Instrumentation & Measurement Magazine 24-2 - 109

FOPID Control with Parameter
Optimization for HydrostaticallyActuated Autonomous Excavators
Amirreza Mirbeygi Moghaddam, Witold Kinsner, Gustavo Koury Costa,
Lokesh Kumar, Khurram Butt, and Nariman Sepehri

T

his article presents our recent work towards development of a controller for the new class of modernized
excavators. There is an increasing demand to develop
autonomous earth-moving machines that are: more efficient
than the conventional ones and capable of operating with
minimal supervision by operators. A fractional-order proportional-integral-derivative (FOPID) control is applied to a
newly designed electro-hydrostatic actuator (EHA) circuit for
these machines. We further employ the Oustaloup recursive
method for which the parameters of the controller are chosen
based on the modified Nelder-Mead optimization algorithm.
Our experimental results indicate that the proposed controller
is capable of controlling the speed of the link with a negligible
error. This work paves the road for development of autonomous, energy efficient, off-road mobile machines.

Problem Statement
Electro-hydrostatic actuators (EHA) are a type of hydraulic actuators which use pumps rather than valves. As a result,
they are more efficient than the valve actuated systems [1]. Recently, new circuit designs have been proposed for application
of EHA to heavy-duty excavator machines. Energy efficiency
is the main reason for using the new layouts. This article further develops a simple to implement, yet robust controller that
allows autonomous operation of these machines. Since the
control aspects of EHA systems have nonlinearities and uncertainties, the task of designing model-based controllers (such
as fuzzy and model predictive controllers [2]) could be challenging. Consequently, a robust controller should be used to
control the high nonlinearities and the parameter changes in
the operation range of such systems. Furthermore, since sufficiently accurate models for those systems are difficult to
acquire, model-free methods should be utilized.
While standard proportional-integral-derivative (PID)
controllers are used extensively in industry due to their simplicity and straightforward implementation, they are not
robust enough to produce satisfactory results under a wide
range of system uncertainties [1], [3]. The shortcomings of the
standard PID controller have been mitigated considerably
April 2021	

by generalizing the main concept of the fractional-order PID
(FOPID) controller.
The FOPID controller generalizes the integer-order derivative and integral to fractional-order derivative and integrator.
This class of controllers has the advantage of two more variables (i.e., the exponent of the derivative and the integrator) to
adjust in order to achieve a much-improved performance for
the controller. Furthermore, a fractional-order differentiator
reduces significantly the magnitude amplification of the high
frequency noise as compared to the integer-order one [4], [5].
Such a FOPID controller has been implemented by Maddahi et
al. [5] to control a hydraulically powered actuator. That FOPID
controller was approximated using the Oustaloup recursive
method [6], and the controller parameters were tuned experimentally based on iterative feedback tuning (IFT).
The novelty of this work is in the design of a FOPID control
scheme for an excavator EHA system to control the velocity of
the system. The parameters of the FOPID controller are tuned
using the modified Nelder-Mead optimization algorithm [7] to
achieve a minimum error.
After the excavator system and its model are described, the
control strategy is introduced. Subsequently, experimental simulation results are discussed, and conclusions close the article.

Excavator System
An experimental setup of the excavator system used for our
simulations is shown in Fig. 1. The rod position is measured
by an incremental encoder (Fig. 1a). Load masses are adjusted
by mounting disks on the arm, and the pressure signals are acquired by two pressure sensors, each located on one side or the
other of the cylinder. As shown in Fig. 1b, the excavator arm
linkage carries the load mLg by the actuator force FL that is generated by the perpendicular movement of the cylinder piston.
This force can be obtained from:
	

FL  mL gl2 sin  /  l1 cos  	(1)
 

where θ is the rotational angle, l1 and l2 are top and bottom
lengths of the arm respectively, and g is the gravitational

IEEE Instrumentation & Measurement Magazine	109
1094-6969/21/$25.00©2021IEEE



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