Fractional order control of conducting polymer artificial muscles
Introduction
Conducting polymer actuators (CPAs) are a novel class smart material based actuators, which change their shape and volume upon implementation of a sufficient electrical potential difference or current. They are also known as artificial muscles as they can mimic the motion of biological muscles very well. Moreover, they have attracted great attention because of their superior properties such as biocompatibility, high force output to weight ratio and elasticity (Kim & Tadokoro, 2007). Selection of the controller parameters in applications of CPAs is of great importance as they are also used in precise positioning systems. As they are in their infancy, there are some challenges in achieving the desired control performance requirements such as fast settling time, minimum steady state error and overshoot out of these actuators. In addition, the control voltage to drive CPAs must be limited below 1–2 V in order to prevent possible damages. Some advanced control methods have been proposed to achieve a significant positioning performance from CPAs: Intelligent control based on fuzzy logic PD + I control and neuro-fuzzy adaptive neural fuzzy inference system (ANFIS) control (Druitt & Alici, 2014), robust adaptive control (Fang, Tan, & Alici, 2008), adaptive sliding mode control (Wang, Alici, & Nguyen, 2013), repetitive control (Itik, 2013), etc. Moreover, Wang, Alici, and Tan (2014) established a hysteresis model for CPAs and controlled the tip displacement of a CPA using inverse feedforward control. Blanchard and Nguyen (2014) proposed a robust controller which is based on quantitative feedback theory to improve the accuracy of the tip displacement positioning of a CPA. Beyhan and İtik (2015) used adaptive fuzzy-Chebyshev network control to identify and control the position of a CPA without utilizing a physical model. The common aim of these works is to improve the positioning accuracy of CPAs. They achieved this aim using very complicated control methods none of which pre-considered the aforementioned important performance requirements for CPAs. Moreover, to show the effectiveness of all these controllers, their responses were compared to those of classical PID controllers which were not tuned optimally by using a desired performance index.
Fractional calculus extends the theory of ordinary differential equations to fractional order differential equations which have non-integer order of integrals and derivatives. Conventional integral operator ‘1/s’ and derivative operator ‘s’ are replaced to ‘’ and ‘’ in fractional calculus where and are the fractional order parameters of integral and derivative operators, respectively. Fractional calculus has recently become widespread in engineering applications especially in control system design. Several fractional order controllers have been proposed as alternatives to their non-fractional counterparts. One of the most common and practical fractional order control methods for linear systems is the fractional order PID (FOPID) control which is an extension of the classical PID control. Due to easy design and implementation, FOPID controllers have gained attention and found many applications such as robot manipulators (Sharma, Rana, & Kumar, 2014), power electronics (Calderón, Vinagre, & Feliu, 2006), drive systems (Xue, Zhao, & Chen, 2006) and process control (Monje, Vinagre, Feliu, & Chen, 2008). For systems including nonlinearities and uncertainties, nonlinear fractional order controllers such as fractional order sliding mode controller (FOSMC) can be used (Dadras & Momeni, 2012). Aghababa (2013) proposed a fractional order sliding mode controller for vibration suppression of uncertain structures. Fractional order control has also been implemented effectively in synchronization of chaotic systems (Tavazoei and Haeri, 2008, Aghababa, 2012a, Aghababa, 2012b).
A FOPID controller, which is denoted as , consist of 5 independent parameters: the proportional gain , integral gain , derivative gain , order of integrator and differentiator . The parameters and are additional to the traditional PID, which give control engineers more design flexibility to further enhance the control systems performance. Heuristic methods such as genetic algorithms (Copot et al., 2013, Bingul and Karahan, 2012, Machado, 2010), particle swarm optimization (PSO) (Bingul and Karahan, 2012, Zamani et al., 2009), differential evolution (DE) (Biswas, Das, Abraham, & Dasgupta, 2009), chaotic ant swarm method (Li, Yang, Peng, & Wang, 2006) and more recently Cuckoo search algorithm (Sharma et al., 2014) were used to find the optimal parameters for the FOPID control all of which agreed on the improvements in the control systems performance compared to optimized PID controllers. Optimally tuned FOPID control have been applied to many systems such as (Majhi et al., 2015, Pradeepkannan and Sathiyamoorthy, 2015, Zamani et al., 2009). When the parameters of a FOPID controller are optimally tuned based on some pre-defined objectives, they may also improve the positioning performance of CPAs. This may reduce the complexity of control design while satisfying the tracking error, maximum overshoot requirements and control constraints.
