Inverted Pendulum

A fascinating and essential control problem for researchers is the inverted pendulum. It remains a generally accepted standard used in control and robotics for validation of emerging control technologies. A mathematical model of the inverted pendulum on a moving base system was derived, an expression of the linearised state space representation of the system was also presented, a controller to achieve specific criterion of the steady state error, rise and settling time, and was obtained, an implementation of this control on MATLAB was carried out together with the simulated animation of the system using Simulink and Simscape.

In this project a remote controlled self-balancing mobile robot was designed, built and controlled. This paper gives a summary of the work done in the fields of mechanical design, electronics, software design, system characterization and control theory. This wide array of fields necessary for the realization of the project holds the project up as a leading example in the field of mechatronics. In the paper special focus will be on the modelling of the robotic system and the simulation results of various control methods required for the stabilization of the system.

Surprisingly, despite millions of years of bipedal walking evolution, the gravity-related pendulum mechanism of walking does not seem to be implemented at the onset of independent walking, requiring each toddler to develop it. We discuss the precursor of the mature locomotor pattern in infants as an optimal starting point strategy for gait maturation.

To provide engineering students the ability to act in various scenarios related to systems control, it is important to improve classes with practical demonstrations. Inverted pendulum systems have been used as basis for presenting various concepts related to the topic. This paper presents the development of a didactic tool for this practice that can be easily assembled by students due to its simplicity and low cost. It consists of a two parallel wheels supported robot constructed with low cost parts and materials. The robot has a simple arduino control electronics and two small engines. By activating the engines the robot can compensate its inclination stand in vertical position autonomously depending on the control algorithm embedded into its firmware. All documentation is available on a online wiki tool in order to facilitate its reproducibility.

Resistojets operating at low power (less than lOO W) and using liquid propellants have re-emerged as attractive propulsion options for orbit-raising small satellites deployed at Space Shuttle altitudes (approx. 2OO km). Compared to low power pulsed plasma thrusters (PPT), the resistojet produces two orders of magnitude more thrust (approximately 1.4 mN compared to 140 mN) which is required to overcome drag at solar maximum. The wet mass of both systems is approximately equal although the propellant volume for the PPT is significantly lower since it is stored in solid form. The major disadvantage of the resistojet propulsion system compared to the PPT, is in the complexity added from the propellant tanks. Shuttle integration concerns for the solid Teflon (trademark) propellant of the PPT are minimal or non-existent. Although non-toxic, the water or nitrous oxide propellant of the resistojet requires pressurized tanks and valves which increase safety requirements. To investigate the usefulness of the resistojet for small satellite applications, a series of performance tests have been completed at the AFRL Electric Propulsion Laboratory using the JPL inverted pendulum thrust stand. The tests were conducted for two types of resistojet thrusters developed at the University of Surrey which utilize a packed bed of SiC particles for the heat exchanger. Performance testing eas accomplished at power levels from 0-600 W for five propellants: water, nitrous oxide, water/ methanol, nitrogen, and helium. Two endurance tests were conducted to determine possible failure modes. Performance characterization and thermal models were developed for future design applications of these thrusters. Future USAF and Surrey Satellite Technology, Ltd. (SSTL) missions using these resistojets are also discussed.

This paper deals with the design of a swing up controller for the inverted pendulum, which brings the pendulum from any initial position to the unstable up position. Classical method of swing-up control demands large range of movement of cart. Proposed method is assigned for systems with limited movement of cart. This method is based on position control of cart. Reference position is changing according to the state of pendulum. Simulation and experiments on a real pendulum illustrate the results.

Inverted pendulum control is one of the fundamental but interesting problems in the field of control theory. This paper describes the steps to design various controllers for a rotary motion inverted pendulum which is operated by a rotary servo plant, SRV 02 Series. In this paper some classical and modern control techniques are analyzed to design the control systems. Firstly, the most popular Single Input Single Output (SISO) system, is applied including 2DOF Proportional-Integral-Derivative (PID) compensator design. Here the common Root Locus Method is described step by step to design the two compensators of PID controller. Designing the control system using 2DOF PID is quiet challenging task for the rotary inverted pendulum because of its highly nonlinear and open-loop unstable characteristics. Secondly, the paper describes the two Modern Control techniques that include Full State Feedback (FSF) and Linear Quadratic Regulator (LQR). Here FSF and LQR control systems are tested both for the Upright and Swing-Up mode of the Pendulum. Finally, experimental and MATLAB based simulation results are described and compared based on the three control systems which are designed to control the Rotary Inverted Pendulum.

