# Top PDF Design Controller of Pendulum System using Imperialist Competitive Algorithm ### Design Controller of Pendulum System using Imperialist Competitive Algorithm

Abstract—Due to development of technology in recent years, complexity and nonlinearity of mechanical and electrical system are increasing significantly. Inverted pendulum is nonlinear system that has become popular in recent years. However, inverted pendulum is nonlinear and unstable system. Therefore appropriate design controller of inverted pendulum system is crucial. Hence, this paper proposed, design of inverted pendulum system based on imperialist competitive algorithm (ICA). In order to design the controller, dynamic model of inverted pendulum system is used. Time domain simulation is used to address the controller performance. From the simulation result, it is found that imperialist competitive algorithm can be used to design inverted pendulum system controller. ### DESIGNING A PID CONTROLLER TO CONTROL A FUEL CELL VOLTAGE USING THE IMPERIALIST COMPETITIVE ALGORITHM

achieving high-quality power. However, the out- put voltage of the fuel cell changes due to differ- ent charges. Employing a controller is necessary to fix the output voltage. The simplest controller that can be used is the PID controller. There are many studies within the context of technical and parametric examinations of the proton exchange membrane fuel cell. In , a PEM fuel cell at low voltage was modeled for hybrid applications.  explained the general facts about the fuel cell. In , controlling the output voltage of a PEM fuel cell using metal refrigerating algorithm was done. And in , a dynamic model of the fuel cell has been studied. In this work, a simple PID con- troller for the fuel cell has been used, with the difference that the coefficients of this controller are calculated using the imperialist competitive algorithm, rather than trial and error method. At first, the problem is formulated as an optimiza- tion problem and will be optimized based on an imperialist competitive algorithm to calculate the optimum result of the PID controller. This system was simulated in simulink environment of MAT- LAB software. ### Optimizing locomotive body structures using imperialist competitive algorithm

In today's design, system complexity and increasing demand for safer, more efficient and less costly systems have created new challenges in science and engineering. Locomotives are products which are designed according to market order and technical needs of customers. Accordingly, targets of companies, especially designers and manufacturers of locomotives, have always been on the path of progress and seek to offer products with higher technology than other competitors. Quality of body structures is based on indicators such as natural frequency, displacement, fatigue life and maximum stress. Natural frequency of various components of the system and their adaption to each other are important for avoiding the phenomenon of resonance. In this study, body structures of ER24 locomotive (Iran Safir Locomotive) was studied. A combination of imperialist competitive algorithm (ICA) and artificial neural network was proposed to find optimal weight of structures while natural frequencies were in the determined range. Optimization of locomotive's structure was performed with an emphasis on maintaining locomotive abilities in static and dynamic fields. The results indicated that use of optimization techniques in the design process was a powerful and effective tool for identifying and improving main dynamic characteristics of structures and also optimizing performance in stress, noise and vibration fields. Received: 19/06/2013 ### The Optimal Steering Control System using Imperialist Competitive Algorithm on Vehicles with Steer-by-Wire System

In this paper was developed an AI-based control system that applied to the model fully automatic steer- by-wire system that represented on the vehicle model with 10 Degree Of Freedom (DOF) [9, 16]. DOF are the vector movement of the vehicle dynamics that describes the state of the physical dynamics of vehicle, where the 10 DOF is meant is, 10 mathematical equations of Newtonian force equation for the longitudinal, lateral, yawing, pitching, rolling, bouncing and the vertical movement of each wheel. The strategy of control system that was developed, consisting of two stages of control, in cascade, namely, the first is FLC as a major control on the lateral motion and the second is Proportional-Integral-Derivative controller (PID) as an advanced control on the yaw motion. To obtain the parameters of the optimal control system on the FLC and PID used an optimization method of ICA. The expected results of this simulation on active steering control with the use of FLC and PID control tuned by ICA can improve vehicle dynamic performance. ### Design of a Robust Controller for Inverted Pendulum

The PID controller is the most common form of feedback. It was an essential element of early governors and it became the standard tool when process control emerged in the 1940s. The PID controller calculation involves three separate parameters; the proportional, the integral and derivative values. The proportional value determines the reaction to the current error, the integral value determines the reaction based on the sum of recent errors, and the derivative value determines the reaction based on the rate at which the error has been changing. The weighted sum of these three actions is used to adjust the process via a control element such as the position of a control valve or the power supply of a heating element. . Note that the use of the PID algorithm for control does not guarantee optimal control of the system or system stability  . ### Optimal Controller Design for Inverted Pendulum System: An Experimental Study

