International Journal of Automation and Computing 10(3), June 2013, 242-255 DOI: 10.1007/s11633-013-0717-x Type-2 Fuzzy Control for a Flexible-joint Robot Using Voltage Control Strategy Majid Moradi Zirkohi 1 Mohammad Mehdi Fateh 1 Mahdi Aliyari Shoorehdeli 2 1 Department of Electrical and Robotic Engineering, Shahrood University of Technology, Shahrood 3619995161, Iran 2 Department of Electrical Engineering, Khaje Nasir Toosi University of Technology, Tehran, Iran Abstract: Type-1 fuzzy sets cannot fully handle the uncertainties. To overcome the problem, type-2 fuzzy sets have been proposed. The novelty of this paper is using interval type-2 fuzzy logic controller (IT2FLC) to control a flexible-joint robot with voltage control strategy. In order to take into account the whole robotic system including the dynamics of actuators and the robot manipulator, the voltages of motors are used as inputs of the system. To highlight the capabilities of the control system, a flexible joint robot which is highly nonlinear, heavily coupled and uncertain is used. In addition, to improve the control performance, the parameters of the primary membership functions of IT2FLC are optimized using particle swarm optimization (PSO). A comparative study between the proposed IT2FLC and type-1 fuzzy logic controller (T1FLC) is presented to better assess their respective performance in presence of external disturbance and unmodelled dynamics. Stability analysis is presented and the effectiveness of the proposed control approach is demonstrated by simulations using a two-link flexible-joint robot driven by permanent magnet direct current motors. Simulation results show the superiority of the IT2FLC over the T1FLC in terms of accuracy, robustness and interpretability. Keywords: Type-2 fuzzy controller, flexible-joint robots, voltage control strategy, particle swarm optimization (PSO), actuator. 1 Introduction Electrically driven robots are efficiently used in various applications. Because their motors provide low torque at high speed, the robotic systems are equipped with power transmission systems to provide high torque at low speed for performing the tasks. However, deformation of the trans- mission system produces flexibility in the joints. This phe- nomenon is the main source of vibration in industrial robot manipulators. Compared with rigid robots, the number of degrees of freedom becomes twice as the number of control actions due to flexibility in the joints, and the matching property between nonlinearities and inputs is lost [1] . Per- forming high-precision tasks by a flexible-joint robot seems to be difficult since the link position cannot follow the ac- tuator position directly. As a result, flexibility in joints should be compensated to improve the performance and avoid unwanted oscillations. However, controlling such sys- tems still faces numerous challenges such as the severe non- linearities, weak coupling, joint flexibility, varying operating conditions, and wide range of uncertainties [2] . Over the years, researchers attempted various control methods for flexible-joint manipulators including singular perturbation theory [3] , feedback linearization [4] , adaptive control [5] , sliding mode control [6] , robust control [7] , fuzzy control [8] and neural control [9] . The presented methods be- long to the class of the commonly used control strategy, which is called torque control strategy. The torque con- trol strategy pays attention to dynamics of robot manipula- tor. However, model of the flexible robot is so complicated, Manuscript received June 27, 2012; revised November 14, 2012 highly nonlinear, heavily coupled, computationally exten- sive and uncertain. Thus, torque control approaches, par- ticularly the model-based techniques, face the challenging problems associated with manipulator dynamics [10] . It is found that the voltage control strategy [11] is superior to the torque-control strategy for the robust control of the rigid manipulators [12] in terms of simplicity in the controller de- sign and performance of the control system. Since flexibility in the joints provides complex dynamics, the voltage con- trol strategy is more efficient than the torque-control strat- egy. Recently, robust control [10] and adaptive control [13] of flexible-joint robots have been developed using the voltage control strategy. In [14], a neural-network-based adaptive controller has been proposed for the tracking problem of manipulators with uncertain kinematics, dynamics and ac- tuator model, using voltage control strategy. On another aspect, tools of computational intelligence, such as artificial neural networks and fuzzy logic controllers, have been credited in various applications as powerful tools. They can provide robust controllers for mathematically ill- defined systems subjected to structured and unstructured uncertainties [15] . Fuzzy control, as a model-free approach, is simply designed for complicated systems that may be difficult to model analytically [16, 17] . Type-1 fuzzy logic control systems (T1FLC) are known for their ability to compensate for structured and unstructured uncertainties to a certain degree. Compared to T1FLC, type-2 fuzzy logic control systems (T2FLC) have been credited to be more powerful in compensating for even higher degrees of uncertainties [18] . The concept of type-2 fuzzy set was in- troduced by Zadeh in 1975 as an extension of the type-1
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International Journal of Automation and Computing 10(3), June 2013, 242-255
DOI: 10.1007/s11633-013-0717-x
Type-2 Fuzzy Control for a Flexible-joint
Robot Using Voltage Control Strategy
Majid Moradi Zirkohi1 Mohammad Mehdi Fateh1 Mahdi Aliyari Shoorehdeli21Department of Electrical and Robotic Engineering, Shahrood University of Technology, Shahrood 3619995161, Iran
2Department of Electrical Engineering, Khaje Nasir Toosi University of Technology, Tehran, Iran
Abstract: Type-1 fuzzy sets cannot fully handle the uncertainties. To overcome the problem, type-2 fuzzy sets have been proposed.
