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**.

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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 [2], a PEM fuel cell at low voltage was modeled for hybrid applications. [4] explained the general facts about the fuel cell. In [7], controlling the output voltage of a PEM fuel cell **using** metal refrigerating **algorithm** was done. And in [8], 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.

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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

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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.

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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 [9] [11].

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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 [4]. The effect of Inverted **Pendulum** under the linear state feedback has been analyzed in [5], 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 [6], a tutorial has been presented wherein, the concept of digital control **system** **design** by pole placement with and without state estimation has been introduced.

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comparison with the conventional differentiator. Afterward, PID **controller** has been widely proposed in the literature for LFC of power systems. In [11], 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 [12] for LFC in an intercon- nected power **system**. In [13], 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 [14] for optimizing PID gains used in Sugeno fuzzy logic based automatic generation control (AGC) of multi-area **system** with thermal generating plants. In [15], 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 [16].

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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) [2], Particle Swarm Optimization (PSO) [3], Ant Colony Optimization (ACO) [4], Differential Evolution (DE) [5], Gravitation **Algorithm** (GA) [6] and Firfly **Algorithm** [7] 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 [8]. The ICA is a multi-agent **algorithm** with each agent being a country [9]. In ICA, the countries divided into two groups based on their power, colonies and imperialists [8]. But these algorithms have defects to deal with the local optimum trap and the accuracy rate [1]. 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 [10]. 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** [11], initial and boundary-value problems [12] , a new hybrid data-clustering **algorithm** [13 ,14], economic problems [15,16,17] and many engineering problems [1,9,18,19,20].

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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 [3], active noise control [4] and echo cancelation [5]. **System**

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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.

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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 [1] developed a tracking control law for underactuated RIP by applying nonlinear back stepping, differential flatness, and small gain theorem. Mirsaeid and Zarei [2] presented a mechatronic **system** case study on adaptive modeling and control of an inverted **pendulum**. Hassanzadeh et al. [3] 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 [4] 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. [5] have described different **controller** designs for rotary **pendulum**. Experimental and MATLAB based simulation results are given. Hassanzadeh et al. [6] 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. [7] presented the dynamic model of RIP. ANN **controller** is used for controlling the **system**.

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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 [7]. 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.

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In literature, little attention has been paid to reliability en- hancement in feeder reconfiguration. Duan et al. in [7] 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 [8]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 [9] 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-

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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 [3].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[4].

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In 1996, Jung and Dorf proposed a new structure of con- troller and termed as proportional- integral-derivative and ac- celeration (PIDA) **controller** [2]. 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 [4].

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**:

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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.

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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.

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The newly formed PID **controller** is placed in a unity feedback loop with the **system** transfer function. This will result in a reduce of the compilation time of the program. The **system** transfer function is defined in another file and imported as a global variable. The controlled **system** is then given a step input and the error is assessed **using** an error performance criterion such as Mean Square Error or in short MSE. The MSE is an accepted measure of control and of quality but its practical use as a measure of quality is somehow limited [4]. The chromosome is assigned an overall fitness value according to the magnitude of the error, the smaller the error the larger the fitness value. Below is the codes used to implement the MSE performance citeria.

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