# US 2013/0278196 A1 · Method for automatically estimating inertia in a mechanical system

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- Number: US 2013/0278196 A1
- Document ID: US20130278196A1
- Status: Published application
- Kind: A1
- Application number: 13/451,924
- Filed: 2012-04-20
- Published: 2013-10-24
- Earliest claimed: 2012-04-20
- Assignees: Linestream Technologies
- Inventors: Gang Tian
- Web page: https://patentgrep.com/patent/US20130278196A1

## CPC

- G05B 13/0265: {the criterion being a learning criterion}
- B25J 9/1638: {compensation for arm bending/inertia, pay load weight/inertia}
- G01M 1/10: Determining the moment of inertia
- G01M 13/025: Test-benches with rotational drive means and loading means; Load or drive simulation
- G05B 2219/41163: Adapt gain to friction, weight, inertia
- G05B: CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS (systems for controlling or regulating non-electric variables G05D; systems for regulating electric or magnetic variables G05F; control devices or systems insofar as characterised by mechanical features only G05G)
- B25J: MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES ({manipulators specially adapted for use in surgery A61B34/70; manipulators used in cleaning hollow articles B08B9/04}; manipulators associated with rolling mills B21B39/20; manipulators associated with forging machines B21J13/10; {manipulators associated with picking-up and placing mechanisms B23P19/007}; means for holding wheels or parts thereof B60B30/00; {vehicles with ground-engaging propulsion means, e.g. walking members B62D57/02, B62D57/032; devices for picking-up and depositing articles or materials between conveyors B65G47/90, B65G47/91; manipulators with gripping or holding means for transferring packages B65H67/065}; cranes B66C; {manipulators used in the protection or supervision of pipe-line installations F17D5/00; walking equipment adapted for nuclear steam-generators F22B37/006}; manipulators specially adapted for, or associated with, nuclear reactors G21C; {apparatus used for handling wafers during manufacture or treatment of semiconductor H10P72/50})
- G01M: TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR

## Abstract

Systems and methods for estimating an inertia and a friction coefficient for a controlled mechanical system are provided. In one or more embodiments, an inertia estimator can generate a torque command signal that varies continuously over time during a testing sequence. The velocity of a motion system in response to the time-varying torque command signal is measured and recorded during the testing sequence. The inertia estimator then estimates the inertia and/or the friction coefficient of the motion system based on the torque command data sent to the motion system and the measured velocity data. In some embodiments, the inertia estimator estimates the inertia and the friction coefficient based on integrals of the torque command data and the velocity data.

## Claims

### Claim 1

A method for estimating parameters of a motion system, comprising:
generating a torque command signal that varies continuously over time;
measuring velocity data for a motion device representing a velocity of the motion system in response to the torque command signal; and
determining at least one of an inertia or a friction coefficient of the motion system based at least in part on the velocity data and the torque command signal.

### Claim 2 (depends on 1)

The method of claim 1, wherein the determining comprises determining the at least one of the inertia or the friction coefficient based at least in part on one or more integrals of the velocity data over a time range and one or more integrals of the torque command signal over the time range.

### Claim 3 (depends on 1)

The method of claim 1, wherein the generating the torque command signal comprises adjusting the torque command signal in accordance with a predefined testing sequence.

### Claim 4 (depends on 3)

The method of claim 3, wherein the adjusting the torque command signal comprises changing at least one of a direction or a rate of change of the torque command signal in response to the velocity of the motion system reaching a predefined velocity checkpoint.

### Claim 5 (depends on 2)

The method of claim 2, wherein the determining comprises:
designating a first segment of the time range as an acceleration phase;
designating a second segment of the time range as a deceleration phase;
integrating the torque command signal and the velocity data over the acceleration phase to yield Uacc and Vacc, respectively;
integrating the torque command signal and the velocity data over the deceleration phase to yield Udec and Vdec, respectively; and
determining the at least one of the inertia or the friction coefficient as a function of Uacc, Vacc, Udec, and Vdec,
where:
Uacc=∫uacc(t),
Vacc=∫vacc(t),
Udec=∫udec(t),
Vdec=∫vdec(t),
uacc(t) is a portion of the torque command signal corresponding to the acceleration phase,
vacc(t) is a portion of the velocity data corresponding to the acceleration phase,
udec(t) is a portion of the torque command signal corresponding to the deceleration phase, and
vdec(t) is a portion of the velocity data corresponding to the deceleration phase.

### Claim 6 (depends on 5)

The method of claim 5, wherein the determining the at least one of the inertia or the friction coefficient comprises at least one of determining the inertia according to:
J
=
U
dec

V
acc
-
U
acc

V
dec
Δ


v
dec

(
t
)

V
acc
-
Δ


v
acc

(
t
)

V
dec
,
or determining the friction coefficient according to:
B
=
Δ


v
dec

(
t
)

U
acc
-
Δ


v
acc

U
dec
Δ


v
dec

(
t
)

V
acc
-
Δ


v
acc

(
t
)

V
dec
,
where:
J is the inertia,
B is the friction coefficient,
Δvacc(t) is a difference between a velocity of the motion system at an end of the acceleration phase and a velocity of the motion system at a beginning of the acceleration phase, and
Δvdec(t) is a difference between a velocity of the motion system at an end of the deceleration phase and a velocity of the motion system at a beginning of the deceleration phase.

### Claim 7 (depends on 1)

The method of claim 1, further comprising determining at least one controller gain coefficient for the motion system based on the at least one of the inertia or the friction coefficient.

