Ball-beam System Research Articles

Fuzzy Fractional Order PID Tuned via PSO for a Pneumatic Actuator with Ball Beam (PABB) System

This study aims to improve the performance of a pneumatic positioning system by designing a control system based on Fuzzy Fractional Order Proportional Integral Derivative (Fuzzy FOPID) controllers. The pneumatic system’s mathematical model was obtained using a system identification approach, and the Fuzzy FOPID controller was optimized using a PSO algorithm to achieve a balance between performance and robustness. The control system’s performance was compared to that of a Fuzzy PID controller through real-time experimental results, which showed that the former provided better rapidity, stability, and precision. The proposed control system was applied to a pneumatically actuated ball and beam (PABB) system, where a Fuzzy FOPID controller was used for the inner loop and another Fuzzy FOPID controller was used for the outer loop. The results demonstrated that the intelligent pneumatic actuator, when coupled with a Fuzzy FOPID controller, can accurately and robustly control the positioning of the ball and beam system.

Fractional order robust adaptive control design for actuator failure compensation in dual ball-beam system

This paper is to proposes a fractional order adaptive control scheme design for actuator failure compensation in order to balance of a ball-beam system with redundant actuators. The proposed controller is based on a fractional order sliding surface from which an adaptive actuator failure compensation control scheme is obtained. In order to control the dual ball-beam system with redundant motors, a linearized model is derived, which is subjected to actuator failures. A set of numerical simulation tests representing few selected types of actuator failures scenarios are carried out to assess the output tracking performance of the proposed controller design when dealing with such failures

Ballbeam System Analysis and Design Based on Root Locus Correction and State Space Correction

The ballbeam control system is one of the most perfect and classic experimental equipment for the research and analysis of automatic control theory. Other nonlinear and unstable systems have important dynamic performance, but because the ball bar system is nonlinear and unstable, it is necessary to design a controller to correct it. In this paper, the root locus and the state space theory are used for correction. In the root locus correction, the curve of the root locus is changed by adding open-loop zeros and poles to make the system stable; in the state space, a state feedback observer is designed by using the principle of pole assignment, and the state feedback matrix K is obtained to make the system stable. Using the visual tool Simulink in MATLAB to simulate, we can see the specific control effect of the controller intuitively. The real-time control was carried out on gbb2004, and the results were observed.

Optimal design of an adaptive robust proportional-integral-derivative controller based upon sliding surfaces for under-actuated dynamical systems

This paper presents a novel adaptive robust proportional-integral-derivative (PID) controller for under-actuated dynamical systems via employing the advantages of the PID control and sliding surfaces. The related control gains as adjustable parameters are computed during the control process using gradient descent techniques and the chain derivative rule. Based on the design of control rules, the genetic algorithm optimization is utilized in order to find the optimal values of the learning rates and initial conditions of the control gains. The suggested strategy is implemented successfully to stabilize the cart-pole and ball-beam systems. Lastly, the simulation results demonstrate the efficacy of the proposed controller to control such under-actuated dynamical systems as well as its superiority in comparison with other recently introduced methods.

Variable Cut-Off Frequency Observer-Based Positioning for Ball-Beam Systems Without Velocity and Current Feedback Considering Actuator Dynamics

This paper develops an observer-based positioning scheme for ball-beam systems considering actuator dynamics. The practical constraints are handled systematically, including the mechanical dynamical nonlinearities, mismatched load disturbances, and parameter uncertainties. This result provides contributions as follows. First, parameter-independent observers exponentially estimate the ball velocity, motor speed, and its acceleration to remove the velocity, motor speed, and current feedback. Second, the auto-tuner automatically adjusts the desired closed-loop input-output behaviors to update its cut-off frequency in the transient operations. Third, observer-based active damping injection reduces the closed-loop ball position and actuator speed dynamics to 1 by pole-zero cancellation. Finally, disturbance observers act as a dynamic compensator by estimating the disturbances from model-plant mismatches such as dynamic nonlinearities, mismatched load disturbances, and parameter variations. The experimental study verifies the applicability of the proposed technique using the Quanser Ball-Beam hardware driven by an SRV02 servomotor.