An inverted pendulum on cart is an object which is a
nonlinear, unstable system, is used as a standard for designing
the control methods and finds most versatile application in the
field of control theory. To achieve the stabilization of a inverted
pendulum system pole placement method is used to design a state
feedback controller and then optimal linear quadratic regulator
has been applied to the system. The results shown that are the
comparison between the performance of two controllers, first the
state feedback controller, which is designed by pole placement
method and the optimal LQR controller. Both controller
stabilizes the inverted pendulum system but deviates in their
performance. Simulation has been carried out to show two
different approaches for comparative study of their
performance.

Design of a robust computer control system for balancing a triple pendulum mounted on a moving cart is considered. The controller is based on Discrete-time linear regulator theory
implemented via a 'robust' reduced order observer. The use of integral action eliminates effects of small constant sensor offsets and rail inclinations. Relative stability and disturbance
attenuation properties are investigated using frequency response methods. Experimental results are included.

The present work deals with the study, construction and control of an inverted pendulum system using fuzzy logic embedded in a low cost microcontroller. To this end, we performed extensive research on the topic where they were shown the basics of inverted pendulum system and discussed some models of control, especially the fuzzy logic operation and applicability.
We built a simple prototype for initial testing of fuzzy logic and behavior mechanisms, was later designed and built a larger plant and more robust control tests. To realize the processing, we used a microcontroller ATmega 2560 embarked on an open hardware language called ARDUINO. The program was written in C language version suitable for this type of microcontroller.
The implementation of the control system to the prototype possible to analyze the performance of the controller in the plant and set it in order to get the best response. Computer simulations were used in order to assist the construction of the membership functions of fuzzy logic and comparisons were modified when the quantity of rules and pertinence. Arduino a second plate was used to perform data acquisition in real time of the plant in conjunction with Matlab. The results were satisfactory, showing that it is possible to control a complex problem such as inverted pendulum, fuzzy logic in microcontroller embedded with the same speed limits and information storage thereof.

Inverted pendulum systems are excellent test beds for control theory. An identification method for an inverted pendulum based on simulation models is considered. This method is able to search dynamic parameters effectively even if the pendulum has low resolution position encoders. Friction in the motor-cart system can be modeled with three components: viscous friction, and static (dry) friction terms Coulomb friction and stiction. The presented method is based on the pendulum time response, by using optimization tools. Experiments made both with Simulink based simulation model and a real electromechanical device have proven the full functionality of the proposed model in the real life conditions.

Wheeled systems are energy efficient on prepared surfaces like roads and tracks. Legged systems are capable of traversing different terrains but can be lossy. At low speeds and on off-road surfaces, legged systems using dynamic walking can be efficient. Towards this objective, the dynamics of the walker needs to be modelled and controlled. This thesis presents analysis and experiments on the dynamics and control of a rimless wheel based mobile robot (Chatur ) in a category between wheeled and legged systems. It is effectively a 2D dynamic walker that serves as a platform for investigating inverted pendulum walking. A pulsed actuation torque is proposed for the system resulting in four torque regimes defined by the ratio of energy losses to available actuator torque. Five physical constraints that limit the choice of operating points of a generic inverted pendulum walker are expounded and location of optimal operating points is discussed. Chatur’s hardware design is elaborated and a control topology is proposed for pulsed actuation of the dual brushless dc (BLDC) motor driven platform with wheel synchronization.

The subject of this paper is a comparison of two control strategies of an inverted pendulum on a cart. The first one is a linear-quadratic regulator (LQR), while the second is a state space model pre-dictive controller (SSMPC). The study was performed on the simulation model of an inverted pendulum, determined on the basis of the actual physical parameters collected from the laboratory stand AMIRA LIP100. It has been shown that the LQR algorithm works better for fixed-value control and disturbance rejection, while the SSMPC controller is more suitable for the trajectory tracking task. Furthermore, the system with SSMPC controller has smoother changes in the control signal, that can be beneficial for an actuator, while LQR controller may generate adverse, rapid changes in the control signal.