The main contribution of this paper is that we design a fractional order controller to improve the positioning performance of CPAs.To the best of author’s knowledge a FOPID controller has not been designed for CPAs yet. As a second contribution, a specific cost function which considers maximum overshoot, control signal, settling time, rise time and tracking error, is used in the controller design process. Such performance requirements are very important for the position control of CPAs and should be given a careful consideration. This has not been considered for CPAs neither. To obtain the best controller parameters based on the defined performance index, we employ Cuckoo search algorithm and compare the results with those obtained by the PSO algorithm. PID controllers are also designed by using both search algorithms and their responses are also compared to those of FOPID controllers.
The rest of this paper is organized as follows. Section 2 presents a brief background about fractional calculus and the fractional PID control. In Section 3, we introduce the trilayer CPA and obtain its fractional order model. Section 4 discuses the meta-heuristic algorithms used in this study and their implementation to FOPID control design. Simulation and experimental results are given in Section 5. Finally, the conclusions are drawn.
Section snippets
Fractional calculus and fractional order PID controller
Fractional calculus is a non-integer order operator that represents differentiation and integration. Because of the fact that many systems and subjects in engineering such as control theory (Bohannan, 2008), robotics (da Graça Marcos, Duarte, & Tenreiro Machado, 2008), electronics (Krishna & Reddy, 2008) and signal processing (Kumar, Singh, & Saxena, 2013) manifest a memory effect and they are described more accurately by fractional order dynamics, fractional calculus has attracted great
Trilayer conducting polymer actuator and experimental setup
The CPA used in this study is shown in Fig. 2(a). The actuator has a rectangular shape with the dimensions of 14 mm × 5 mm × 0.17 mm and two polypyrrole (PPy) layers on the outer surfaces each of which has a thickness of approximately 30 μm. The porous nonconductive layer is made of 110 μm Polyvinylidene Difluoride (PVDF) and both sides of this layer is coated with 0.2 μm gold which the PPy electrodes can be electrochemically deposited. The electrolyte consists of Lithium triflouromethanesulfonimide in
Optimization of the FOPID controller using meta-heuristic algorithms
A FOPID controller has 5 parameters explained in Section 2 to be optimized: and μ. Both CSA and PSO are employed in order to minimize a specific objective function by tuning the parameters of the FOPID controller. In general, error based objective functions such as integral of absolute error (IAE), integral of squared-error (ISE) and integral of time-weighted-squared-error (ITSE) are often employed in controller design process since they can be easily evaluated analytically. However,
Simulation and experimental results
In the experiments, a tri-layer CPA was used with the aforementioned dimensions. Because of the fact that ambient conditions such as temperature and humidity have influence on the dynamics of the CPA, the experiments were conducted in the same day under the same conditions, where the ambient temperature was 21 °C and the relative humidity was 65%. Before starting the experiments, the actuator was bathed in the electrolyte lithium triflouromethanesulfonimide (Li+TFSI−) in order for enabling the
Conclusion
In this paper, we proposed a fractional order controller in order to improve the positioning performance of a CPA rather than using complicated control methods as proposed in the literature (Beyhan and İtik, 2015, Druitt and Alici, 2014, Itik, 2013, Wang et al., 2013). We showed that FOPID control could provide high accuracy in controlling the tip displacement of the CPA if the parameters of the controller were tuned optimally based on a specific performance index. The performance index was
Acknowledgment
This work was supported by The Scientific and Technological Research Council of Turkey, Project No. 114M781. The authors would also like to thank Professor Gursel Alici from the Australian Research Council (ARC) Centre of Excellence for Electromaterials Science (CE0561616) at the University of Wollongong.
