The double inverted pendulum is unstable, meaning that it will fall down unless it is controlled in some way. Pdf fuzzy optimal control for double inverted pendulum. Balancing of an inverted pendulum using pd controller. The actuator of the double inverted pendulum is a dc motor from the maxon company. The inverted pendulum system usually used to test the effect of the control policy, and it is also an ideal experimental instrument in the study of control theory 1, 2. To reach longer distances within the same rise time, the controller needs more accurate models at different angle to improve prediction. In sukontanakarn and parnichkun, 8 a rotary single inverted pendulum system was successfully controlled using optimal control. The double inverted pendulum is a nonlinear system with a high level of nonlinearities, which is extensively used in testing new control methods. Control of double inverted pendulum first approach. And a solution of this problem is applicable to other nonlinear and underactuated control problems. Hence, this paper considers the swingup control problem for the.
The inverted pendulum is a classical control problem, which involves developing a system to balance a pendulum. To implement the above control strategy, a minor loop is. The double inverted pendulum is a highly nonlinear and openloop unstable system. Inverted pendulum system is a complicated, nonlinear, unstable system of high order. Pdf optimal control of a double inverted pendulum on a cart. Its popularity derives in part from the fact that it is unstable without control, that is, the pendulum will simply fall over if the cart isnt moved to balance it. It can be suspended stably in this inverted position by using a control system to monitor the angle of the pole and move the pivot point horizontally back under the center of mass when it starts to fall over, keeping it balanced.
A swingup control scheme for a serial double inverted pendulum is proposed. The control of an inverted pendulum is of two folds with two different controllers. Parnichkun,8 arotary single inverted pendulum system was successfully controlled using optimal control. Jan 29, 2017 in this video, we introduce an example system to control. Scribd is the worlds largest social reading and publishing site.
Unlike a normal pendulum, inverted pendulum is unstable and would fall down without any external action of force. The simulation and analysis of a single and double inverted pendulum with a verticallydriven pivot group 7. Gustavo lee abstractthe inverted pendulum is a simple system in which both stable and unstable con. The cart a slides on a horizon tal frictionless track that is. Double click on the block and change the parameters as shown below. Fuzzy control of a doubleinverted pendulum sciencedirect. Control tutorials for matlab and simulink inverted. To study this problem, this project incorporated a full system design. Alhadithi antonio javier barragan jose manuel andiijar agustin jimenez abstractin this paper a fuzzy optimal control for stabilizing an upright position a double inverted pendulum dip is developed and compared.
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. The cart with an inverted pendulum, shown below, is bumped with an impulse force, f. This boomstrick example is a twodegreeoffreedom single inverted pendulum. It contains information to setup and configure the laboratory, outlines the control design and its implementation, as well as the experimental procedure. Determine the dynamic equations of motion for the system, and linearize about the pendulums angle, theta 0 in. The weight variable fuzzy inputs is gained by combining the fuzzy control theory with the optimal control. In this project pid proportionalintegralderivative type of control is used to balance the inverted. We describe the statespace, find the fixed points, and simulate the system in matlab. Another example gainscheduled mpc control of an inverted pendulum on a cart shows how to use gain scheduling mpc to. Fuzzy control research for stabilization a double inverted pendulum at an upright position successfully is proposed based on weight variable fuzzy inputs. Paper open access related content optimal control of. The swingup controller, which diverge the pendulum from the stable position is. Many di erent methods have been established for its control.
Mahbubeh moghaddas received the ms degree in control engineering from the control department, islamic azad university of gonabad, iran, in 2009 and 2011, respectively. Control of a double inverted pendulum on a free download as powerpoint presentation. Energy and passivity based control of the double inverted. Pdf the problem of stabilization of a double inverted pendulum mounted on a cart is presented. This is made for the minicomputer nova 1200 and uses 24k words memory. The simulation and analysis of a single and double inverted. It needs constant external force to keep it in upright position. Elsevier fuzzy sets and systems 79 1996 315321 fuizy sets and systems fuzzy control of a doubleinverted pendulum fuyan cheng, guomin zhong, youshan li, zhengming xu hebei institute of mechanoelectric engineering, shi jia zhuang, 050054 peoples republic of china yanshan university, qin huang dao, 066000 peoples republic of china received i. Control of rotary double inverted pendulum system using mixed. Rotary double inverted pendulum user and lab manual. Control tutorials for matlab and simulink inverted pendulum.
