Successful build and control of the furuta pendulum careful modeling and parameter estimation are key highly nonlinear, unmodeled phenomena e. We describe the statespace, find the fixed points, and simulate the system in matlab. The inverted pendulum benchmark has in addition maintained its usefulness in nonlinear control theory. Balancing the pendulum in the vertical unstable equilibrium position requires continuous correction by a control mechanism.
Firstly, by a suitable partial feedback linearization that allows to linearize only the actuated coordinate of the system, we proceed to find a candidate lyapunov function. Simulation of simple nonlinear pendulum note that the drag force must change sign based on the angular velocity of the pendulum. The furuta pendulum, or rotational inverted pendulum, is a system found in many control labs. Ge420 laboratory assignment 10 discrete full state. The equation of motion are then simulated by ode45 to show they are the same. It provides a compact yet impressive platform for control demonstrations and draws the attention of the control community as a platform for the development of nonlinear control laws. The final expressions were also independently validated using kinematical models using the simmechanics toolbox in simulink. Furuta pendulum matlab simulink ansim simulation youtube. Paper open access related content optimal control of inverted. Controlling the furuta pendulum may be described by referring to the old trick known as the br. Pdf simulation, modelling and control of the furuta pendulum. You will first create a nonlinear simulink model based on the equations of motion for the furuta pendulum. Pdf simulation, modelling and control of the furuta.
Furuta rotary pendulum in matlab download free open. Introduction the furuta pendulum consists of a driven arm which rotates in the horizontal plane and a pendulum attached to that arm which is free to rotate in the vertical plane fig 1. Simulink matlab video tutorial and example low pass filter bode plots part 2 duration. Introduction in this laboratory session we will design a nonlinear controller for an inverted pendulum on a rotating base known as a furuta pendulum. Force analysis and system equation setup below are the two free body diagrams of the system. Geometric formulations of furuta pendulum control problems taeyoung lee1, melvin leok2, harris mcclamroch3 1 george washington university. Simulation studies for stabilization control of furuta. Simmechanics is used to simulate a pendulum at the tip of a rotating arm, called a furuta pendulum.
For this problem the outputs are the carts displacement in meters and the pendulum angle in radians where represents the. The main experiment featured in this thesis is the furuta pendulum, also known as the. From the main problem, the dynamic equations of the inverted pendulum system in statespace form are the following. It was invented in 1992 at tokyo institute of technology by katsuhisa furuta and his colleagues. Publishers pdf, also known as version of record includes final page, issue and volume. Stabilization of rotational modes for the furuta pendulum. It needs constant external force to keep it in upright position. The proposed control strategy of the inverted pendulum system is verified by both simulation and experiments. The present report contains detailed information of the analyzed system the furuta pendulum and the most important.
Full state feedback of furuta pendulum file exchange. Furuta pendulum pole positioning control take home labs. Simulink can work directly with nonlinear equations, so it is unnecessary to linearize these equations as was done in the inverted pendulum. Frtn05 nonlinear control and servo systems laboration 2. There is important this, we note that these oscillations. Furuta pendulum pole positioning control by sean hendrix 1 objective in this experiment you will use state variable feedback, with gains set using pole positioning, to control a furuta pendulum also known as a rotary inverted pendulum. If the pendulum is at rest hanging down, the swing up sequence is started by moving the joystick in any direction along the xaxis. Figure1 a schematic picture of the furuta pendulum 1. The simulink model of rip is developed based on the derived equations. If you want to perform simulations on another pc, you will need to download the simulink files found at the se420 web site. Since most of these techniques are based on invariants andor integrals of motion then, the dynamic model plays an important role. A fundamental benchmark in control theory and robotics olfa boubaker national institute of applied sciences and technology insat, centre urbain nord bp. Both control of the real pendulum and simulation using a model is possible. It is composed of a pendulum attached to the end of a motor.
The system is underactutated and extremely nonlinear due to the gravitational forces and. Chapter 15 control of a furuta pendulum the furuta pendulum is depicted in fig. The control force ut acts along the x direction of the cart. A pendulum rod with a weight attached to its end is joined to the end of the arm in a way that it can rotate freely around the axis of the arm see. We can build the inverted pendulum model in simulink employing the equations derived above by following the steps given below. The furuta pendulum, or rotational inverted pendulum, consists of a driven arm which rotates in the horizontal plane and a pendulum attached to that arm which is free to rotate in the vertical plane.
