Showing papers on "Ball and beam published in 2017"

A Comparative Experimental Study of Robust Sliding Mode Control Strategies for Underactuated Systems

Abstract: This paper presents a comprehensive comparative study for the tracking control of a class of underactuated nonlinear uncertain systems. A given nonlinear model of the underactuated system is, at first stage, transformed into an input output form and the driving applied control input of the transformed system is then designed via four sliding mode control strategies, i.e., conventional first order sliding mode control, second order sliding mode, fast terminal sliding mode, and integral sliding mode. At second stage, a ball and beam system is considered and the aforementioned four control design strategies are experimentally implemented. A comprehensive comparative study of the simulation and experimental results is then conducted which take into account the tracking performance, i.e., settling time, overshoots, robustness enhancement, chattering reduction, sliding mode convergences, and control efforts.

From PID to Nonlinear State Error Feedback Controller

Abstract: In this paper an improved nonlinear state error feedback controller (INLSEF) has been proposed for perfect reference tracking and minimum control energy. It consists of a nonlinear tracking differentiator together with nonlinear combinations of the error signal. The tracking differentiator generates a set of reference profile for the input signal, which is the signal itself in addition to its derivatives. On the other hand, the 12-parameters nonlinear combinations of the error signal make the INLSEF controller can handles with time-varying and system’s nonlinearity. Digital simulation studies have been conducted for the proposed controller and compared with several works from literature survey on two case studies, mass-spring-damper which is a very nonlinear system and nonlinear ball and beam systems. The parameters of the nonlinear combination of the error signal are tuned to satisfy the optimality condition by minimizing the OPI performance index defined in this work. From the simulations results one can conclude that the proposed INLSEF controller performance is better than that of its counterpart in terms of speed and control energy and minimum error. Also, the results showed that the proposed controller is effectively enhancing the stability and performance of the closed loop system.

Design and Implementation of Ball and Beam System Using PID Controller

Abstract: The ball and beam system is laboratory equipment with high nonlinearity in its dynamics. The main ideas of the paper are to model the ball and beam system considering nonlinear factors and coupling effect and to design Proportional Integral Derivative (PID) controller to control the ball position. The system consists of an Arduino microcontroller. It receives the ball position from ultrasonic distance sensor and compares it with the desired distance which can be set by the user. PID algorithm has built in Arduino to process the difference in signal between desired and real position into control signal. Arduino sends control signal to the DC servomotor which rotate to change the ball position and meet the desired distance. MATLAB software program has been used to plot instant system response by interfacing Arduino with computer to determine the system characteristics with different values of controller parameters in order to choose parameters values which obtained best performance for the system.

Design and evaluation of fuzzy PID controller for ball and beam system

Abstract: Ball and beam control system is specially designed to study nonlinear control methodology on an unstable system. The point of the ball is hard to manage because it will move continuously on a beam, makes it becoming open-loop unstable. PID controller had been successfully applied for this application by previous researchers. However, incorporation of fuzzy in the system to facilitate PID tuning could basically simplify the design problem. Therefore, this paper presents an approach of fuzzy proportional integral derivative (fuzzy PID) controller for position control of ball and beam system. The effectiveness of the proposed controller was verified by simulation and compared with a PID controller obtained using auto-tuned function in Simulink Toolbox. The results from step response and input tracking show that the proposed controller had a better performance in both evaluations compared to PID.

Design and Implementation of an Embedded Ball-beam Controller Using PID Algorithm

Abstract: Ball and beam system is found in most laboratories of control systems engineering due to its simplicity and easiness in construction and control theoretically. The system consists of a motor attached with a beam at the center and a ball, which is placed on the top of beam. The problem with this system, is in the time of an electrical control signal is applied to the motor, the beam can be tilted about its horizontal axis and the ball will roll on the top of the beam. Therefore, if the system cannot be controlled properly, the ball may fall down from the beam. In this paper, PID controller Algorithm based on Arduino microcontroller which depends on the feedback signal is used to control the ball position using linear potentiometer position sensor. MATLAB software program has been used to plot the system response by observing the ball position for a predefined amount of time. The controller parameters have been tuned using trial and error method, tested for different set point tracking and for disturbance rejection in order to obtain a good system characteristic.

Position Control of a Ball & Beam Experimental Setup Based on Sliding Mode Controller

Abstract: In this paper, a sliding mode control (SMC) method is introduced to design a control methodology for the ball and beam experimental setup (BBS) that consists of a servo motor, beam and ball. The proposed control method is realized in two cascaded control structures such that primary and secondary, respectively. In the primary part, called outer loop, the position of the ball is controlled by changing the angle of the beam. In the secondary part, called inner loop, the needed voltage is generated to determine appropriate position angle of the servo motor to adjust the position of the beam. Furthermore, a well-tuned conventional PI controller is also applied to the system to indicate the priority and effectiveness of the SMC. The results obtained in real-time show that the SMC is better than the PI controller in the aspect of reference tracking, fast response to the changes and accuracy as well.