Since we will run our simulation for 10 seconds, this will ensure that only a single pulse is generated. A double inverted pendulum is successfully stabilized at the upright position by using a computer control. The upward inverted state is unstable, though it has long been. A typical arrangement of the double inverted pendulum dynamics involves eulerlagrangian equation as in 3. The additional challenge of a second pendulum can be used to demonstrate advanced controls concepts, or as a basis for research. Design of optimal pid controller for inverted pendulum.
Modeling is based on eulerlagrange equations derived by specifying a lagrangian, difference between kinetic and potential energy of the dipc system. Comparison of lqr and pd controller for stabilizing double. Pdf in this report a number of algorithms for optimal control of a double inverted pendulum on a cart dipc are investigated and compared. Control of rotary double inverted pendulum system using. Maxon offers us 2 devices, figure 3 and figure 4, in order to control the power part and the control part for the dc motor. Double inverted pendulum, nonlinear system, unstable dynamic system, dc motor, maxon.
Inverted pendulum on a cart control bootcamp youtube. Also shown are free body diagrams for the forces on each mass. Jun 20, 2008 inverted pendulum system is a complicated, nonlinear, unstable system of high order. A simple plane pendulum left and a double pendulum right. It is this property that makes the dualinvertedpendulum system harder to stabilize than the articulatedinvertedpendulum system often called the doubleinvertedpendulum system. It is unstable and without additional help will fall over. A double inverted pendulum is the combination of the inverted pendulum and the double pendulum. Rotary double inverted pendulum laboratory guide madefor. Determine the dynamic equations of motion for the system, and linearize about the pendulum s angle, theta 0 in. Pdf balancing a double inverted pendulum using optimal control. Proceedings of the american control conference, 2003. Swing up control of the inverted pendulum so that it can swing up from normal position to inverted position and then balance itself.
Balancing control of a rotary double inverted pendulum system is a challenging research topic for researchers in dynamics control field because of its nonlinear, high degreeoffreedom, under actuated and unstable characteristics. Modeling and simulation of inverted pendulum system using matlab. The two main methods of controlling a double inverted pendulum are moving the base, as with the inverted pendulum, or by applying a torque at the pivot point between the two pendulums. Analysis and design of controllers for a double inverted. The goal was to learn controllers for balancing and swingup, without using any. Pdf balancing a double inverted pendulum using optimal. It has been known as a more difficult problem to design a fuzzy. A double inverted pendulum plant has been in the domain of control researchers as an established model for studies on stability.
Designing a controller that balances two links adds an extra challenge when compared to the single inverted pendulum system. Optimal control of double inverted pendulum using lqr. Control of inverted double pendulum using reinforcement. The two main methods of controlling a double inverted pendulum are moving the base, as with the inverted pendulum, or by applying a torque. Open the inverted pendulum simscape model generated above. Using modern control techniques, it is possible to control multi. The furuta pendulum is a rotational pendulum that is actuated at its basis by a direct current motor with a gear.
This laboratory manual describes how to design a statefeedback control system that balances a rotary double inverted pendulum and positions the rotary arm to. A fundamental benchmark in control theory and robotics olfa boubaker national institute of applied sciences and technology insat, centre urbain nord bp. Pdf on may 30, 2018, bowen xu and others published estimation and control of a doubleinverted pendulum find, read and cite all the. Until now, the structure of the inverted pendulum has been the railcart type which consists of a cart running on a rail and a pendulum attached to the cart. Control of inverted double pendulum using reinforcement learning. Computer control of a double inverted pendulum 73 the simulation, a computer aided design program with the function of the simulation is developed for the design of a controller for a double inverted pendulum and is named cados. Fuzzy optimal control for double inverted pendulum. For visualization purposes, this is similar to trying to balance a broomstick on a finger.