The novelty of this paper is using interval type-2 fuzzy logic controller (IT2FLC) to control a flexible-joint robot with voltage control
strategy. In order to take into account the whole robotic system including the dynamics of actuators and the robot manipulator, the
voltages of motors are used as inputs of the system. To highlight the capabilities of the control system, a flexible joint robot which
is highly nonlinear, heavily coupled and uncertain is used. In addition, to improve the control performance, the parameters of the
primary membership functions of IT2FLC are optimized using particle swarm optimization (PSO). A comparative study between the
proposed IT2FLC and type-1 fuzzy logic controller (T1FLC) is presented to better assess their respective performance in presence of
external disturbance and unmodelled dynamics. Stability analysis is presented and the effectiveness of the proposed control approach
is demonstrated by simulations using a two-link flexible-joint robot driven by permanent magnet direct current motors. Simulation
results show the superiority of the IT2FLC over the T1FLC in terms of accuracy, robustness and interpretability.
Keywords: Type-2 fuzzy controller, flexible-joint robots, voltage control strategy, particle swarm optimization (PSO), actuator.
1 Introduction
Electrically driven robots are efficiently used in various
applications. Because their motors provide low torque at
high speed, the robotic systems are equipped with power
transmission systems to provide high torque at low speed for
performing the tasks. However, deformation of the trans-
mission system produces flexibility in the joints. This phe-
nomenon is the main source of vibration in industrial robot
manipulators. Compared with rigid robots, the number of
degrees of freedom becomes twice as the number of control
actions due to flexibility in the joints, and the matching
property between nonlinearities and inputs is lost[1]. Per-
forming high-precision tasks by a flexible-joint robot seems
to be difficult since the link position cannot follow the ac-
tuator position directly. As a result, flexibility in joints
should be compensated to improve the performance and
avoid unwanted oscillations. However, controlling such sys-
tems still faces numerous challenges such as the severe non-
The speed of convergence versus iteration is shown in
Fig. 13. It indicates that the fitness values have converged.
Another observation is that the additional mathematical di-
mension provided by the FOU enables IT2FLC to achieve
a lower MRSE than T1FLC. Set point performance and
tracking errors are shown in Figs. 14 and 15, respectively.
The control system behaves well in these cases, as well. As a
result of applying optimized T1FLC, the maximum value of
tracking error for joint 1 and 2 in the simulations is reached
to the value of 7×10−3 and 8×10−3, respectively. As a re-
sult of applying optimized IT2FLC, the maximum value of
tracking error for joint 1 and 2 in the simulations is reached
to the value of 6 × 10−3 and 7.98 × 10−3, respectively. It
is seen that the results are much better than simulation 1.
To assess the performance of control system better, another
desired trajectory is considered as
θd = sin(t), θ(0) = 1, 0 6 t 6 10. (59)
The performance of control system is shown in Fig. 16,
where the joint tracking error is reduced as well.
Fig. 13 The cost function of PSO
Fig. 14 Set point performance
Fig. 15 Tracking performance
Simulation 4. In this case, for the robustness evalu-
ation of the controllers, external disturbances are added to
the robot system. The disturbance is inserted to the input
of each motor as a periodic pulse function with a period of
2 s, having a different value of amplitude, with time delay
of 0.7 s, and pulse-width 30% of the period[32]. This form
of disturbance is general. But it includes jumps to cover
the complex cases. All the values of the cost functions for
different amplitude of disturbance in the cases of T1FLC
and IT2FLC are given in Table 5.
Table 5 Comparison between type-1 and type-2 FLC for
different amplitudes of disturbance
Amplitude Type-1 FLC (MRSE) Type-2 FLC (MRSE)
A=0 0.1892 0.1860
A=1 0.1958 0.1879
A=2 0.2044 0.1910
A=4 0.2337 0.2022
As seen from Table 5, the performance of the T1FLC
is similar to IT2FLC to some extent as long as the am-
plitude of disturbance is low or there is no disturbance.