Two-wheeled self-balancing robot is a popular model in control system experiments which is more widely known as inverted pendulum and cart model. This is a multi-input and multi-output system which is theoretical and has been applied in many systems in daily use. Anyway, most research just focus on balancing this model through try-on experiments or by using simple form of mathematical model. There were still few researches that focus on complete mathematic modeling and designing a mathematical model based controller for such system. This paper analyzed mathematical model of the system. Then, the authors successfully applied a Linear Quadratic Regulator (LQR) controller for this system. This controller was tested with different case of system condition. Controlling results was proved to work well and tested on different case of system condition through simulation on matlab/Simulink program. 1. INTRODUCTION The research on two-wheeled Self-balancing robot has gain momentum over the last decade due to its nonlinearity and unstable nature dynamic system. Motion of two-wheeled self-balancing robot is governed by under-actuated configuration, i.e., the number of control input is less than the number degrees of freedom to be stabilized which makes it difficult to apply the conventional robotic approach for controlling the system therefore, the two-wheeled self-balancing robot is a good platform for researchers to investigate the efficiency of various controllers in control system. The research on two-wheeled self-balancing robot is originally based on inverted pendulum and cart model. However, the two-wheeled self balancing robot system is no longer constrained to the guide rail but moves in its terrain while balancing the pendulum. Thus, it needs a good controller to control itself in upright position and desired heading angle without the needs from outside [1]. Various design of controllers and analysis technique had been proposed by numerous researchers to control the two-wheeled self-balancing robot such that the robot able to balance itself. In [2-4] a fuzzy logic based controller was designed and proven successful to control an inverted pendulum model. In [5], motion control of two-wheeled self-balancing robot was proposed using linear state-space model. In [6], dynamics was derived using a Newtonian approach and the control was design by the equations linearized around an operating point. In [7-9], and [10] a linear stabilizing Proportional Integral Derivative (PID) and Linear Quadratic Regulator (LQR) controller was derived by a planar model without considering robot's heading angle. The above control law was designed by a planar model without considering robot's heading angle therefore still cannot be implemented into a real system. In [11], a comparison between PID and LQR has

A fascinating and essential control problem for researchers is the inverted pendulum.
It remains a generally accepted standard used in control and robotics for validation of emerging
control technologies. A mathematical model of the inverted pendulum on a moving base
system was derived, an expression of the linearised state space representation of the system
was also presented, a controller to achieve specific criterion of the steady state error, rise and
settling time, and was obtained, an implementation of this control on MATLAB was carried
out together with the simulated animation of the system using Simulink and Simscape.

Rotary inverted pendulum is a nonlinear system and a popular model in testing the control algorithm. When using PID control for rotary inverted pendulum system, parameters Kp, Ki, Kd are selected by experimental methods. Nevertheless, those parameters make the system stable but with large swing. This paper applies artificial neural network to calibrate online PID parameters (PID-neuron). These parameters are changed progressively to ensure the stability of the system and smaller swing. The simulation performed in Matlab/Simulink environment shows that parameters Kp, Ki, Kd which are adjusted online make the system stable. The control algorithm is tested in the real rotary inverted pendulum in Matlab/Simulink environment with data acquisition card DSP-F2812. Experimental results show that the proposed PID-neuron controller gives less swing for the pendulum angle than the static PID controlller does.

