Geometric formulations of furuta pendulum control problems. Dec 20, 2011 control of a furuta pendulum using an arduino microcontroller and mosfet hbridge amplifier. This replaces the cart in the conventional pendulum. Ge420 laboratory assignment 10 discrete full state feedback. Stabilization of the furuta pendulum based on a lyapunov. Computer control of a double inverted pendulum 71 l, l2, l, 12, m, and m2 are measured directly and mo, fo, go, f, f2, j, and. It was invented in 1992 at tokyo institute of technology by katsuhisa furuta and his colleagues. The applet shows the control of nonlinear unstable system using state feedback. Control of the furuta pendulum using a full order observer week of december 2. The inverted pendulum system the inverted pendulum system is a popular demonstration of using feedback control to stabilizeanopenloopunstablesystem. We have modeled the pendulum as consisting of a massless rod of length l, with a mass m attached at the end. In this video, we introduce an example system to control.
Computer control of a double inverted pendulum pdf free. The inverted pendulum system is a favorite example system and lecture demonstration of students and educators in physics, dynamics, and control. The furuta pendulum, or rotational inverted pendulum, is a system found in many control labs. Swingup control of an invertedpendulum system was demonstrated by mori et al. The uncertainty considered in this paper is possibly fast timevarying and bounded, which may exist in any stage of the pendulum subsystem. The inverse system is obtained by reversing the roles of input and output. The robot had to have a low cost, and enough capability to enable the students to explore and test the ideas presented in lecture and to engage in collaborative learning experiences. Control tutorials for matlab and simulink inverted pendulum. If we do a root locus analysis from the transfer function, we can see that only proportional and derivative control is required to balance an inverted pendulum. Control of a furuta pendulum using an arduino microcontroller and mosfet hbridge amplifier. The pendulums main function is to determine a yes or no answer, to a properly phrased question.
Oct 11, 2006 we propose a lyapunov function based control for the stabilization of the underactuated furuta pendulum. Rotary inverted pendulum 1, also known as furuta pendulum, as a typical nonlinear control system, is a good. The inverted pendulum system is a favorite experiment in control system labs. Full state feedback of furuta pendulum file exchange. Lqr control with refined pid to balance rotary inverted. Inverted pendulum mechatronics exercises aalto university. Friction and friction compensation in the furuta pendulum. We propose a lyapunov function based control for the stabilization of the underactuated furuta pendulum. The reason is that the furuta pendulum belong to the class of underactuated.
Derivation of transfer function for the inverted pendulum. Jan 29, 2017 in this video, we introduce an example system to control. Controlling an inverted pendulum involves two stages. A novel robust control of uncertain furuta pendulum based. 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. This paper describes, in detail, the successful dynamical model. Bugeja introduction the rotational inverted pendulum also known as the furuta pendulum, consists of a twolink mechanism were a motorized arm, which can rotate in a horizontal plane, is used to control the movement of a freely attached rod5. Swinging up the furuta pendulum and its stabilization via model predictive control pavol seman boris rohalilkiv martin juh. Despite the popularity of the platform, there are very few papers which employ the correct dynamics and only one that. It provides a compact yet impressive platform for control demonstrations and draws the attention of. Controlling the furuta pendulum may be described by referring to the old trick known as the br. Since the angular acceleration of the pendulum cannot be controlled directly, the furuta pendulum is an underactuated mechanical system 2. The controller should be robust to keep with various types of disturbances. Nonsmooth approach for contact dynamics and impulse.
Balancing of an inverted pendulum using pd controller. Paper open access related content optimal control of. The rotary pendulum system was suggested as an alternative to the cartontrack system by furuta et al. The aim is to stabilize the pendulum in upper position. If the button is released during an experiment, the pendulum will immediately stop responding. In the above, the block is the controller designed for maintaining the pendulum vertical. Filtered dynamic model, furuta pendulum, leastsquares, parameter identi. 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. Stabilization of rotational modes for the furuta pendulum. Section 3 discusses the system that has been developed.
We describe the statespace, find the fixed points, and simulate the system in matlab. Paper open access related content optimal control of inverted. Inverted pendulum on a cart control bootcamp youtube. It has been used to find buried land mines and tunnels during wartime, finding lost objects, finding people, finding ghosts, increasing your. Swingup control of an inverted pendulum system was demonstrated by mori et al. 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. In addition, we use the skewsymmetric matrix function s. Bicchi abstractthis paper presents experimental results of the application of packetbased control approach with dynamic controller on a real plant. Nonsmooth approach for contact dynamics and impulsebased. System modeling page, the transfer function for is defined as follows. The robot had to have a low cost, and enough capability to enable the students to explore and test the ideas presented in lecture and to.
