It is a collection of MATLAB functions and scripts, and SIMULINK models, useful for **analyzing** **Inverted** **Pendulum** **System** and **designing** **Control** **System** for it. Automatic **control** is a growing field of study in the field of Mechanical Engineering. This covers the proportional, integral and derivative (PID). The principal reason for its popularity is its nonlinear and unstable **control**. The reports begin with an outline of research into **inverted** **pendulum** design **system** and along with mathematical model formation. This will present introduction and review of the **system**. Here one dimensional **inverted** **pendulum** is analyzed for simulating in MATLAB environment. **Control** of **Inverted** **Pendulum** is a **Control** Engineering project based on the flight simulation of rocket or missile during the initial stages of flight. The aim of this study is to stabilize the **Inverted** **Pendulum** such that the position of the carriage on the track is controlled quickly and accurately so that the **pendulum** is always erected in its **inverted** position during such movements.

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Development of new **control** methods and the improvement of existing **control** techniques have been interest of researchers for many years. **Inverted** **pendulum** systems have been used to test the performance of various **control** methods in many studies due to their unstable and nonlinear structures. In this work, the use of Particle Swarm Optimization algorithm is presented for the parameter optimization of a Linear Quadratic Regulator controller designed to stabilization and position **control** of an **inverted** **pendulum**. Equations of motion of the **cart** **pendulum** derived by Lagrange formulation have been linearized and presented as state-space model. A Linear Quadratic Regulator controller has been designed for position **control** and stabilization of **pendulum** **system**. Parameters of the controller have been optimized by Particle Swarm Optimization algorithm to obtain best **control** results. Simulation studies were carried out in the MATLAB/Simulink environment and performance of the designed controller has been evaluated through simulation results. KEYWORDS:Inverted **pendulum**, Position **control**, LQR **control**, PSO algorithm, Optimization.

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The objective of this study was achieved by **designing** an adaptive neuro-fuzzy inference **system** (ANFIS) to **control** the **inverted** **pendulum** **system** within a brief time. The controller was implemented in the MATLAB environment using the ANFIS editor. The ANFIS controller provided an efficient and quick response with a small error in both simulation and experiment. It also showed better performance in terms of overshoot, stability and settling time compared to Sugeno FIS. However, the ANFIS controller performance depended heavily on the input-output data collected from a closed loop controlled **system**. Therefore, this step should be implemented only after in-depth and careful planning.

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The **inverted** **pendulum** is a classic problem in dynamics and **control** theory and widely used as benchmark for testing **control** algorithms (PID controllers, neural networks and genetic algorithms). Variations on this problem include multiple links, allowing the motion of the **cart** to be commanded while maintaining the **pendulum**, and balancing the **cart**-**pendulum** **system** on a see-saw. The **inverted** **pendulum** is related to rocket or missile guidance, where thrust is actuated at the bottom of a tall vehicle. Another way that an **inverted** **pendulum** may be stabilized, without any feedback or **control** mechanism, is by oscillating the support rapidly up and down. If the oscillation is sufficiently strong (in terms of its acceleration and amplitude) then the **inverted** **pendulum** can recover from perturbations in a strikingly counterintuitive manner (Jeffers, 2001).

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Next problem in this project is faced by hardware part, where the selection of the appropriate tools and equipment to ensure the **system** is always running smoothly. The device selection is involved in this project including microcontroller circuit and also the device to allow the **pendulum** to know differ angles depending on the situation. In terms of equipment, the selection of **designing** a **cart**, the materials used for the **pendulum** and also the selection motor to drives a **cart** from dropping the **pendulum**. Lastly, the problem is faced from installation software into the hardware part which is to ensure the **pendulum** always maintain in upward position by using controlling the speed of wheel. Then to strength the result for performance this **system**, data from simulation will be compared where all the equipment and tools will combine together to get the **Inverted** **Pendulum** (IP) systems with movement a **cart** in full functioning.