Adaptive sliding mode control of ball and plate systems for its practical application

Abstract: In this paper, an adaptive sliding mode controller is proposed, which is robust against external disturbances and parameter uncertainties The proposed controller is designed to solve the trajectory tracking problem of ball and plate systems Furthermore, it considers not just theoretical approach but practical approach The external disturbances should be solved since there are various external disturbances in real systems such as circuit noise, mechanical vibration and so on Another important issue for implementing the ball and beam system is an unknown parameter problem since the change of the ball weight should be considered Therefore, an indirect adaptive sliding mode control technique is adopted to overcome both problems Before the proposed controller is applied to the implemented ball and plate system, its stability analysis is performed by Lyapunov stability theory and some simulation verifies its performance

Neural Fuzzy Control of Ball and Beam System

Abstract: This paper presents an offline control of ball and beam system using fuzzy logic. The objective is to control ball position and beam orientation using fuzzy controllers. A Matlab/Simulink model of the proposed system has been designed using Newton's equations of motion. The fuzzy controllers were built using seven gbell membership functions. The performance of proposed controllers was compared in terms of settling time, steady state error and overshoot. The simulation results are shown with the help of graphs and tables which illustrates the effectiveness and robustness of proposed technique.

Optimal control of a ball and beam nonlinear model based on Takagi-Sugeno fuzzy model

Abstract: In this work, an improved approach for Takagi-Sugeno system identification is used. Linear Quadratic Regulator is applied for an optimal state feedback. Duality theorem and Linear Quadratic Regulator is applied for an optimal state estimation. Simulation results over the ball and beam nonlinear model show a stable closed loop in the full range and good transient response.

Fruit conveyor prototype based on ball and beam system

Abstract: This study investigates a high friction fruit conveyor system based on a traditional frictionless ball-and-beam system (BBS). Both share commonalities of behavior i.e. controlling an object by manipulating the platform angle. The BBS system includes a rubberised strip to make increase its friction slightly. The inherently unstable BBS is stabilised with a simple PID controller to permit system identification techniques. Various model structures have been identified but the state space model was ultimately selected for the design of an optimal controller. A camera vision system was used for sensing to keeping in line with the requirements of the fruit conveyor system. The results of simulation illustrate that the designed controller, based on the identified system model from experimental data, is satisfactory and can be used to develop a model that incorporates friction as will be the case in the fruit conveyor system.

Fuzzy-modal control for the ball and beam system

Abstract: The article is devoted to the development of a fuzzy-modal controller for the ball-beam position control system. This nonlinear dynamic plant is often considered when developing various control strategies. One option here is to use modal controls based on the linearized system model. However, the peculiarity of the linear controller is that the duration of the transient process does not depend on the initial state of the system. The proposed nonlinear control algorithm is based on the use of a set of modal control laws synthesized for different eigenvalues of a closed loop system. The signals of the modal controllers are matched by a fuzzy inference circuit using an a priori linguistic description of the states of the system. The simulation results show that fuzzy-modal control provides a transient time proportional to the initial deviation of the system.

A Ball and Beam Module for a Haptic Paddle Education Platform

Abstract: Single degree of freedom force-feedback mechatronic devices, often called haptic paddles, are used in university curriculum as well as massive open online courses (MOOCs). While devices differ based on the goals of a given course, broadly speaking they provide hands-on learning for students studying mechatronics and dynamics. We introduce the third iteration of the Haptic Paddle at Rice University, which has been modified to improve haptic performance and robustness. The modifications to the design increased device up time as well as the devices Zwidth. The performance improvement enables the addition of experimental plants to the haptic paddle base, which can be directed at advanced dynamics and controls courses, or special topics in mechatronics and haptics. The first module, a Haptic Ball and Beam, adds an underactuated plant for teleoperation or more complex control structures, and a testbed for haptic motor learning experiments in undergraduate coursework.

Control of a Ball and Beam System using Switching Control Method

Abstract: We propose a switching control scheme for the control of a ball and beam system. It was reported in [4] that a ball and beam system is a nonlinear system which has an ill-defined relative degree. So, the traditional control approaches have been mostly either Jacobian-based control or approximate input-output linearized control in nature. In this paper, motivated by [7], we combine these two traditional control approaches and operate each controller via a pre-designed switching logic so that the improved control result can be obtained without any excessive use of control input. Switching algorithm is developed based on both analysis and actual experimental observation. We verify the effectiveness of our proposed controller via actual experimental results.