Estabilidad y diseño de un controlador LQR para un sistema Bola-Viga

This article presents the design of an LQR controller for a Ball-Beam system, as well as its stability analysis, the control of a Ball-Beam system is one of the most interesting for control engineering since it is a highly non-dynamic system linear. The objectives of this document focus on the performance of the system using an LQR control for different disturbances as well as obtaining the phase plans. The work starts with the modeling of the ballgirder system, which consists of two mechanical arms, a gear box and a DC servomotor, later the LQR control is designed, this allows simulation and obtaining the response of the controller under different conditions. In the system the input torque is generated from the DC servo motor to control the position of the ball on the beam, where the ball rolls freely on the beam. Performance analysis is performed using robust LQR and the performance characteristics of the system are presented. Finally, the stability analysis is carried out by plotting the phase planes.

Velocity Observer-Based Nonlinear Self-Tuning Position Stabilizer for Ball-Beam System Applications

This brief exhibits a nonlinear self-tuning position stabilization algorithm for ball-beam system applications under the consideration of parameter uncertainties and actuator dynamics.; there are two major contributions. First, a first-order ball velocity estimator is proposed using only the ball position feedback without dependence on system parameters. Second, the resulting nonlinear controller incorporates the time-varying feedback gain driven by the proposed self-tuner. Third, a first-order disturbance observer (DOB) is introduced to remove the high-frequency disturbance attenuation performance. The various simulation results-based-on MATLAB/Simulink validate the practical merits of the proposed scheme.

A New Multi-objective Artificial Bee Colony Algorithm for Optimal Adaptive Robust Controller Design

Artificial bee colony algorithm as a recent meta-heuristic algorithm, inspired from the foraging behavior of honey bees, can be considered as a proper technique to handle optimization problems. In this paper, a multi-objective artificial bee colony algorithm is introduced in which an archive is defined to store non-dominated solutions. Furthermore, to reduce computations and to have evenly distributed solutions, the archive is pruned using a technique based on neighborhood radius concepts. A group of bees that is responsible for improvement of the solutions chooses and exploits one solution of the archive. Because of the definition of neighborhood radius and retaining adjacent solutions, the remaining solutions have an equal chance to be selected by onlooker bees. In order to examine the proposed algorithm, some benchmark functions are used and the results are compared with true Pareto fronts. Moreover, the algorithm is utilized to optimize the coefficients of a new combined controller applied to a ball-beam system. In fact, the proposed controller is a combination of robust decoupled sliding mode and adaption laws based on the gradient decent method. The objective functions are considered as the integral time of absolute of errors of the ball position and the beam angle that should be minimized with a constraint on the control effort. To evaluate and validate the suggested approach, the obtained time responses of the ball-beam system are compared with those of other recently reported controllers.

Fast nonsingular terminal decoupled sliding-mode control utilizing time-varyingsliding surfaces

In this paper, a fast form of nonsingular, terminal, decoupled, sliding-mode control, which utilizes time-varying sliding surfaces, is proposed for a class of fourth-order, single-input, multioutput, nonlinear systems. The novel control law features a fast term, in the manner of fast terminal sliding-mode control, which markedly improves the finite-time sliding-mode convergence speed near zero. Numerical simulation results, which are illustrated with a cart-pole inverted pendulum system and a ball-beam system, demonstrate that the proposed control law achieves, in general, favorable transient response and lower steady-state errors compared to state-of-the-art decoupled terminal sliding-mode control methods.

On stability for sampled-data nonlinear ADRC-based control system with application to the ball-beam problem

This paper mainly concerns with the stability analysis of the sampled-data nonlinear active disturbance rejection control (ADRC)-based control system. Firstly, a class of single-input-single-output (SISO) continuous plant is discretized using zero-order-hold (ZOH), and several kinds of digital implementation methods for the nonlinear extended state observer (NLESO) are newly proposed. Then the sampled-data nonlinear ADRC (NLADRC) based closed-loop system is transformed into a discrete-time Lurie-like system, to which linear matrix inequality (LMI)-based sufficient conditions for absolute stability and robust absolute stability are obtained. The sufficient conditions provide convenient and effective methods for determining the stability and its relationship with the parameters of the controller, the plant and the sampling period. Using the ball-beam system as an example, the proposed results are verified in both simulations and experiments.