However, when the amplitude of disturbance in the Table 5
is increased, it is seen that the performance of T1FLC de-
grades significantly. Hence, the performance of the T1FLC
will be unacceptable under this disturbance. Thus, the
T1FLC cannot be used in such noisy environment. On the
other hand, IT2FLC can handle the external disturbances
to give a very good performance effectively. As a result, the
IT2FLC is able to handle the uncertainty and outperform
the type-1 controller.
Simulation 5. In this case, the ability of the T1FLC and
IT2FLC to handle unmodelled dynamics is investigated. To
this end, transport delay is deliberately introduced into the
feedback loop[20]. First, a transport delay equalling to 0.2 s
is artificially added to the nominal system. The step re-
sponses are shown in Fig. 17. When a the transport delay
equalling to 0.3 s is added to the system, the corresponding
254 International Journal of Automation and Computing 10(3), June 2013
step responses are shown in Fig. 18. As shown in Figs. 17
and 18, large oscillations are obtained when T1FLC is used
to control the plant. Of the two controllers, IT2FLC pro-
vided the best performance as its step responses have the
smallest overshoot and are least oscillatory. The simulation
results again confirm that the IT2FLC is able to handle the
uncertainty and unmodelled dynamics, and outperform the
T1FLC controller.
Fig. 16 Tracking performance
Fig. 17 Set point performance under unmodelled dynamics with
time delay 0.2 s
Fig. 18 Set point performance under unmodelled dynamics with
time delay 0.3 s
As a result, the main advantage of the IT2FLC is its
ability to eliminate persistent oscillations, especially when
unmodelled dynamics is introduced.
8 Conclusions
In this paper, interval type-2 fuzzy logic controller was
used to control a two-joint articulated flexible-joint robot
driven by permanent magnet direct current motors using
voltage control strategy. Stability analysis was presented
and the performance of the IT2FLC was compared with
that of T1FLC. In addition, an optimal IT2FLC for flexible-
joint robot was introduced using particle swarm optimiza-
tion. In fact, parameters of the primary membership func-
tions of IT2FLC were optimized to improve the performance
and increase the accuracy of IT2FLC. We observed using
performance criteria such as MRSE, when the amplitude of
external disturbance is low, the performance of both T1FLC
and IT2FLC is somehow identical. However, it is known
that T1FLC can handle the nonlinearities and uncertain-
ties up to some extent. Therefore, by increasing amplitude
of external disturbance and considering unmodelled dynam-
ics, the results demonstrate that IT2FLC can outperform
T1FLC. Thus, the IT2FLC is more appealing than its type-
1 counterpart with regards to accuracy and interpretability.
The main advantage of the IT2FLC appears to be its abil-
ity to eliminate the persistent oscillations, especially when
unmodelled dynamics is introduced. This ability to han-
dle modeling error is particularly useful when fuzzy logic
controllers are tuned off-line using PSO.
Acknowledgments
The authors would like to thank Dr.Dong Wu for his
valuable advices.
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Majid Moradi Zirkohi received theB. Sc. degree in electrical engineering fromKerman University, Iran in 2006, and theM. Sc. degree in electrical engineering fromShahrood University of Technology, Iran in2008. Currently, he is a Ph.D. candidate atShahrood University of Technology, Iran.
His research interests include soft com-puting, control theory, and fuzzy logic.
Mohammad Mehdi Fateh receivedthe B. Sc. degree from Isfahan Universityof Technology, Iran in 1988, the M. Sc. de-gree in electrical engineering from TarbiatModares University, Iran in 1991, and thePh.D. degree from Southampton Univer-sity, UK in 2001. He is a full professor atDepartment of Electrical and Robotic En-gineering, Shahrood University of Technol-
ogy, Iran.His research interests include nonlinear control, fuzzy control,
robotics, intelligent systems, mechatronics and automation.E-mail: [email protected]
Mahdi Aliyari Shoorehdeli receivedthe B. Sc. degree in 2001, the M. Sc. andPh.D. degrees in electrical engineering fromKhaje Nasirling Toosi University of Tech-nology, Iran in 2003 and 2008, respectively.He joined Khaje Nasir Toosi University ofTechnology in 2008, where he is currentlyan assistant professor of electrical engineer-ing.
His research interests include system identification, intelligentsystems and hybrid control.