Model 205
Torsional
Apparatus
Model 205
Torsional
Apparatus
Model 205
Torsional
Apparatus
Configurations: 6 std, 9 with optional 3rd disk, 18 with second-
ary drive accessory
Dynamics: Adjustable to 2nd, 4th, and 6th (3 disk
option) order, Systems types 0 and 2
I/O: SISO, SIMO, MIMO (with sec. drive accessory)
Poles and Zeros: Adjustable 0.8-7 Hz
Inertia Adjustment Ratio: 10:1
Spring Adjustment Ratio: 2:1 (certain configurations)
Feedback: High resolution encoder (16,000 count/rev)
Actuator: High torque brushless motor, 2.0 N-m
Bench-top size: 30x30x96 cm. (12x12x36 in.)
Safety Features: Amplifier over-current protection. In firmware
(complete system only): relative displacement (spring) protec-
tion, over-speed protection, i2t thermal protection
θ(t)
T(t)
J
T(t) θ2(t)
J1
k1
θ1(t)
J2
θ(t)
k
T(t)
J
S-Domain
Equations
Character-
istics
Plant
Models
T(t) θ2(t)
J1
k1
θ1(t)
J2
k2
Rigid body Free-free, 2 DOF Free-clamped, 2 DOF
Free-clamped
θ(s)
T(s) =1
Js2θ(s)
T(s) =1
Js2+k
Time
Domain
Equations Jθ(t) ++ kk θ(t) == TT(t)
Jθ(t) == TT(t) J1θ1(t) + k(θ1(t)-θ2(t) = T(t)
J2θ2(t) + k(θ2(t)-θ1(t) = 0
J1θ1(t)+k1(θ1(t)-θ2(t))+k2θ1(t) = T(t)
J2θ2(t)+k1(θ2(t)-θ1(t))+k2θ2(t) = 0
θ1(s)
T(s) =J2s2+k1+k2
D(s) ,θ2(s)
T(s) =k1
D(s)
• Rigid body model.
• See page 5.
• Classic spring-mass oscillator
• Single vibration mode
• Rigid body plus 1 oscillatory mode.
• θ1/T: 2 imag zeros, pole excess = 2
• θ2/T: no zeros, pole excess = 4
• 2 oscillatory modes.
• Type 2 system. • Type 0 system • Type 2 system. • Type 0 system.
θ1(s)
T(s) =J2s2+k
D(s) ,θ2(s)
T(s) =k
D(s)
• θ1/T: 2 imag zeros, pole excess = 2
• θ2/T: no zeros, pole excess = 4
D(s) = J1J2s4+ J1(k1+k2)+J2k1s2+k1k2D(s) = s2J1J2s2+(J1+J2)k
Easily Transforms to 6 Distinct Plants That Include...
(Nine plants with optional third disk*)
* Three disk Model 205a plant provides sixth dynamic order with third normal mode.
Feedback Sensor
At Each Disk
(High resolution optical encoder)
Torsional Spring
(Hardened steel. Adjustable
k for 2 DOF Plants)
Adjustable Inertia
(Movable/removable brass weights)
Actuator
(High Torque brushless
DC servo motor)
Motor drives lower disk
via rigid timing belt
(View obstructed)
Bearing Support
(Precision bearings @ each disk)
The Model 205 apparatus is a highly versatile platform that
is ideal for introductory undergraduate lab use and
intermediate controls study. It has also been used
extensively in advanced research. In its several configura-
tions, this system represents a broad and important class of
practical plants including: rigid bodies, flexibility in drives,
and coupled discrete vibrating systems. It easily transforms
into second, fourth, and sixth (optional) order plants with
collocated or noncollocated sensor / actuator control. An
optional secondary drive may be positioned at any output
(disk) to create a MIMO plant (requires Executive USR™
software) and provides for the study of disturbance rejection.
The ability to readily adjust physical parameters such as
inertia values and spring constants make it ideal for multiple
student work group assignments. This apparatus closely
follows its dynamic model and the theoretical predictions of
open and closed loop behavior provided in the manual. It
has proven to be highly robust and reliable in the field.
Three disk Model 205a
shown. Basic Model 205
has 2 inertia disks
Easy Removal Disks
(Rapidly changes to 1, 2, or 3
disk plant)
