30-01-2013, 04:36 PM
Fuzzy Self-Tuning PID Semiglobal Regulator for Robot Manipulators
[attachment=48955]
Abstract
In this paper, we present a semiglobal asymptotic
stability analysis via Lyapunov theory for a new proportionalintegral-
derivative (PID) controller control scheme, proposed in
this work, which is based on a fuzzy system for tuning the PID
gains for robot manipulators. PID controller is a well-known set
point control strategy for industrial manipulators which ensures
semiglobal asymptotic stability for fixed symmetric positive definite
(proportional, integral, and derivative) gain matrices. We
show that semiglobal asymptotic stability attribute also holds for
a class of gain matrices depending on the manipulator states.
This feature increases the potential of the PID control scheme to
improve the performance of the transient response and handle
practical constraints in actual robots such as presence of actuators
with limited torque capabilities. We illustrate this potential by
means of a fuzzy self-tuning algorithm to select the proportional,
integral, and derivative gains according to the actual state of a
robotic manipulator. To the best of the authors’ knowledge, our
proposal of a fuzzy self-tuning PID regulator for robot manipulators
is the first one with a semiglobal asymptotic stability proof.
Real-time experimental results on a two-degree-of-freedom robot
arm show the usefulness of the proposed approach.
INTRODUCTION
THE classical proportional-integral-derivative (PID) regulator
is still widely used in industrial applications due to
its design simplicity and its excellent performance, particularly
in applications in which the process parameters are not well
known [1]–[9]. Specifically, most of the robots employed in industrial
operations are controlled by PID algorithms; in spite of
this fact, there is a relative lack of theoretical results. It has been
pointed out that the stability results presented in the literature
are far from being conclusive [10]–[13], [15]. Moreover, it is
known that, under linear PID control, the asymptotic stability
is valid only in a local sense [16] or, in the best of the cases,
in a semiglobal sense [14], [15], [17].
PROPOSED PID CONTROL WITH NONLINEAR GAINS
The PID controller is a well-known set point control strategy
for manipulators which ensures asymptotic stability for fixed
symmetric positive definite gain matrices. In order to improve
the performance of the closed-loop system, a possible solution
could be to use variable gains [30].
We introduce a new PID controller with variable gains whose
main feature is that stability holds even though the gains depend
on the robot states.
SEMIGLOBAL ASYMPTOTIC STABILITY ANALYSIS
In this section, we show that the stability also holds for a
class of nonconstant state-depending proportional, integral, and
derivative gain matrices; specifically, we consider the control
law (9) corresponding to a PID control scheme with nonlinear
gain matrices. The stability analysis is based on a preliminary
version described in [26]. The semiglobal stability is established
in the sense that the region of attraction can be arbitrarily
enlarged with an adequate selection of the controller gains.
FUZZY APPROACH FOR SELF-TUNING THE PID
CONTROLLER GAINS
Freedom to select the proportional, integral, and derivative
gain matrices in a nonlinear manner for the PID control scheme
may be of worth in real applications where manipulators are
under effects of disturbances and constraints. Fuzzy logic is a
suitable approach as a mechanism to determine the nonlinear
gains of the PID control scheme according to previous practical
specifications. This is because the input–output characteristics
of fuzzy logic systems could be easily suited in order to fulfill
the stability requirements established in Proposition 1.
CONCLUSION
In this paper, we have proposed a fuzzy adaptation scheme
for tuning the proportional, integral, and derivative statedependent
gains of a PID controller for robot manipulators.
Moreover, a semiglobal asymptotic stability proof for the proposed
fuzzy self-tuning PID controller for robot manipulators is
presented. The proposed approach allows to consider important
practical features in real robots, such as achievement of desired
accuracy and avoidance of working of the actuators’ torques beyond
their capabilities. The performance of the proposed fuzzy
scheme has been verified by means of real-time experimental
tests on a two-degree-of-freedom direct-drive robot arm.
[attachment=48955]
Abstract
In this paper, we present a semiglobal asymptotic
stability analysis via Lyapunov theory for a new proportionalintegral-
derivative (PID) controller control scheme, proposed in
this work, which is based on a fuzzy system for tuning the PID
gains for robot manipulators. PID controller is a well-known set
point control strategy for industrial manipulators which ensures
semiglobal asymptotic stability for fixed symmetric positive definite
(proportional, integral, and derivative) gain matrices. We
show that semiglobal asymptotic stability attribute also holds for
a class of gain matrices depending on the manipulator states.
This feature increases the potential of the PID control scheme to
improve the performance of the transient response and handle
practical constraints in actual robots such as presence of actuators
with limited torque capabilities. We illustrate this potential by
means of a fuzzy self-tuning algorithm to select the proportional,
integral, and derivative gains according to the actual state of a
robotic manipulator. To the best of the authors’ knowledge, our
proposal of a fuzzy self-tuning PID regulator for robot manipulators
is the first one with a semiglobal asymptotic stability proof.
Real-time experimental results on a two-degree-of-freedom robot
arm show the usefulness of the proposed approach.
INTRODUCTION
THE classical proportional-integral-derivative (PID) regulator
is still widely used in industrial applications due to
its design simplicity and its excellent performance, particularly
in applications in which the process parameters are not well
known [1]–[9]. Specifically, most of the robots employed in industrial
operations are controlled by PID algorithms; in spite of
this fact, there is a relative lack of theoretical results. It has been
pointed out that the stability results presented in the literature
are far from being conclusive [10]–[13], [15]. Moreover, it is
known that, under linear PID control, the asymptotic stability
is valid only in a local sense [16] or, in the best of the cases,
in a semiglobal sense [14], [15], [17].
PROPOSED PID CONTROL WITH NONLINEAR GAINS
The PID controller is a well-known set point control strategy
for manipulators which ensures asymptotic stability for fixed
symmetric positive definite gain matrices. In order to improve
the performance of the closed-loop system, a possible solution
could be to use variable gains [30].
We introduce a new PID controller with variable gains whose
main feature is that stability holds even though the gains depend
on the robot states.
SEMIGLOBAL ASYMPTOTIC STABILITY ANALYSIS
In this section, we show that the stability also holds for a
class of nonconstant state-depending proportional, integral, and
derivative gain matrices; specifically, we consider the control
law (9) corresponding to a PID control scheme with nonlinear
gain matrices. The stability analysis is based on a preliminary
version described in [26]. The semiglobal stability is established
in the sense that the region of attraction can be arbitrarily
enlarged with an adequate selection of the controller gains.
FUZZY APPROACH FOR SELF-TUNING THE PID
CONTROLLER GAINS
Freedom to select the proportional, integral, and derivative
gain matrices in a nonlinear manner for the PID control scheme
may be of worth in real applications where manipulators are
under effects of disturbances and constraints. Fuzzy logic is a
suitable approach as a mechanism to determine the nonlinear
gains of the PID control scheme according to previous practical
specifications. This is because the input–output characteristics
of fuzzy logic systems could be easily suited in order to fulfill
the stability requirements established in Proposition 1.
CONCLUSION
In this paper, we have proposed a fuzzy adaptation scheme
for tuning the proportional, integral, and derivative statedependent
gains of a PID controller for robot manipulators.
Moreover, a semiglobal asymptotic stability proof for the proposed
fuzzy self-tuning PID controller for robot manipulators is
presented. The proposed approach allows to consider important
practical features in real robots, such as achievement of desired
accuracy and avoidance of working of the actuators’ torques beyond
their capabilities. The performance of the proposed fuzzy
scheme has been verified by means of real-time experimental
tests on a two-degree-of-freedom direct-drive robot arm.