constant velocity, and joint2
is fixed to 0 [rad]. Then we obtain the estimated disturbance
torque of joint3 as shown in Fig. 7(a). From this result, we can
find it easy to know the gravity effect represented by the
sinusoidal function.
Then, its amplitude corresponds to A, in (12). On the other hand,
in Fig.6(b), joint2 moves from 0 [radl to 27 [rad] with constant
velocity, and joint3 is fixed to 0 [rad]. Fig. 7(b) is the estimated
disturbance torque of joint2. In this result, the amplitude of the
sinusoidal wave is A, + A,. From these results, A, and A, are
calculated separately. The friction effect of each joint is also
measured by the constant angular velocity motion test. Then, the
dynamics identification observer is constructed as follows:
In the calculation of (16), only the friction effect is estimated.As described
before, the estimated disturbance torque of the disturbance observer is
fed back to cancel out the total disturbance effect imposed on the
manipulator.So the velocity control is well realized, and the friction effect
is measured in the wide range of velocity. This is a remarkable point of the
proposed identification method. In the conventional method, it is difficult
to know the friction effect in the low-velocity area. The measured friction
effects are hown in Fig. 8. The results obtained by the constant angular
velocity motion tests are summarized in Tables I1 and 111. To calculate the
reaction torque, the obtained results are used.
C. Sensorless Force Control
Fig. 5(a) shows the tested motion of sensorless force control. The
force command is applied to the -y direction and the position
control is done in the +x direction.Fig. 9 is the step response of
sensorless force control. In the upper result of Fig. 9, the force
response coincides with force command. This means that the
disturbance torque is well cancelled out by the feedback of the
estimated disturbance torque, and the high-performance force
control is realized. The lower result of Fig. 9 shows that the
calculated reaction force and the output of force sensor are
almost same. Fig. 10 shows the correlation between the
calculated reaction force and the output of force sensor in case
the sinusoidal force reference is applied to the sensorless force
controller. From these results, we can find that the reaction force
is well estimated by the proposed method. These results also
show the feasibility of the proposed sensorless force control.
V. CONCLUSIONS
The paper presents a novel approach to sensorless
torque control. This is one of the industrial applications of
the disturbance observer. In the observer-based
manipulator,the following abilities are added to the
manipulator.
●The robustness of the manipulator is increased by the
feedback of the estimated disturbance torque.
●By resolving the estimated disturbance torque, it is
possible to know each nonlinear effect imposed on the
manipulator and to obtain the exact model of manipulator.
In the DaDer, the sensorless torque control is realized by
using ;he above abilities. The fiist ability is important to realize
the robust force controller. In the proposed sensorless force
control, it is necessary to know the friction and the gravity effects
as precisely as possible since these effects give much effect to
the force response.
Under the constant angular velocity motion test, these effects
are measured by using the estimated disturbance torque, which
is the application of the second ability. The feasibility of the
proposed sensorless force control is confirmed by several
experiments.
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