There are two sets of poles one set is fast and other set is sluggish, the faster set of poles determine the angle dynamics and the slower set of poles determines the position dynamics. The cart position error always overshoots initially to catch up with the falling pendulum. Only after the rod is stabilized the position comes back to origin . The effect of Inverted Pendulum under the linear state feedback has been analyzed in , the dynamic equations indicate the existence of stability regions in four dimensional state-space and an algorithm has been developed that transforms the four dimensional state space to three dimensional space. In , a tutorial has been presented wherein, the concept of digital control system design by pole placement with and without state estimation has been introduced. ### Fractional order PID controller design for LFC in electric power systems using imperialist competitive algorithm

comparison with the conventional differentiator. Afterward, PID controller has been widely proposed in the literature for LFC of power systems. In , an intelligent PID controller based on the principle of anthropomorphic intelligence was suggested. Designing PID controller using particle swarm opti- mization algorithm is presented in  for LFC in an intercon- nected power system. In , Artiﬁcial Bee Colony (ABC) algorithm has been used to tune the automatic generation con- trollers in an interconnected reheat thermal power system. The results of this paper show the better performance of ABC in comparison with PSO. Several novel heuristic stochastic search techniques are presented in  for optimizing PID gains used in Sugeno fuzzy logic based automatic generation control (AGC) of multi-area system with thermal generating plants. In , uniﬁed tuning of PID was proposed for LFC in power systems via internal model control. LFC has been carried out by a new decentralized robust optimal MISO PID controller based on matrix eigenvalues and Lyapunov method in . ### An Improved Imperialist Competitive Algorithm based on a new assimilation strategy

F IND the optimal solution is a major challenge in many scientific problems. The heuristic algorithms have widely been used to reach global optimum of different problems. Genetic Algorithm (GA) , Particle Swarm Optimization (PSO) , Ant Colony Optimization (ACO) , Differential Evolution (DE) , Gravitation Algorithm (GA)  and Firfly Algorithm  are some familiar meta-heuristic studies. Recently, inspired by a socio-politically motivated, a meta- heuristic algorithm called Imperialist competitive algorithm (ICA) is proposed by Atashpaz and Lucas . The ICA is a multi-agent algorithm with each agent being a country . In ICA, the countries divided into two groups based on their power, colonies and imperialists . But these algorithms have defects to deal with the local optimum trap and the accuracy rate . The local optimum trap is an important shortcoming in optimization. A local optimum is a solution that is optimal within a neighboring set of solutions. This is in contrast to a global optimum, which is the optimal solution among all possible solutions that may occur under different situations . ICA is much more successful than other optimization methods to eradicate these problems [8, 9, and 10]. It has been used to solve different kinds of problems, such as PID controller design , initial and boundary-value problems  , a new hybrid data-clustering algorithm [13 ,14], economic problems [15,16,17] and many engineering problems [1,9,18,19,20]. ### Design of IIR Digital Filter using Modified Chaotic Orthogonal Imperialist Competitive Algorithm (RESEARCH NOTE)

Digital filters apply mathematic functions on discrete signals and change some of their properties. For example, they remove noise from them or allow a particular frequency range of a signal to pass and omit the others. These filters have two typesincluding Infinite Impulse Response (IIR) and Finite Impulse Response (FIR). Compared to FIR filters, IIRs require less delay, adder and multiplier elements. In other words, they need fewer coefficients and attract more attention as they can reduce the filter order significantly compared to FIR filters. If there is not sufficient data about desired system or the characteristics are not fulfilled by time invariant filters, adaptive filters would be utilized [1, 2]. Adaptive filters adjust their transfer function according to the input and adapt themselves with it. These filters are applied to channel equalization , active noise control  and echo cancelation . System ### Applying an Imperialist competitive algorithm for scheduling parts in a green cellular manufacturing system with consideration of production planning