Epoch-incremental Dyna-learning and prioritized sweeping algorithms

Abstract Dyna-learning and prioritized sweeping (PS in short) are the most commonly used reinforcement learning algorithms which use the model of the environment. In this paper, the modified versions of these algorithms are presented. The modification exploits the breadth-first search (BFS) to conduct additional modifications of the policy in the epoch mode. The experiments, which are performed in the dynamic grid world and in the ball-beam system, showed that the proposed modifications improved the efficiency of the reinforcement learning algorithms.

Design of Disturbance Observer Based Sliding Mode Control for Fuzzy Systems

In this paper, the disturbance observer (DO) based sliding mode control (SMC) for fuzzy system is proposed. Compared with conventional sliding mode control, this approach incorporates the disturbance estimates into the design of the sliding surface and sliding mode controllers. The new approach can deal with the problem of mismatched disturbance for fuzzy system effectively while those problems can’t be solved by traditional sliding mode control. The disturbance observer, sliding surface and DO-based sliding mode controllers are proposed in the paper, respectively. An adaptive DO-based sliding mode controller is also established in order to deal with the problem about unknown upper norm bound of disturbance. Finally, the effectiveness of the new approach is illustrated by the ball-beam system.

Visual Feedback Balance Control of a Robot Manipulator and Ball-Beam System

In this paper, we present a vision guided robotic ball-beam balancing control system, consisting of a robot manipulator (actuator), a ball-beam system (plant) and a machine vision system (feedback). The machine vision system feedbacks real-time beam angle and ball position data at a speed of 50 frames per second. Based on feedback data, the end-effector of a robot manipulator is driven to control the ball position by maneuvering of the inclination angle of the ball-beam system. The overall control system is implemented with two FPGA chips, one for machine vision processing, and one for robot joints servo PID controllers as well as ball position PD controller. Experiments are performed on a 5-axes robot manipulator to validate the proposed ball beam balancing control system.

Multi-objective optimized fuzzy-PID controllers for fourth order nonlinear systems

In this paper, the Multi-objective Genetic Algorithm (MOGA) is used to obtain the Pareto frontiers of conflicting objective functions for the fuzzy-Proportional-Integral-Derivative (fuzzy-PID) controllers. The ball–beam and inverted pendulum fourth order nonlinear systems are regarded as nonlinear benchmarks. The considered objective functions for the ball–beam system are the distance error of the ball, the angle error of the beam, and the control effort. For the inverted pendulum system, the objective functions are the distance error of the cart, the angle error of the pendulum, and the control effort, which must be minimized simultaneously. The Pareto fronts are compared with those obtained by Multi-objective Particle Swarm Optimization (MOPSO). Four points are chosen from nondominated solutions of the obtained Pareto fronts based on the three conflicting objective functions and used for illustration of the state variables of the controlled systems. Obtained results elucidate the efficiency of the proposed controller in order to control nonlinear systems.

Integrating Servo-Pneumatic Actuator with Ball Beam System based on Intelligent Position Control

The purpose of this paper is to design a controller that can control the position of the cylinder pneumatic stroke. This work proposes two control approaches, Proportional-Integral-Derivative Fuzzy Logic (Fuzzy-PID) controller and Proportional-Derivative Fuzzy Logic (PD-Fuzzy) controller for a Servo-Pneumatic Actuator. The design steps of each controller implemented on MATLAB/Simulink are presented. A model based on position system identification is used for the controller design. Then, the simulation results are analyzed and compared to illustrate the performance of the proposed controllers. Finally, the controllers are tested with the real plant in real-time experiment to validate the results obtained by simulation. Results show that PD-Fuzzy controller offer better control compared to Fuzzy-PID. A Pneumatic Actuated Ball & Beam System (PABBS) is proposed as the application of the position controller. The mathematical model of the system is developed and tested simulation using Feedback controller (outer loop)-PD-Fuzzy controller (inner loop). Simulation result is presented to see the effectiveness of the obtained model and controller. Results show that the servo-pneumatic actuator can control the position of the Ball & Beam system using PD-Fuzzy controller.