Fuzzy PID tracking performance for ball and beam system

Abstract: This paper presents a design of Fuzzy PID controller to control the position of ball and beam system. The design objective is to improve the transient performance and to evaluate the controller ability to track a sine and square wave input signal. Fuzzy controller is proposed to overcome the problem of PID controller especially in obtaining optimal parameters. The effectiveness of the proposed controller was verified by simulation and compared with a PID controller obtained using PID auto-tune function in Simulink Toolbox. The results from step response and input tracking show that the proposed controller had a better performance in both evaluations compared to PID.

Switching Control of Ball and Beam System using Partial State Feedback: Jacobian and Two-Step Linearization Methods

Abstract: We propose a new switching control scheme for a ball and beam system by utilizing two linearization methods. First, the Jacobian linearization is applied and state observer is developed afterward. Then, motivated [6], the approximate input-output linearization is carried out, and after that, the Jacobian linearization is applied along with the design of state observer. Since the second approach requires two linearizations, it is called a two-step linearization method. The state observer is needed for the estimation of the velocities of ball and motor movement. Since the Jacobian linearization based controller tends to provide faster response at the initial time, and after that, the two-step linearization based controller tends to provide better response in terms of output overshoot and convergence to the origin, it is natural to give a switching control scheme to provide the best overall control response. The validity of our control scheme is shown in both simulation and experimental results.

Bounded control of a ball and beam system in the absence of feedback

Abstract: In this paper, we consider a control problem of a ball and beam system in a situation where feedback is disconnected. Due to feedback disconnection, any feedback controller is not available and as a result, the position of the steel ball cannot be hold for long. The main difficulty is the open-loop environment at the happening of feedback disconnection. We show that bang-bang control input can be a good candidate which holds the ball position with certain bounds for the longest time.

Control of a Modified Ball and Beam System Using Tracking System in Real Time with a DC Motor as an Actuator

Abstract: This paper presents amodified ball and beam system, with the intention of realizing a test bed, to study new control techniques in real-time.The ball and beam system consists of a ball over a long beam where the control objective is to stabilizethe position of the ball on the beam by changing the angular position of the beam.In this paper, the ball of the conventional system is replaced by a cart with an embedded microcontroller, enabling the use of a linear encoder as position sensor and allowing to transmit the position via RF (Radio Frequency). The mathematical model of the ball and beam is obtained through the equations of Newton-Euler and the equations were linearized. The system is controlled using the hardware-in-the-loop technique with MATLAB/Simulink.It is applied a tracking control system with entire eigenstructure assignment to control the position of the cart. The actuator used is a DC motor, and a PID(proportional, integral and derivative) control is used to perform the angular position control of beam.The simulation results and the experimental results are compared to validate the mathematical model. The results obtained were satisfactory with adequate accuracy.

Adaptive sliding mode observer-controller design for nonlinear systems: A fuzzy approach

Abstract: In this paper, the problems of observer-based sliding mode control for a class of nonlinear system are investigated via Takagi-Sugeno (T-S) fuzzy approach. By using the T-S model as the design model, an adaptive sliding mode observer is first constructed to estimate the states of the original nonlinear system without knowing any information of the actuator fault. And then, a sliding mode surface in the state-estimation space is proposed and a new sliding mode controller which can force the motion of closed-loop system onto the surface is designed. Besides, the sufficient conditions of the existence of the observer and controller are provided in terms of linear matrix inequalities (LMIs). Finally, the ball and beam system is used as an example to verify the validity of the proposed method.

H-infinity-PID controller for an open-loop unstable system

Abstract: This paper proposes a H-infinity-PID cascade control technique for the control of an open-loop unstable system, the ball and beam system This property of being open-loop unstable makes this system ideal for investigating the performance of different control techniques A 5th order nonlinear model of the ball and beam plant is derived to include the actuation mechanism A H-infinity-PID controller is proposed and applied to the system using a cascade structure The control goal is to drive the ball to any desired position on the beam A check for robustness of the closed loop is also performed using frequency domain methods The results show that the proposed controller robustly stabilizes the system and equally achieves the setpoint tracking goal The control voltage which is the control input is also found to be within practicable limits

Active set method based model predictive control for a ball and beam system

Abstract: Model predictive control is an optimal control method that requires the solution of a quadratic programming problem with constraints at each sampling time. In this study, an active set method is used to solve the problem. The whole control algorithm is written through Matlab editor so that it can be run in embedded systems. A ball and beam system model is utilized to investigate the performance of the controller structure. The simulations are conducted with two different cost functions. The results illustrate that the constructed control system exhibits satisfactory performance in the sense of system response and constraints.

