Abstract—For linear systems and some of non-severe non- linear systems, classic controllers such as PI and PID have been widely used in industrial control processes because of their simple structure and robust performance in a wide range of operating conditions. Several numerical approaches such as Fuzzy Logic Controller (FLC) algorithm and evolutionary algorithms have been used for the optimum design of PID controllers. In this paper, a pitch displacement of aircraft was controlled by FLC tuned with Bees Algorithm (BA). For a given input, the parameters of Mamdani-type-Fuzzy Logic Controller (the centers and the widths of the triangle membership functions (MFs) in inputs and output) were optimized by the BA with Integral Time Absolute Error (ITAE) as a cost function. In order to compare the optimized Fuzzy Logic Controller with different controller, the PI controller was tuned with BA and also PI controller tuned with Ziegler- Nichols tuning rules. The simulation results show that Fuzzy Logic Controller tuned by bees algorithm is better performance and more robust than the fuzzy-Expert and PI tuned by bees algorithm and Ziegler-Nichols for aircraft pitch control.
INTRODUCTION
FOR linear systems and some of non-severe non-linear systems, classic controllers such as PI and PID have been widely used in industrial control processes because of their simple structure and robust performance in a wide range of operating conditions. However, it is quite difficult to determine optimum parameters of classic controllers. In the tuning process of a classic controller, constants must be selected in such a way that the closed loop system has to give the desired response. The desired response should have minimal settling time with a small or no overshoot in the step response of the closed loop system. Several numerical approaches such as Fuzzy Logic Controller (FLC) algorithm and evolutionary algorithms have been used for the optimum
design of PID controllers [1]-[5].
FLC is popular technique that has seen increasing interest in the past decades since it has a linguistic based structure and its performance are quite robust for controlling systems. However, FLC including some parameters such as linguistic control rules and limits and type of MFs have to be tuned for
Manuscript received October 3, 2011.
Zaeri. Mechanical Engineering Department, University of Shahid Chamran, Ahvaz, Iran (corresponding author to provide phone:
+986115524843; e-mail: [email protected] yahoo.com).
Mechanical Engineering Department, University of Shahid Chamran, Ahvaz, Iran (e-mail: [email protected]).
Mechanical Engineering Department, University of Shahid Chamran, Ahvaz, Iran (e-mail: [email protected] yahoo.com).
Zaeri. Biomedical Engineering Department, IAUD, Ahvaz, Iran (e- mail: [email protected] yahoo.com).
a given system. A major drawback of FLC is that the tuning process becomes more difficult and very time consuming when the number of the system inputs and outputs are increased. Bees algorithm (BA) is relatively new evolutionary algorithm that may be used to find optimal or near optimal solutions in big search space [6]. BA is especially useful for parameter optimization in continuous, multi-dimensional, search spaces and multi-objective, complex optimization [7], [8]. The BA method can generate a high quality solution within shorter calculation time and it tends to converge very fast compared to other stochastic methods. The BA has proven both very effective and quick in diverse set of benchmark optimization problems [9]-[12]. Evolutionary algorithms regarding tuning the MFs parameters of FLC have been studied extensively in the literature. These studies can be divided into four groups as genetic algorithm, particle swarm optimization (PSO), ant colony optimization (ACO) and bees algorithm (BA) [13]- [20]. Attaran and ghanbarzadeh optimized FLC MFs for hydraulic actuator of gun turret using BA [9]. Also BA was used to Fuzzy clustering [11]. Pham et al. tuned a fuzzy logic controller for a robot gymnast using the BA [10]. Myint et al. designed a PID controller for pitch stability of Piper Cherokee aircraft. Their results showed that the PI controller based Ziegler-Nichols tuning rules has better performance respect to PID [21]. Kurnaz et al. proposed an ANFIS (adaptive neuro-fuzzy inference system) based controllers for unmanned aerial vehicles (UAVs). They uesd MATLAB’s standard configuration to control the position of the UAV in three dimensional space as altitude and longitude–latitude location [22].
In this work, BA was used to tune the Mamdani type- fuzzy controller’s antecedent and consequent parameters for the pitch attitude control system. The rest of this article is organized as follows. The components of a pitch attitude control system of the piper aircraft are described as a case study and also the classic PI controller which tuned with Ziegler-Nichols tuning rules was designed in Section II. A fuzzy control algorithm is proposed in Section III. The BA tuning method for the fuzzy controller and the PI controller is described in Section IV. The results and conclusion are given in Sections V and VI, respectively. Results show that the performance of combining Fuzzy-BA is considerably improved.
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