Swinging-up and stabilization control based on natural frequency for pendulum systems (original) (raw)
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A Controller for Swinging-Up and Stabilizing the Inverted Pendulum
Proceedings of the 17th IFAC World Congress, 2008, 2008
The hybrid solution to the pendulum swinging-up and stabilizing problem introduced byÅström and Furuta is based in two steps: an energy injection and a linear stabilization around the desired inverted position. However the energy injection stage only considers the pendulum, and not the motion of the pivot. Furthermore, for the stabilization stage linear law, only a very small basin of attraction can be guaranteed. In this paper the energy controller is enlarged to cope with the pivot dynamics and a nonlinear controller is introduced for the stabilization stage with a larger basin of attraction. The approach proposed allows to cope both with the pendulum on a cart and the Furuta one. Experiments with a laboratory Furuta pendulum are included.
Control Theory Application for Swing Up and Stabilisation of Rotating Inverted Pendulum
Symmetry, 2021
This paper introduces a new scheme for sliding mode control using symmetry principles for a rotating inverted pendulum, with the possibility of extension of this control scheme to other dynamic systems. This was proven for swing up and stabilisation control problems via the new sliding mode control scheme using both simulations and experiments of rotary inverted pendulum (RIP) underactuated systems. According to the Lyapunov theory, a section of the pendulum was compensated with a scale error in the upright position, as the desired trajectory was followed by the pendulum arm section. As the RIP’s dynamic equations were nonlinearly complex and coupled, the complex internal dynamics made the task of controller design difficult. The system control for the pathway of the reference model of the rotational actuator with the application of the sliding mode technique for moving back and forth up the inverted pendulum’s structure, till the arm to reach the linear range round the vertical upr...
Swing Up and Stabilization Control of a Rotary Inverted Pendulum
IFAC Proceedings Volumes, 2013
The control of a Rotary Inverted Pendulum (RIP) is a well-known and a challenging problem that serves as a popular benchmark in modern control system studies. The task is to design controllers which drives the pendulum from its hanging-down position to the upright position and then hold it there. The swing up is achieved using an energy based controller. In energy based control the pendulum is controlled in such a way that its energy is driven towards a value equal to the steady-state upright position. Then a mode controller switches between the swing-up controller and stabilizing controller near the upright position. For stabilization control, two control techniques are analyzed. Firstly, a sliding mode controller (SMC) is designed to stabilize the pendulum. Secondly, a state feedback controller is designed that would maintain the pendulum upright and handle disturbances up to a certain point. The state feedback controller is designed using the linear quadratic regulator (LQR). The responses of the LQR controller and SMC controller are compared in simulation.
Control of an Inverted Pendulum
The balancing of an inverted pendulum by moving a cart along a horizontal track is a classic problem in the area of control. This paper will describe two methods to swing a pendulum attached to a cart from an initial downwards position to an upright position and maintain that state. A nonlinear heuristic controller and an energy controller have been implemented in order to swing the pendulum to an upright position. After the pendulum is swung up, a linear quadratic regulator state feedback optimal controller has been implemented to maintain the balanced state. The heuristic controller outputs a repetitive signal at the appropriate moment and is finely tuned for the specific experimental setup. The energy controller adds an appropriate amount of energy into the pendulum system in order to achieve a desired energy state. The optimal state feedback controller is a stabilizing controller based on a model linearized around the upright position and is effective when the cart-pendulum system is near the balanced state. The pendulum has been swung from the downwards position to the upright position using both methods and the experimental results are reported.
Swinging up and stabilization of a real inverted pendulum
IEEE Transactions on Industrial Electronics, 2006
The basic aim of the present work was to swing up a real pendulum from the pending position and to balance stably the pendulum at the upright position and further move the pendulum cart to a specified position on the pendulum rail in the shortest time. Different control strategies are compared and tested in simulations and in real-time experiments, where maximum acceleration of the pendulum pivot and length of the pendulum rail are limited. A comparison of fuzzy swinging algorithm with energy-based swinging strategies shows advantages of using fuzzy control theory in nonlinear real-time applications. An adaptive state controller was developed for a stabile, and in the same time optimal balancing of an inverted pendulum and a switching mechanism between swinging and balancing algorithm is proposed.