A Cellular Manufacturing System (CMS) is the practical use of Group Technology (GP) in a production environment, which has received attention from researchers in recent years. In this paper, a mathematical model for the design of a cell production system is presented with consideration of Production Planning (PP). Consideration of environmental factors such as energy consumption and waste generated by machines in the proposed model is considered. Also, the problem of scheduling component processing in the presented model has been considered. Due to the complexity of the model presented in this paper, a hierarchical approach is proposed for solving the model. At first, the proposed model is analyzed without considering the scheduling topic using the GAMS software and the results are analyzed. Then an Imperialist Competitive Algorithm (ICA) was used to solve the scheduling problem. To evaluate the performance of the proposed model, numerical examples are used in small, medium, and large dimensions. In addition, the ICA presented in this paper is compared with the methods available in the literature as well as the genetic algorithm and its quality is confirmed. ### Alternative controller design for rotary inverted pendulum

Many studies are found in the area of control issues related to inverted pendulum systems. Some of the studies dealing with inverted pendulum control are summarized herein. Yan  developed a tracking control law for underactuated RIP by applying nonlinear back stepping, differential flatness, and small gain theorem. Mirsaeid and Zarei  presented a mechatronic system case study on adaptive modeling and control of an inverted pendulum. Hassanzadeh et al.  presented an optimum Input-Output Feedback Linearization (IOFL) cascade controller. Genetic Algorithm (GA) was applied for the inner loop with PD controller forming the outer loop for balancing the pendulum in an inverted position. The control criterion was to minimize the Integral Absolute Error (IAE) of the system angles. The optimal controller parameters are found by minimizing the objective function related to IAE using Binary Genetic Algorithm (BGA). Ozbek and Efe  focused on the swing up and stabilization control of a rotary inverted pendulum (RIP) system with linear quadratic regulator (LQR). Sliding Mode Control (SMC) is based on hard boundary switching law and fuzzy logic control (FLC). Akhtaruzzaman et al.  have described different controller designs for rotary pendulum. Experimental and MATLAB based simulation results are given. Hassanzadeh et al.  also studied control by using evolutionary approaches. GA, Particle Swarm Optimization (PSO) and Ant Colony Optimization (ACO) are used for designing the rotational inverted pendulum. Quyen et al.  presented the dynamic model of RIP. ANN controller is used for controlling the system. ### The Application of Imperialist Competitive Algorithm for Fuzzy Random Portfolio Selection Problem

This paper proposes the use of a new evolutionary algorithm known as Imperialist Competitive Algorithm (ICA) to solve fuzzy random portfolio optimization. The ICA is a meta-heuristic optimization method that is based on modeling for the attempts of countries to dominate other countries . The rest of the paper is organized as follow: Section 2 includes basic concepts on fuzzy and fuzzy random theory. In section 3, the problem formulation is presented. Section 4, explains the ICA in detail. In section 5, a numerical example is solved to illustrate the proposed model. Finally, conclusion and future work will be presented in section 6. ### Reconfiguration of distribution systems to improve reliability and reduce power losses using Imperialist Competitive Algorithm

In literature, little attention has been paid to reliability en- hancement in feeder reconfiguration. Duan et al. in  performed network reconfiguration for power loss reduc- tion and reliability enhancement with constraints of volt- age profile and network radiality. The algorithm used to solve the optimization problem is an enhanced Genetic Algorithm (GA). The basis for this work is the informa- tion of a single loop caused by closing a normally open switch and to develop the algorithm on crossover and mu- tation operations of the original GA. Shareef et al.in ap- plied the Quantum-Inspired Binary Firefly Algorithm (QBFA) to network reconfiguration to minimize the num- ber of propagated voltage stages and other reliability in- dices such as System Average Interruption Frequency Index (SAIFI) and Momentary Average Interruption Fre- quency Index (MAIFI). The problem constraints are volt- age profile and network radiality. Kavousi-Fard et al. in  utilized the self-adaptive modified optimization algo- rithm based on the Bat Algorithm (BA) for distribution network reconfiguration with considering several objec- tives of SAIFI, Average Energy Not Supplied (AENS), total active power losses, and total network cost. In order to observe the effect of distributed generation on the reli- ### Data analysis by combining the modified k-means and imperialist competitive algorithm