Packetbased dynamic control of a furuta pendulum over ethernet t. Before you use any pendulum you need to make sure you know its language. The simulation and analysis of a single and double inverted pendulum with a verticallydriven pivot group 7. By the lagrangian formulation of the nonlinear pendulum system, a robust control, based on a general lyapunov function, is designed to render the furuta pendulum a position obedience. We then use the stabilization law for the planar pendulum and prove stability of the controlled furuta pendulum system in x4. Enhancing linear system theory curriculum with an inverted. A pendulum with a moving support point gabriela gonz. Models the analysis of the inverted pendulum system and the. Actuation is rotary, via a direct attachment of the horizontal link to the motor shaft. A novel robust control of uncertain furuta pendulum based on. The invertedpendulum system is a favorite example system and lecture demonstration of students and educators in physics, dynamics, and control. You will not be implementing the swingup control for the furuta until the end of the lab, so initially you will have to manually move the pendulum from the hanging down position to the inverted balancing position.
We can represent the transfer functions derived above for the inverted pendulum system within matlab employing the following commands. The orientation of the arm is represented by the angle. The furuta pendulum a schematic picture of the furuta pendulum is shown in figure 2. As long as an experiment runs, this button must be pressed down. Mo, fo and go are identified from the step response as mentioned before, and ft, f2, jt and. 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. Stabilization of the furuta pendulum based on a lyapunov function. Packetbased dynamic control of a furuta pendulum over.
Chapter 15 control of a furuta pendulum the furuta pendulum is depicted in fig. The transfer function of the system is bs as and the inverse system has the transfer function as bs. Based on this candidate function, we derive a stabilizing controller, in such away that the closedloop system is. 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 highly unstable nature of the plant enables an impressive demonstration of the capabilities of feedback systems. The pendulum consist of a motor driven vertical axis with an arm. The simulation and analysis of a single and double. A lot of papers have used the system to demonstrate linear and nonlinear control laws. It is an example of a complex nonlinear oscillator of interest in control system theory. 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.
Bugeja introduction the rotational inverted pendulum also known as the furuta pendulum, consists of a twolink mechanism were a motorized arm, which can rotate in a horizontal plane, is used to control the movement of a. The system is underactutated and extremely nonlinear due to the gravitational forces and. The control force ut acts along the x direction of the cart. Introduction the furuta pendulum is a very popular experiment used for educational purposes. To obtain the transfer function of the system analytically, the laplace transforms of the system equations were taken. We were tasked with constructing and programming a furuta pendulum, the goal of which is to hold the vertical arm upright through horizontal rotation of the arm connected to the motor shaft. In x5 we present simulation and experimental results that suggest a large region of attraction. Gustavo lee abstractthe inverted pendulum is a simple system in which both stable and unstable con. Since most of these techniques are based on invariants andor integrals of motion then, the dynamic model plays an important role.
The transfer function includes the units necessary to relate the input to the output. Nonsmooth approach for contact dynamics and impulsebased control of frictional furuta pendulum by hantian zhang in this thesis, a nonpenetrated and physically consistent nonsmooth numerical approach has been proposed, by employing the prox formulation and moreaus midpoint. Note that you can give names to the outputs and inputs to differentiate between the carts position and the pendulums position. For safety measures the furuta pendulum is equipped with an emergency button. 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. This is an academic benchmark in modern control theory and underactuated mechanical systems. View notes lecture 7 notes root locus and pid control. The furuta pendulum is a rotational pendulum that is actuated at its basis by a direct current motor with a gear.
And then say out loud or in your mind say yes, the pendulum will slowly start to move this might take a few seconds. The support point moves horizontally with a known function rt xt. The transfer function is an expression relating the output and input of a linear timeinvariant system in terms of the system parameters and is a property of the system itself, independent of the driving function. Two control problems associated to it consist of swingingup the pendulum, in order to move it from the downwards up to the upwards position, and then to equilibrate the pendulum in the unstable, upwards position. To do this hold the pendulum so it can swing freely, however is most comfortable for you. The transfer function for an inverted pendulum using proportional and derivative control is, where, s poles of the equation, l length of the pendulum, g acceleration due to gravity. Furutas 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. 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. The transfer function can thus be viewed as a generalization of the concept of gain. Models the analysis of the invertedpendulum system and the. On the dynamics of the furuta pendulum acm digital library. 7 8, 9 transfer function how pole location affects impulse response by partial fraction. Ge420 laboratory assignment 10 discrete full state.
The mechanical system, consisting of the pendulum and driven links, and the support structure were required to fulfill. The inverted pendulum system the inverted pendulum system is a popular demonstration of using feedback control to. Inverted pendulum with timevarying uncertainty galsanbadam sainzaya. This paper deals with certain options on controlling an inverted rotary pendulum also known as the furuta pendulum. Barton massachusetts institute of technology, cambridge, mass. We have all seen equations to compute pendulum period. Note how the pendulum swings this is its swing for yes. Furuta pendulum control balancing an inverted pendulum.
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