It is a collection of MATLAB functions and scripts, and SIMULINK models, useful for analyzingInvertedPendulumSystem and designingControlSystem 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 invertedpendulum design system and along with mathematical model formation. This will present introduction and review of the system. Here one dimensional invertedpendulum is analyzed for simulating in MATLAB environment. Control of InvertedPendulum 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 InvertedPendulum 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.
Invertedpendulumsystem with the personified intelligent control which is not based on the accurate mathematical model is presented.  It used a method that can develop control laws directly by means of qualitative analysis and synthesis of the plant. The invertedpendulumsystem is a multi-input single-output controlsystem consisting of four inputs; pole angle, change of the pole angle, cart position and change of cart position and single output; control action. The prerequisite of applying this control is to understand the physical structure and behaviour of the controlled object as fully as possible. The model for this control is the invertedcart- pendulum situated on a rail and driven by a single motor. The analysis done by reduction of primary problem until small problems that can be solve. Then, the equations obtained will be programmed in C language and the output can be seen from the graph obtained.
Development of new control methods and the improvement of existing control techniques have been interest of researchers for many years. Invertedpendulum 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 invertedpendulum. Equations of motion of the cartpendulum 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 pendulumsystem. 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.
The objective of this study was achieved by designing an adaptive neuro-fuzzy inference system (ANFIS) to control the invertedpendulumsystem 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.
The invertedpendulum 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-pendulumsystem on a see-saw. The invertedpendulum is related to rocket or missile guidance, where thrust is actuated at the bottom of a tall vehicle. Another way that an invertedpendulum 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 invertedpendulum can recover from perturbations in a strikingly counterintuitive manner (Jeffers, 2001).
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 InvertedPendulum (IP) systems with movement a cart in full functioning.
Fig. 11 and Fig. 12 show two sets of results comparing the application of fuzzy control and conventional control (PID controller) techniques to the invertedpendulum 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 invertedpendulum and more robust to mass variations.
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 , 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 . 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.
The Rotary invertedpendulumsystem is an example of plant that commonly used in controlsystem. Since the invertedpendulum is the most control problem in controlsystem 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 invertedpendulum with high performance algorithm.
Abstract— The InvertedPendulum is one of the most important classical problems of Control Engineering. In this paper, a real-time control for stabilization of invertedpendulum 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.
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 , . 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-pendulumsystem with a finite track length.
In this paper, a SMC decoupling model has been designed and implemented on invertedpendulum 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 invertedpendulum is designed. During second stage, a control function is designed which handles the task of bringing invertedpendulum in equilibrium state in the presence of uncertainties and external disturbance.
The considerations in the thesis are based on the real invertedpendulum trainer situated in the university. A single invertedpendulum 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 invertedpendulum 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.
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 invertedpendulum . Despite its simple structure, the invertedpendulum 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 invertedpendulum are too complex and impractical for real-time implementation . In this paper, we present the successful real-time implementation of a nonlinear controller for the stabilization of a single invertedpendulum (SIP) on a cart. The controller is based on the power series approximation to the solution to the Hamilton
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 InvertedPendulum 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 InvertedPendulumcontrol 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.
• 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.
This section briefly discusses the overall project design including the workflow of activities, controller design and model invertedpendulum design. Figure 3.1 shows the flow chart of this project activity. Basically, the process of developing a fuzzy logic control for invertedpendulum can be divided into three (3) phases: first phase is invertedpendulum design, second phase is fuzzy logic controller and last phase is interfacing the system design with hardware. Before designing the invertedpendulumsystem, 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.
Abstract: A self-erecting single invertedpendulum (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 invertedpendulumsystem 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 invertedpendulumsystem 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 invertedpendulumsystem are presented. Then, the Position-Velocity controller is designed to swing- up the pendulum considering physical behavior. For stabilizing the invertedpendulum, 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.