The k-means algorithm is a major practical clustering method. The main purpose of k-means clustering method is to minimize the aggregate difference of all objects of a cluster from their related cluster centers .This method is generally used due to its simplicity and low repeat number. The k-means algorithm tries to find the cluster centers of so that the sum of squared distances of every from the nearest cluster center is minimum. The performance dependence of this algorithm on the initialization of cluster centers is a major problem. In this algorithm there is a strong connection between data points and nearest cluster centers which does allow the cluster centers to exit from local data dense areas but its ultimate solution is neither unique nor necessarily optimum. ### A Hybrid DEA Based CHAID and Imperialist Competitive Algorithm for Stock ‎Selection

algorithm is capable to implement all variables in creation of the prediction model. At high vol- umes, statistical data are not free of missing val- ues. These values have a major impact on the performance of numerous machine learning algo- rithms. CHAID algorithm is one of the few algo- rithms that act appropriately in the face of miss- ing values . The tree produced by this algo- rithm is not necessarily a binary tree. This is one of the important characteristics of this algorithm. Therefore, the possibility of understanding and recognition of models increases for experts and shows more flexibility in application of model in important decision makings . About the im- plementation of CHAID decision tree, it should be noted that this algorithm is a modeling tech- nique used to study the relationships between a dependent variable and many independent vari- ables. Predictor variables can be qualitative or quantitative. This method used Chi-Square anal- ysis to investigate the role of qualitative indepen- dent variables and used variance analysis meth- ods to investigate the role of independent vari- ables. Based on the P-Value, this algorithm se- lects the effective variables for predicting output variable . About the development method of prediction model and evaluation of its effective- ness, it can be said first using a technique, the data set should be separated to individual sub- sets to create and test the models. To reduce the modeling Bias, the application of K-Fold valida- tion method is recommended for this technique .Law inference algorithms have some differ- ences that are important to users. Below are the differences between these algorithms . ### Design of PIDA Controller Using Bat Algorithm for AVR Power System

In 1996, Jung and Dorf proposed a new structure of con- troller and termed as proportional- integral-derivative and ac- celeration (PIDA) controller . It consists of three numbers of zeros and poles but two poles may be neglected in the de- sign process. It is addition of a zero in the standard PID struc- ture to derive the PIDA structure of the controller.The intro- duction of an extra zero to the PID controller is to change the root locus of the third order plant in order to make dom- inant roots more dominant by eliminating the effects of non- dominant roots . ### Stock Portfolio-Optimization Model by Mean-Semi-Variance Approach Using of Firefly Algorithm and Imperialist Competitive Algorithm

Firefly Algorithm (FA) was designed by Xin-She Yang (2008) benchmarking of the luminance of the firefly. They used rhythmic brightness of firefly for attract hunt and mating. Brightness pattern in each firefly is different. This brightness can be a protective mechanism for firefly. Rate of brightness and distance of brightness cause attraction of the couple together. Each bit is a firefly and is updated a multi-dimension research with attract dynamically and according to science about firefly and its neighbors. The searching process is really surprising in which a firefly is compared with all other fireflies, if it has low brightness in compare of other firefly, its mate will choose the other one. This causes that bits attract to other bit with more brightness(light) and if there is more brightness in other algorithm frequency, bits move to a bit that has more brightness. Search steps depend on maximum of frequencies. There are main rules in the FA algorithm: ### Controller design for two-wheels inverted pendulum vehicle using PISMC

As can be seen in figure 3 to figure 8, the tilt angle of the mass center of the robot cross the horizontal axis were within 5 second for pole- placement controller and about 2 second for PISMC controller. However more than 8 second lapsed for position of the center of the robot to return to its original position. It happen for both controller. But PISMC improve the overshoot magnitude less then 0.12 rad if compared to pole-placement which has about 0.3 rad. Although there is a slight movement (micron radian) of the position in PISMC controller to make the tilted body return to zero angle, the result are satisfactory and upright balancing was successful. ### AN ALGORITHM FOR DESIGN OF A PID CONTROLLER FOR A MULTIVARIABLE SYSTEM USING OUTPUT FEEDBACK

This paper deals with the design of a proportional-plus-integral-plus-derivative (PID) controller for linear multivariable systems using an output feedback control law. Controller is designed as an equivalent proportional- plus-derivative controller for the augmented system formed due to the integral action. The design equations are formulated in terms of coefficient matrix of the transfer function vector of the equivalent single input (or single output) system. The computation of coefficient matrix of a transfer function vector gives a simple and direct procedure for pole assignment. The design procedure does not require cyclicity as an initial condition. The controller design is illustrated with a numerical example. 