Design and Simulation of Different Controllers for Stabilizing Inverted Pendulum System
The Inverted Pendulum system has been identified for implementing controllers as it is an inherently unstable system having nonlinear dynamics. The system has fewer control inputs than degrees of freedom which makes it fall under the class of under-actuated systems. It makes the control task more challenging making the inverted pendulum system a classical benchmark for the design, testing, evaluating and comparing. The inverted pendulum to be discussed in this paper is an inverted pendulum mounted on a motor driven cart. The aim is to stabilize the system such that the position of the cart on the track is controlled quickly and accurately so that the pendulum is always erected in its vertical position. In this paper the linearized model was obtained by Jacobian matrix method. The Matlab-Simulink models have been developed for simulation for optimal control design of nonlinear inverted pendulum-cart dynamic system using different control methods. The methods discussed in this paper are a double Proportional-Integral-Derivative (PID) control method, a modern Linear Quadratic Regulator (LQR) control method and a combination of PID and Linear Quadratic Regulator (LQR) control methods. The dynamic and steady state performance are investigated and compared for the above controllers.
Nonlinear control of swing-up inverted pendulum
Proceeding of the 1996 IEEE International Conference on Control Applications IEEE International Conference on Control Applications held together with IEEE International Symposium on Intelligent Control IEEE International Symposium on Computer-Aided Contro
This paper presents plant modeling, analysis, and nonlinear control design and implementation for swingup, pendulum regulation, and arm tracking of the rotational inverted pendulum plant in Fig. 1. For the ideal case, the equilibrium states are characterized. It is shown, for example, that the pendulum cannot be kept at a fixed angle above the horizontal except in a vertical position. The control design centers on the pendulum regulation and arm tracking controllers. A sliding mode and a variable-gain PID controllers are chosen for regulation and tracking. Due to the strong coupling of the arm and pendulum dynamics, a 2DOF control configuration was used. A simple technique was used to swing-up the pendulum to within the region of attraction of the regulation controller. Results of computer simulations and laboratory photos are presented.
European Journal of Control, 2019
In this paper we derive a modified energy based swing-up controller using Lyapunov functions. During the derivation, all effort has been made to use a more complex dynamical model for the single inverted pendulum (SIP) system than the simplified model that is most commonly used. We consider the electrodynamics of the DC motor that drives the cart, and incorporate viscous damping friction as seen at the motor pinion. Furthermore, we use a new method to account for the limitation of having a cart-pendulum system with a finite track length. Two modifications to the controller are also discussed to make the method more appropriate for real-time implementation. One of the modifications improves robustness using a modified Lyapunov function for the derivation, while the other one incorporates viscous damping as seen at the pendulum axis. We present both simulation and real-time experimental results implemented in MATLAB Simulink.
Modeling and controller design for an inverted pendulum system
2007
The Inverted Pendulum System is an under actuated, unstable and nonlinear system. Therefore, control system design of such a system is a challenging task. To design a control system, this thesis first obtains the nonlinear modeling of this system. Then, a linearized model is obtained from the nonlinear model about vertical (unstable) equilibrium point. Next, for this linearized system, an LQR controller is designed. Finally, a PID controller is designed via pole placement method where the closed loop poles to be placed at desired locations are obtained through the above LQR technique. The PID controller has been implemented on the experimental set up.
Advanced sliding mode control techniques for Inverted Pendulum: Modelling and simulation
Engineering Science and Technology, an International Journal, 2018
Numerous practical applications like robot balancing, segway and hover board riding and operation of a rocket propeller are inherently based on Inverted Pendulum (IP). The control of an IP is a sophisticated problem due to various real world phenomena that make it unstable, non-linear and under-actuated system. This paper presents a comparative analysis of linear and non-linear feedback control techniques based on investigation of time, control energy and tracking error to obtain best control performance for the IP system. The implemented control techniques are Linear Quadratic controller (LQR), Sliding Mode Control (SMC) through feedback linearization, Integral Sliding Mode Control (ISMC) and Terminal Sliding Mode Control (TSMC). Considering cart position and pendulum angle, the designed control laws have been subjected to various test signals so as to characterize their tracking performance. Comparative results indicate that ISMC gives a rise time of 0.6 s with 0% overshoot and over-performs compared to other control techniques in terms of reduced chattering, less settling time and small steady state error.