When the pendulum has reached its upright position the velocity of the pendulum can be controlled. Simulation studies for stabilization control of furuta pendulum system using cascade fuzzy pd controller mukhtar fatihu hamza1,2. Control tutorials for matlab and simulink inverted pendulum. The open loop simulation studies are carried out and the results indicated that. Controlling an inverted pendulum involves two stages. The total potential energy of the system is 9, 10 5. Despite the popularity of the platform, there are very few papers which employ the correct dynamics and only one that. This machine has two rotational degrees of freedom and only one actuator and is thus an underactuated system. Request pdf modeling and construction of a furuta pendulum prototype in order to.
For this problem the outputs are the carts displacement in meters and the pendulum angle in radians where represents the deviation of the pedulums position from equilibrium, that is. Geometric formulations of furuta pendulum control problems. This system is tricky to model in simulink because of the physical constraint the pin joint between the cart and pendulum which reduces the degrees of freedom in the system. From the simulink model you will find a linearized model.
Stabilization of the furuta pendulum based on a lyapunov. The furuta pendulum this paper is devoted to the solution of a new is stabilization of a given rotatory mode of the problem related to the furuta pendulum, which pendulum provided the first arm the analog for the cart in the inverted pendulum tends to a 1 corresponding author given position on the circle. This combination makes it possible to build matlab simulink files. A furuta pendulum is a serial connection of two thin, rigid links, where the. This paper presents a furuta pendulum as a testbed to experimentally validate automatic control strategies or theoretical concepts associated with nonline. Pdf furutas pendulum has been an excellent benchmark for the automatic. Swinging up the furuta pendulum and its stabilization via model predictive control pavol seman boris rohalilkiv martin juh. Inverted pendulum on a cart control bootcamp youtube. Inverted pendulum mechatronics exercises aalto university. This example shows two models of a double pendulum, one using simulink inputoutput blocks and one using simscape multibody. In the present report it will be summarized one entire semester of work and practice in the mechatronics lab of the tuhh facilities. The mass of the cart is represented as m c and the mass of pendulum is represented as m p. All nonlinear dynamics are simulated only one on file exchange ive seen that does that, so the equations can be used to design swing up controller.
Master of science in mechatronics fachlabor mechatronik mechatronics lab simulation, modelling and control of the furuta pendulum with matlab and. Ge420 laboratory assignment 10 discrete full state feedback. The following matlab project contains the source code and matlab examples used for furuta rotary pendulum. Nonlinear control of a furuta rotary inverted pendulum eindhoven. An inverted pendulum is a pendulum a pendulum in inverted position of in other words, it is a pendulum with its centre of gravity above its pivot point. A pd proportional and derivative controller has been used to generate signal to control the speed and direction of the motor. Position of the pendulum because the pendulum is a rigid body, the required position is the its center of mass, figure 2. Note that the furuta pendulum simulink block is found on all the controls lab pcs. Unlike a normal pendulum, inverted pendulum is unstable and would fall down without any external action of force. The potential energy of the pendulum is, 9 where represents the value of gravity. In other words, although the drag force is taken as constant, it. Modelbased friction compensation for the the furuta pendulum. On the dynamics of the furuta pendulum 3 it should be noted that in the derivations that follow, the symbolic toolbox in matlab was used.
In this video, we introduce an example system to control. Based on this candidate function, we derive a stabilizing controller, in such away that the closedloop system is. Furuta s pendulum has been an excellent benchmark for the automatic control community in the last years, providing, among others, a better understanding of modelbased nonlinear control techniques. It provides a compact yet impressive platform for control demonstrations and draws the attention of.
Jan 10, 2012 simmechanics is used to simulate a pendulum at the tip of a rotating arm, called a furuta pendulum. The simulink model uses signal connections, which define how data flows from one block to another. The furuta pendulum consists of an arm, that is actuated by an electric motor and can rotate in the horizontal plane. Nonlinear control of a furuta rotary inverted pendulum. The inverted pendulum benchmark in nonlinear control theory.
Balancing of an inverted pendulum using pd controller. This paper describes, in detail, the successful dynamical model. The system the furuta pendulum is a two link inverted pendulum experiment see figure 1. You will verify both the linear and nonlinear models and then design a linear state feedback controller using pole positioning. Illustrative academic books and survey papers on nonlinear control theory are reported in the first and the second columns, respectively. The furuta pendulum was invented at the tokyo institute of technology by katsuhisa furuta in 1992, and has become a classic system for the application of linear and non. Publishers pdf, also known as version of record includes final page, issue and volume numbers. Simulacion del pendulo invertido en simulink youtube. To see how this problem was originally set up and the system equations were derived, consult the inverted pendulum. It is an example of a complex nonlinear oscillator of interest in control system theory.
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