Walking and running, the two basic gaits used by man, are very complex movements. They can, however, be described using two simple models: an inverted pendulum and a spring. Muscles must contract at each step to move the body segments in the proper sequence but the work done is, in part, relieved by the interplay of mechanical energies, potential and kinetic in walking, and elastic in running. This explains why there is an optimal speed of walking (minimal metabolic cost of about 2 J.kg–1·m–1 at about 1.11 m.s–1) and why the cost of running is constant and independent of speed (about 4 J.kg–1.m–1). Historically, the mechanical work of locomotion has been divided into external and internal work. The former is the work done to raise and accelerate the body centre of mass (m) within the environment, the latter is the work done to accelerate the body segments with respect to the centre of m. The total work has been calculated, somewhat arbitrarily, as the sum of the two. While the changes of potential and kinetic energies can be accurately measured, the contribution of the elastic energy cannot easily be assessed, nor can the true work performed by the muscles. Many factors can affect the work of locomotion - the gradient of the terrain, body size (height and body m), and gravity. The partitioning of positive and negative work and their different efficiencies explain why the most economical gradient is about –10% (1.1 J.kg–1.m–1 at 1.3 m.s–1 for walking, and 3.1 J.kg–1.m–1 at between 3 and 4 m·s–1 for running). The mechanics of walking of children, pigmies and dwarfs, in particular the recovery of energy at each step, is not different from that of taller (normal sized) individuals when the speed is expressed in dynamically equivalent terms (Froude number). An extra load, external or internal (obesity) affects internal and external work according to the distribution of the added m. Different gravitational environments determine the optimal speed of walking and the speed of transition from walking to running: at more than 1 g it is easier to walk than to run, and it is the opposite at less than 1 g. Passive aids, such as skis or skates, allow an increase in the speed of progression, but the mechanics of the locomotion cannot be simply described using the models for walking and running because step frequency, the proportion of step duration during which the foot is in contact with the ground, the position of the limbs, the force exerted on the ground and the time of its application are all different.

The basic theme of this research paper is self erecting the inverted pendulum by via ARDUINO controller and stabilizes the system through PID algorithm of linear control system. ARDUINO controller acquires the data from the sensors in terms of position and angle of the
pendulum and commands the motor through PWM signal after that swing the pendulum from rest position to get and balance the inverted position. Controller read the pendulum’s angular position through potentiometer then calculates and removes errors via PID algorithm. MATLAB-Simulink and LABVIEW sent and receives runtime formation from controller.

The system behavior of a dual-axis inverted pendulum in the presence of parametric uncertainty could be very challenging from the perspective of control handling. It becomes more challenging in the presence of model uncertainties, external disturbances and chattering phenomenon. In this paper, a sliding mode-based control design is proposed to handle the dynamics, system disturbances and uncertainty effects of an inverted pendulum. This is achieved by: a) approximating the discontinuity in the control law, b) handling the origin of chatter effect by using a continuous function, and c) Euler method with small step size. Simulation results show that the sliding mode controller in the presence of disturbance can eliminate the chattering phenomenon, improve the control precision, and suppress the effects of external disturbance and model uncertainties effectively.

This study shows the latest advances in the application of intelligent control to the inverted-pendulum problem. A complete review regarding intelligent control design is presented in this study in order to show the most important artificial intelligence methods used for controlling an Inverted-Pendulum. Also this study proposed the use of a neural-fuzzy-with-genetic-algorithms controller for the inverted pendulum problem which gives good results. Conventional controllers are presented in order to observe implementation problems. The study goes deeply in the details that have to take into account in order to understand design problems and limitations.

an efficient feedback scheduling scheme based on the proposed Feed Forward Neural Network (FFNN)
scheme is employed to improve the overall control performance while minimizing the overhead of feedback
scheduling which exposed using the optimal solutions obtained offline by mathematical optimization methods. The
previously described FFNN is employed to adapt online the sampling periods of concurrent control tasks with
respect to changes in computing resource availability. The proposed intelligent scheduler will be examined with
different optimization algorithms. An inverted pendulum cost function is used in these experiments. Then,
simulation of three inverted pendulums as intelligent Real Time System (RTS) is described in details.
Numerical simulation results demonstrates that the proposed scheme can reduce the computational
overhead significantly while delivering almost the same overall control performance as compared to optimal
feedback scheduling

... 2 System description and modelling ... 693-707 15 BERGEMAN, M., LEE, C., and XU, Y.: 'Dynamic coupling of under-actuated manipulators'. ... 407-420 17 WAhG, C.-YE., TIMOSZYK, WK, and BOBROW, JE: 'Weightlifiing motion planning for a Puma 762 robot'. ...