Optimum design of fuzzy controllers for nonlinear systems using multi-objective particle swarm optimization

In this paper, a multi-objective particle swarm optimization algorithm is used to obtain the Pareto frontiers of the different commensurable and conflicting objective functions for fuzzy controller design. Also, the Lorenz dominance method is used to illustrate the equitable solutions. The nonlinear benchmarks are the inverted pendulum and ball-beam systems. The objective functions for the inverted pendulum system are the normalized angle error of the pendulum and the normalized distance error of the cart; and for the ball-beam system they are the distance error of the ball and the angle error of the beam, which must be minimized simultaneously. The comparison of the obtained results with those in the literature demonstrates the superiority of the results of this work.

Takagi-Sugeno Fuzzy System based Stable Direct Adaptive Control of Nonlinear Systems

paper proposes a novel idea for stable direct adaptive control of nonlinear systems using Lyapunov function with fuzzy approach. Stable direct adaptive control law consists of an ideal control, and a sliding mode control. Sliding mode controller is used to ensure the stability of Lyapunov function. Stability of direct adaptive control law is tested on two nonlinear systems. Non linear systems analyzed are ball beam system and cart pole system. A computer simulation is performed on nonlinear systems by using MATLAB. Keywordssystem, Lyapunov function, adaptive control, ball beam system and cart pole system.

Adaptive hierarchical sliding mode control for ball-beam systems

Ball-beam system is one of the most enduringly popular and important laboratory models for teaching control systems engineering. It is very simple to understand as a system, but there exist strong non-linearities and dynamic couplings to illustrate control methods and control concepts. It belongs to a class of second-order under-actuated systems with gravity term and two degrees of freedom. The methodology of hierarchical sliding mode control (SMC) is developed for the class. But it excludes the ball-beam system due to its special dynamic model. In this paper, an adaptive hierarchical SMC law is addressed for the class. By modifying the expression of the hierarchical SMC, the presented method is able to cover the special case. The adaptive law and the control law are deduced from Lyapunov direct method. The asymptotic stability of all the sliding surfaces is proven by Barbalat’s lemma and Lasalle’s invariance principle. Simulation results show the feasibility of this method by stabilisation control of a b...

Robust Stabilization of a Class of Underactuated Mechanical Systems Using Time Scaling and Lyapunov Redesign

This paper presents a controller-design methodology for a class of underactuated mechanical systems that are affected by parametric uncertainties and external disturbances. The perturbations due to parametric uncertainties are mismatched, whereas those caused by external disturbances are of the matched type. Their effects are canceled by employing a novel strategy that combines time scaling and Lyapunov redesign. The control methodology is applied to a two-wheeled mobile inverted pendulum and a ball–beam system. Along the way, the nonexistence of a smooth control law for point-to-point stabilization of the mobile inverted pendulum is established. Simulation and experimental studies are used to verify the efficacy of the proposed controller-design method.

Design of Ball-Beam Control System Based on Machine Vision

The nonlinear Ball-beam system combine with a CCD camera is studied in this paper. The images which include Ball-beam system and a ruler are collected by CCD sensor. The image is segmented using the adaptive image binarization threshold algorithm, and then the ruler, the ball position and the pointer position are extracted from the image. The ruler is scaled and the pointer position is also calculated. Finally, the value of pointer position is input into Ball-beam system as an expected ball balance position. A Fuzzy self-tuning PID controller and a BP neural network PID controller are designed for ball balance stable control. After experimental, the Ball-beam balance control in any position can be fulfilled using both of algorithms.