IEEE Robotics & Automation Magazine - June 2022 - 86

two-inertia system, and this fact makes its torque control
problem relatively more challenging [7]. In earlier studies,
classical control methods were chosen, for instance, Pratt
et al. proposed a conventional proportional-integral-derivative
(PID) control to
achieve torque tracking
[6]. However, the torque
control performance was
deemed insufficient, and,
later, they additionally
implemented a feed-forward
(FF) term to cancel
out the unmodeled
dynamics [8].
To tackle the twodegrees-of-freedom
control
problem of SEAs,
Wyeth proposed a cascaded
control algorithm
with an inner-loop velocity
control and outer-loop
torque control to miniThe
robust torque control of SEAs introduces another
The robust torque control
of SEAs introduces another
challenging dimension
as there are internal and
external disturbances, such
as friction and load-side
dynamics.
mize the nonlinearities, such as backlash and stiction [9]. This
method requires relatively less computational resources and,
thus, allows higher sampling rates in real-time implementation.
Internal and external disturbances can be suppressed by
using fast inner velocity control. By the same token, Vallery
et al., studied the stability of this cascaded control method
and obtained a satisfactory torque-tracking performance [10].
challenging dimension as there are internal and external disturbances,
such as friction and load-side dynamics. To ensure
robustness, the implementation of observer-based control
methods is a common approach described in the literature
[11]. In [12], Oh and Kong proposed a robust control method
based on a conventional PID controller with a model-based
FF term and a disturbance observer (DOB), which was
applied directly to the SEA model using the transfer function
between the output torque and motor torque.
In a different approach, the sliding mode control (SMC)
method was adopted for its disturbance suppression ability
[13]. However, a chattering problem was reported as the main
concern. The addition of a DOB has been experimentally verified
to reduce chattering [14]. Using this information, it is
possible to implement a torque controller through the use of
SMC and DOB, leading to fine torque tracking with reduced
chattering [15], [16].
Another powerful tool for controlling SEA units is based
on differential flatness (DF), which reduces the control problem
to simple algebraic expressions and, thus, provides computationally
effective solutions [17]. Combined with a
second-order DOB, Sariyildiz and Yu showed that a DF-based
control strategy was efficient in suppressing disturbances for
the robust control of an SEA-powered joint [18], even in the
presence of modeling uncertainties and unknown environmental
effects.
Other highly effective control methods include adaptive
τs
τref
-
s +
PID-1
θref
.
m
+
-
θm
.
Td s+1
1
Figure 1. The cascaded PID Control with an inner velocity loop.
PI-2
Ks
τm
SEA
θs
θm
.
control methods and optimization-based methods [19], [20].
While they exhibit satisfactory torque-tracking performance,
the algorithmic complexity and computational power
requirements associated with these controllers limit their
real-time implementation. In particular, the torque control
loop must be simple, fast, and computationally efficient since
it serves as a servo loop in each SEA-powered robot joint
when implementing a decentralized control architecture [3].
In doing so, computational power can be saved for higherorder
controllers that are hierarchically built on top of the
torque control loop.
In light of these aspects, we investigated the effectiveTable
1. Cascaded PID controller parameters.
Parameter
Outer loop proportional gain Kp1^
Outer loop integral gain Ki1^
Outer loop derivative gain Kd1^
Cutoff frequency of PID-1 (wd)
Inner loop proportional gain Kp2^
Inner loop integral gain Ki2^
h
h
h
h
Motor velocity filter time constant (Td)
h
Value
16
7
0.8
1,600 Hz
0.045
0.012
1/600 s
ness of torque controllers that are real-time applicable and
could exhibit high-fidelity torque tracking. Considering
these requirements, the following five candidates were
considered: 1) cascaded control [10], 2) cascaded control
with DOB [21], 3) observer-based direct torque control
[12], 4) SMC with DOB [13], [15], [16], and 5) DF control
with DOB [18]. We implemented a square wave reference
input, sine wave reference inputs at four distinct frequencies,
and a chirp signal reference input with a varying frequency
ranging from 0.1 to 25 Hz. Torque-tracking
performances and Bode plots are presented for a quantifiable
benchmarking.
Comparison studies have been performed for the modeling
and design aspects of SEAs [22], [23]; however, to
the authors' knowledge, a benchmarking study to compare
the existing controllers is yet to be found in the
86 * IEEE ROBOTICS & AUTOMATION MAGAZINE * JUNE 2022
IEEE Robotics & Automation Magazine - June 2022

Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - June 2022