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Fig. 11 and Fig. 12 show two sets of results comparing the application of fuzzy **control** and conventional **control** (PID controller) techniques to the **inverted** **pendulum** problem simulation. For the same **system** parameters here, the PID controller proportional gain, Kp, derivative gain, Kd and integral gain, Ki are found to be 9, 14, and 0.06 respectively. The first two graph show that the fuzzy logic controller gives a smaller overshoot and shorter settling time. In the second set, the mass of the **cart** is changed without modifying the controllers. Fig. 14 shows that the conventional controller totally failed to balance the **pendulum** as it was designed for the nominal value of **cart** mass. On the other hand, the fuzzy logic controller exhibited small performance degradation due to this parameter change as shown in Fig. 13. This proves that fuzzy logic is not based on the mathematical model of the **inverted** **pendulum** and more robust to mass variations.

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Researchers that have worked on this issues, have developed different HIL applications, to make it possible to interact and modify elements that proposed plants must have, and thus to function properly to stimuli that occur within its operation. An example of HIL applications is presented in [1], where a **system** of wind tunnels with 6 degrees of freedom was represented, in order to test it and improve it, before moving on to the manufacturing stage. Another application of HIL in the **designing** field is the validation of combustion engines models, with the aim of increasing energy efficiency by varying the physical and geometric properties of the piston-crank elements set [2]. This applications rely on simulation tools and software **control**, which lead to decreases in time and development costs, as well as making **system** changes available in real time.

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The Rotary **inverted** **pendulum** **system** is an example of plant that commonly used in **control** **system**. Since the **inverted** **pendulum** is the most **control** problem in **control** **system** engineering, it became important plant in testing, **designing**, evaluating and comparing the new **control** technique method. These **control** methods are necessary to stability and balance in the robotic field or robotic application. In robotics, they faced the problem in stability the arm robot which it is unstable when it centre of pressure lies below the gravity. The fact that it is the **pendulum** will simply fall over if the disturbance was occurring in sensitivity to parameter variations. Thus, the **control** algorithm method are purpose to design a non-linear self-elected **inverted** **pendulum** with high performance algorithm.

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Abstract— The **Inverted** **Pendulum** is one of the most important classical problems of **Control** Engineering. In this paper, a real-time **control** for stabilization of **inverted** **pendulum** is developed using PID controller. The implementation platform chosen here is FPGA because it exhibits some superior qualities over traditional processors such as parallel processing capability, high sampling rates, flexibility in design, and reliability. In this **system** controller commands the motor through PWM signal, which drives the **cart** to balance the **pendulum** in an **inverted** position. Pendulum's angular position is fed back by an incremental encoder mounted on its base, which is read by controller. Controller then calculates error and runs the PID algorithm to generate a new command signal.

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One of the most popular **control** methods for swinging up the **pendulum** is where the **control** law is chosen such that the energy of the **pendulum** builds until reaching the upright equilibrium. This technique was first proposed and implemented by Astrom and Furuta [6], [7]. Here, we present a modified approach based on a more complex dynamical model for the SIP **system** than the simplified model that is most commonly used. We also consider the electrodynamics of the DC motor that drives the **cart**, incorporate viscous damping friction as seen at the motor pinion, and account for the limitation of having a **cart**-**pendulum** **system** with a finite track length.

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In this paper, a SMC decoupling model has been designed and implemented on **inverted** **pendulum** in MATLAB environment. A decoupled sliding mode controller is designed to stabilize the **pendulum** at upright position point while moving the **cart** to a desired position. The whole **system** design is divided in two stages. At first stage, sliding mode surface which satisfies the desired specification of **inverted** **pendulum** is designed. During second stage, a **control** function is designed which handles the task of bringing **inverted** **pendulum** in equilibrium state in the presence of uncertainties and external disturbance.

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The considerations in the thesis are based on the real **inverted** **pendulum** trainer situated in the university. A single **inverted** **pendulum** is mounted on a moving **cart**. A DC motor controls the translation motion of the **cart**, through a belt mechanism. The motor is driven by DC electronic **system**, which also contains controller circuit. The **inverted** **pendulum** as an object of **control** is inherently unstable and nonlinear **system**. In order to balance the **pendulum** in the **inverted** position the pivot must be continuously and quickly moved to correct the falling **pendulum**.