References (40)
Robust stabilization and synchronization of a class of fractional-order chaotic systems via a novel fractional sliding mode controller
Communications in Nonlinear Science and Numerical Simulation
(2012)A fractional-order controller for vibration suppression of uncertain structures
ISA Transactions
(2013)- et al.
Design of fractional-order pid controllers with an improved differential evolution
Engineering Applications of Artificial Intelligence
(2009) - et al.
Fractional order control strategies for power electronic buck converters
Signal Processing
(2006) - et al.
Fractional terminal sliding mode control design for a class of dynamical systems with uncertainty
Communications in Nonlinear Science and Numerical Simulation
(2012) - et al.
Fractional dynamics in the trajectory control of redundant manipulators
Communications in Nonlinear Science and Numerical Simulation
(2008) Fractional-order controller design
Computers & Mathematics with Applications
(2013)Repetitive control of a trilayer conjugated polymer actuator
Sensors and Actuators A: Physical
(2013)- et al.
Parameters identification of chaotic systems via chaotic ant swarm
Chaos, Solitons & Fractals
(2006) - et al.
Tuning and auto-tuning of fractional order controllers for industry applications
Control Engineering Practice
(2008)
Design of intelligent pid/pid speed controller for chopper fed dc motor drive using opposition based artificial bee colony algorithm
Engineering Applications of Artificial Intelligence
Performance analysis of fractional order fuzzy pid controllers applied to a robotic manipulator
Expert Systems with Applications
Great spotted cuckoos improve their reproductive success by damaging magpie host eggs
Animal Behaviour
Synchronization of chaotic fractional-order systems via active sliding mode controller
Physica A: Statistical Mechanics and its Applications
Design of a fractional order pid controller for an avr using particle swarm optimization
Control Engineering Practice
Chaos in a fractional-order micro-electro-mechanical resonator and its suppression
Chinese Physics B
Adaptive fuzzy-Chebyshev network control of a conducting polymer actuator
Journal of Intelligent Material Systems and Structures
Fractional pid controllers tuned by evolutionary algorithms for robot trajectory control
Turkish Journal of Electrical Engineering & Computer Sciences
Identification and control of a trilayer conjugated polymer actuator
Smart Materials and Structures
Analog fractional order controller in temperature and motor control applications
Journal of Vibration and Control
Cited by (17)
Intelligent PID control of an industrial electro-hydraulic system
2023, ISA TransactionsA simple modelling strategy for integer order and fractional order interval type-2 fuzzy PID controllers with their simulation and real-time implementation
2022, Expert Systems with ApplicationsCitation Excerpt :As the primary target of this section is to demonstrate the applicability of the proposed fuzzy controllers, except GA, other kinds of optimization algorithms are not explored here. For clarity, the performances of the PID (Itik et al., 2015), FOPID (Itik et al., 2015), and IOIT2FPID controllers are compared, and the summary of the comparison is encapsulated in Table 5. By comparing the transient performance data in Table 6, it is concluded that the newly derived FOIT2FPID controller is better than the FOFPID controllers, developed by Das et al. (2012), in controlling the nonlinear plant in Eq. (31).
A graphical tuning method for fractional order controllers based on iso-slope phase curves
2020, ISA TransactionsCitation Excerpt :Nonlinear equations need a numerical solution, but the problem formulation is still analytical. Numerical approaches used in fractional order controller tuning are based on different optimization methods, such as Particle Swarm Optimization (PSO) [20], Artificial Bee Colony (ABC) [21], Firefly Algorithm (FA), Cuckoo Search (CS), or Differential Evolution (DE), as in [22–26], respectively. Recent developments have explored the use of iterative methods for parameter tuning, as in [27], but flat phase specification is still solved through optimization.
Impedantiometric Behavior of Solid Biopolymer Electrolyte Elaborated from Cassava Starch Synthesized in Different pH
2022, International Journal of TechnologyFractional-order PID Controller for Four Rotor Aircraft Based on Genetic Algorithm
2020, Proceedings of 2020 IEEE 4th Information Technology, Networking, Electronic and Automation Control Conference, ITNEC 2020Model-free control of an electro-active polymer actuator
2019, Materials Research Express