We consider the swingup control of this newtype inverted pen dulum in this paper. The onedimensional swinging inverted pendulum with two degrees of freedom i. Swingup control of a serial double inverted pendulum. Here, the control objective is to control the system such that when the cart reaches a desired position the inverted pendulum stabilizes in the upright position. Double carts inverted pendulum closed loop control 5. Double pendulum on a cart 12 x pointtopoint control and 4 x sidestepping twodegreesoffreedom design. This results in a system of nonlinear differential equations consisting of three 2nd order equations. The system when running the balance controller is shown in figure 1. Balancing a double inverted pendulum using optimal control and. 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. Pdf swingup control of a serial double inverted pendulum. The inverted pendulum system is an example commonly found in control system textbooks and research literature.
Fujimoto, controller design for an inverted pendulum based on approximate linearization, int. The problem of balancing an inverted pendulum is one. In this video, we introduce an example system to control. Double inverted pendulum dip is a nonlinear, multivariable and unstable system. Double inverted pendulum is stable when its two pendulums allocated in vertically position and have no oscillation and movement and also inserting force should be zero. Stabilization control of double inverted pendulum system. By restricting consideration to only one degree of freedom gives the classic textbook example of a nonlinear unstable system. This is the only actuator of the system to control the displacement of the 2 limbs that constituted the double inverted pendulum. Implementing pid control closedloop response problem setup and design requirements the cart with an inverted pendulum, shown below, is bumped with an impulse force, f. Fuzzy optimal control for double inverted pendulum basil m. Add a pulse generator block from the simulinksources library. Rotary dual inverted pendulum system with two parallel pendulums attached to a rotary arm was designed and controlled by pakdeepattarakorn et al. International journal of advanced control of rotary double.
The control system is designed based on the state space approach by using a computer aided design program named cados developed for this purpose. Computer control of a double inverted pendulum sciencedirect. There are several different algorithms that can be used to balance an inverted pendulum. An inverted pendulum is a pendulum that has its center of mass above its pivot point. The simulation and analysis of a single and double. Optimal control of a double inverted pendulum on a cart citeseerx. The control scheme is to swing up the pendulum in three steps, step 1. The aim of the paper is to design and performance analysis of the double inverted pendulum and simulation of linear quadratic regulator lqr. Design of optimal pid controller for inverted pendulum using. Pdf estimation and control of a doubleinverted pendulum. To stabilize a double inverted pendulum is not only a challenging problem but also a useful. Double inverted pendulum is a nonlinear system, unstable and fast reaction system.
Edit the gain value of this block by double clicking it and change it to 1i. The important system parameter state variables include x. The goal of controlling ip is to balance the pendulum in upright position when it initially starts with some nonzero angle off the vertical position. Balancing a double inverted pendulum using optimal control. Mar 29, 2011 double pendulum on a cart 12 x pointtopoint control and 4 x sidestepping twodegreesoffreedom design. The inverted pendulum control problem has been widely used as an example to demonstrate the effectiveness of modern control theory. It seems to have been one of attractive tools for testing linear and nonlinear control laws 6, 17, 1.
In this report a number of algorithms for optimal control of a double inverted pendulum on a cart dipc are investigated and compared. Examples include the linear quadratic regulator feedback design 6, its a nonlinear extension. Analysis and design of controllers for a double inverted pendulum henrik niemann dzlrstedodtu, automation technical university of denmark building 326, dk2800 lyngby, denmark email. This is a very typical nonlinear control problem, and many techniques already exist for its solution 6. A double inverted pendulum system is an extension of the single inverted pendulum, mounted on a cart. Realtime swingup double inverted pendulum by nonlinear. The upper segment is given by the trunk including head and arms and the lower segment by the legs excluding the feet. Optimal control of a double inverted pendulum on a cart. Pdf optimal control of a double inverted pendulum on a. Doubleclick on the block and change the parameters as shown below. Realtime swingup of double inverted pendulum by nonlinear model predictive control pathompong jaiwat 1 and toshiyuki ohtsuka 2 abstract in this study, the swingup of a double inverted pendulum is controlled by nonlinear model predictive control nmpc. Analysis and design of controllers for a double inverted pendulum. Pdf computer control of a double inverted pendulumf.