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The important activity and most early step in object-oriented software construction phase is the domain model; this model is converted to PIM (Platform Independent Model) as class diagram that will be transformed to PSM (Platform Specific Model), then generate code (classes) to begin actions implementation. This gives a light that domain model is valuable and fired in mind the idea that we must think object, we must concentrate on objects and consider them as the core and as the backbone when **analyzing** and **designing**.

I N 1990 the International Federation of Automatic **Control** (IFAC) Theory Committee published a set of benchmark problems that can be used to compare the benefits of new and existing **control** methods. One of these problems involves the stabilization of an **inverted** **pendulum** [1]. Despite its simple structure, the **inverted** **pendulum** is among the most difficult systems to **control**. This difficulty arises because the equations of motion governing the **system** are inherently nonlinear and because the upright position is an unstable equilibrium. Furthermore, the **system** is under-actuated as it has two degrees of freedom, one for the cart’s horizontal motion and one for the pendulum’s angular motion, but only the cart’s position is actuated, while the pendulum’s angular motion is indirectly controlled. Many of the previously proposed nonlinear **control** techniques for the stabilization of an **inverted** **pendulum** are too complex and impractical for real-time implementation [2]. In this paper, we present the successful real-time implementation of a nonlinear controller for the stabilization of a single **inverted** **pendulum** (SIP) on a **cart**. The controller is based on the power series approximation to the solution to the Hamilton

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The Proportional Integral Derivative (PID) and Proportional Derivative (PD) controllers are the simplest form of feedback **control** designs. These are most commonly used, and widely accepted in **control** engineering. Whereas, the Sliding Mode **Control** (SMC) strategy is highly robust in nature that has many advantages over the above mentioned traditional methods. This paper is systematized in the following parts. Modeling of **Inverted** **Pendulum** is described in second section. Conventions, parameter standards, and **system** analysis are also presented under second sub sections. Third segment deals with the **designing** portion, where the **Inverted** **Pendulum** **control** is implemented with the use of three different ideas. End results and their analysis are worked out under fourth fragment. In five, conclusions and future effort are portrayed.

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• The mass on the **pendulum** should be within about 2 or three inches from the pivot. Remember that the **cart** must be able to get under the center of mass of the **pendulum** in order to right it, so if the center of mass of the **pendulum** is too far away the **cart** will never be able to get under it. The ECP **system** should be moved to the edge of the bench, so that the **pendulum** is completely free to swing without hitting the bench.

Since the 1950s, the inverted pendulum, especially the cart version, was used for teaching linear feedback control theory [8] and it also one of an example studied that had been used as [r]

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This section briefly discusses the overall project design including the workflow of activities, controller design and model **inverted** **pendulum** design. Figure 3.1 shows the flow chart of this project activity. Basically, the process of developing a fuzzy logic **control** for **inverted** **pendulum** can be divided into three (3) phases: first phase is **inverted** **pendulum** design, second phase is fuzzy logic controller and last phase is interfacing the **system** design with hardware. Before **designing** the **inverted** **pendulum** **system**, their mathematical model needs to be obtained in the first place. From the mathematical model, the transfer function of the **system** can be derived. Then LabVIEW VI is used to generate the output response.

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Abstract: A self-erecting single **inverted** **pendulum** (SESIP) is one of typical nonlinear systems. The **control** scheme running the SESIP consists of two main **control** loops. Namely, these **control** loops are swing-up controller and stabilization controller. A swing-up controller of an **inverted** **pendulum** **system** must actuate the **pendulum** from the stable position. While a stabilization controller must stand the **pendulum** in the unstable position. To deal with this **system**, a lot of **control** techniques have been used on the basis of linearized or nonlinear model. In real-time implementation, a real **inverted** **pendulum** **system** has state constraints and limited amplitude of input. These problems make it difficult to design a swing-up and a stabilization controller. In this paper, first, the mathematical models of **cart** and single **inverted** **pendulum** **system** are presented. Then, the Position-Velocity controller is designed to swing- up the **pendulum** considering physical behavior. For stabilizing the **inverted** **pendulum**, a Takagi- Sugeno fuzzy controller with Adaptive Neuro-Fuzzy Inference **System** (ANFIS) architecture is used to guarantee stability at unstable equilibrium position. Experimental results are given to show the effectiveness of these controllers.

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