### Claim 8 (depends on 7)

The method of claim 7, wherein the determining the at least one controller gain coefficient comprises determining the at least one controller gain coefficient further based on a manually adjustable control system bandwidth.

### Claim 9

A system for estimating mechanical parameters of a motion system, comprising:
a memory;
a processor configured to execute computer-executable components stored on the memory, the computer-executable components comprising:
a torque command generator configured to generate a torque command signal that varies continuously over time during a testing sequence;
a velocity monitoring component configured to obtain velocity data representing a velocity of a motion system over time in response to the torque command signal; and
at least one of:
an inertia component configured to estimate an inertia of the motion system based on the torque command signal and the velocity data, or
a friction coefficient component configured to estimate a friction coefficient of the motion system based on the torque command signal and the velocity data.

### Claim 10 (depends on 9)

The system of claim 9, wherein the at least one of the inertia component or the friction coefficient component is further configured to estimate the inertia or the friction coefficient, respectively, based at least in part on one or more integrals of the velocity data over a time range and one or more integrals of the torque command signal over the time range, wherein the time range is at least a portion of a duration of the testing sequence.

### Claim 11 (depends on 9)

The system of claim 9, wherein the torque command generator is further configured to control the torque command signal in accordance with a torque function u(t), where u(t) is based on a set of predefined instructions associated with respective phases of the testing sequence.

### Claim 12 (depends on 11)

The system of claim 11, wherein the respective phases are triggered in response to the velocity of the motion system reaching respective defined velocity checkpoint values.

### Claim 13 (depends on 10)

The system of claim 10, wherein the at least one of the inertia component or the friction coefficient component is further configured to estimate the inertia as a function of Uacc, Vacc, Udec, and Vdec,
where:
Uacc=∫uacc(t),
Vacc=∫vacc(t),
Udec=∫udec(t),
Vdec=∫vdec(t),
uacc(t) is a portion of the torque command signal corresponding to an acceleration phase of the testing sequence,
vacc(t) is a portion of the velocity data corresponding to the acceleration phase,
udec(t) is a portion of the torque command signal corresponding to a deceleration phase of the testing sequence, and
vdec(t) is a portion of the velocity data corresponding to the deceleration phase.

### Claim 14 (depends on 13)

The system of claim 13, wherein the inertia component is further configured to estimate the inertia based on:
J
=
U
dec

V
acc
-
U
acc

V
dec
Δ


v
dec

(
t
)

V
acc
-
Δ


v
acc

(
t
)

V
dec
,
where:
J is the inertia,
Δvacc(t) is a difference between a velocity of the motion system at an end of the acceleration phase and a velocity of the motion system at a beginning of the acceleration phase, and
Δvdec(t) is a difference between a velocity of the motion system at an end of the deceleration phase and a velocity of the motion system at a beginning of the deceleration phase.

### Claim 15 (depends on 13)

The system of claim 13, wherein the friction coefficient component is further configured to estimate the friction coefficient based on:
B
=
Δ


v
dec

(
t
)

U
acc
-
Δ


v
acc

U
dec
Δ


v
dec

(
t
)

V
acc
-
Δ


v
acc

(
t
)

V
dec
,
where,
B is the friction coefficient,
Δvdec(t) is a difference between a velocity of the motion system at an end of the acceleration phase and a velocity of the motion system at a beginning of the acceleration phase, and
Δvdec(t) is a difference between a velocity of the motion system at an end of the deceleration phase and a velocity of the motion system at a beginning of the deceleration phase.

### Claim 16 (depends on 9)

The system of claim 9, further comprising an interface component configured to receive input specifying at least one of a limiting value for the torque command signal or velocity checkpoint used by the torque command generator to control the torque command signal.

### Claim 17 (depends on 9)

The system of claim 9, further comprising a tuning component configured to generate at least one controller gain coefficient as a function of at least one of the inertia or the friction coefficient.

### Claim 18

A non-transitory computer-readable medium having stored thereon computer-executable instructions that, in response to execution, cause a computer system to perform operations, including:
generating a torque command signal that varies continuously over time;
obtaining velocity data from a controlled mechanical system; and
estimating at least one of an inertia or a friction coefficient of the controlled mechanical system based at least in part on the velocity data and the torque command signal.

### Claim 19 (depends on 18)

The non-transitory computer-readable medium of claim 18, the operations further including estimating the at least one of the inertia or the friction coefficient based at least in part on one or more integrals of the velocity data over a time interval and one or more integrals of the torque command signal over the time interval.

### Claim 20 (depends on 19)

The non-transitory computer-readable medium of claim 19, wherein the estimating comprises:
integrating the torque command signal and the velocity data over an acceleration phase of the time interval to yield Uacc and Vacc, respectively;
integrating the torque command signal and the velocity data over a deceleration phase of the time interval to yield Udec and Vdec, respectively; and
estimating the at least one of the inertia or the friction coefficient as a function of Uacc, Vacc, Udec, and Vdec,
where:
Uacc=∫uacc(t),
Vacc=∫vacc(t),
Udec=∫udec(t),
Vdec=∫vdec(t),
uacc(t) is a portion of torque command signal corresponding to the acceleration phase,
vacc(t) is a portion of the velocity data corresponding to the acceleration phase,
udec(t) is a portion of the torque command signal corresponding to the deceleration phase, and
vdec(t) is a portion of the velocity data corresponding to the deceleration phase.