Hardware in the Loop (HIL) Analysis of Fuzzy Controller for Ball and Beam System

Abstract: Ball and beam system is a nonlinear and unstable system which is used as an applied sample in research laboratories as a tool to represent the performance of different control algorithms. The present study utilizes hardware in the loop realization of classic (PID type) and fuzzy controllers by Sugeno fuzzy inference approach in order to evaluate their performances. All activities for design and simulation of controller were performed by MATLAB and Simulink software. Then, the simulation environment of MATLAB was linked to the operator interface as well as actuators and sensors in hardware in the loop structure by writing a real time kernel through DAQ interface cards. Simulation results show the appropriate performance of fuzzy controller in comparison to PD and PID controllers. By using fast processors for implementation of fuzzy controller, settling time, overshoot percentage and steady state error of the closed loop system were significantly improved in comparison to the common classic structure. Also, all simulation results were verified by hardware in the loop test.

Nonlinear dynamic surface control design for ball and beam system with parameter uncertainties

Abstract: This paper considers the design of nonlinear dynamic surface control (DSC) scheme for the ball and beam system with parameter uncertainties. It invokes adaptive nonlinear-inparameter (NIP) approximator to model the uncertainty terms of the system. Then, the proposed scheme is designed by combining the DSC approach and the adaptive NIP approximator to control the position of the ball in the presence of parameter uncertainties. No prior knowledge about the uncertainties is required and all parameters of the approximator are adjusted during real time operation. Stability analysis of the closed-loop system is guaranteed by the Lyapunov theorem. Also, it is shown that all the signals of the closed-loop system are uniformly ultimately bounded. Finally, some simulation results are presented to verify the robustness and effectiveness of the propose scheme.

Analysis of field-programmable gate array-based safety systems in lightweight applications

Abstract: The current approach to implementing safety measures for the purposes of preserving human-life and property as either hardware or software has a number of inherent limitations. This report explores and evaluates the use of the Field Programmable Gate Array (FPGA) available on the National Instruments myRIO-1900 platform as means of combining the strengths of both approaches, with the classical ball and beam control problem used as a basis of testing a number of common features of safety-systems. Two different ball and beam configurations were used. During the prototyping phase, the beam was directly driven by a stepper motor while the final project apparatus utilised a standard servo and push-rod configuration. The change occurred due to a failure of the operational failure of the stepper motor. As a result, limited useful test data was gathered. However, feedback and analysis addressed a number of larger issues encountered during prototyping prior to the development of the final project build. Results gathered during testing of the final prototype provided arguments for and against the use of an FPGA for the purpose of implementing safety systems. It was demonstrated that FPGA-based redundancy provides a means of reliably executing a multitude of time-dependent safety and monitoring processes at once. However, it was also demonstrated that FPGA-based systems lack some important benefits associated with hardware and software systems. FPGA function complexity and size is quite limited and time consuming to implement, and the chip itself lacks the robustness commonly associated with hardware.

Application of Underactuated mechanism motor control in ball and beam system

Abstract: Motor control in ball and beam system consists of a beam structure which can be constructed with server electric motor to simulate the Underactuated mechanism system of robot. It can be contacted with a control theory and robot operation in balance behavior. It is well-known that robot structure in 1-D space with a motor to control system balance, which a simple ball and beam system to observe open-loop performance is unstable. When the motor torque and current parameter record from control broad, it will control the beam in balance situation to restrict unstable condition if even it is to be very nearly horizontal. In order to stabilize the ball in beam system, measurement of the ball position and to regulate the beam should be adjusted by the motor device. The control voltage signal goes to the DC motor then the torque generated from the motor drives to regulate the beam to rotate a desired angle. Thus, the ball can be located at the desired position, which is used to simulate the robot behavior system. This study presents a new reduction approach to simplify the type reduction procedure for an interval type-2 fuzzy sliding controller. It should be considered as a collection of a large number type-1 fuzzy set regulated by an interval type-2 fuzzy set. It is shown that a simplified type reduction approach can be used to a hybrid interval type-2 fuzzy sliding controller for a ball-and-beam system. By using the Extended-Karnik-Mendel (EKM) type reduction method, it is indicated that a better results and effectiveness of a hybrid interval type-2 fuzzy sliding controllers, in motor position, torque, current and voltage can be performed a faster position results, at least, reduction of 20%.

IDA-PBC Controller Tuning Using Steepest Descent

Abstract: The optimization of controller parameters or gains is a challenge usually approached using empirical methods that consume valuable time, without the certainty that the obtained gains actually produce the desired behaviour of the controlled plant. There are several analytical and numerical methodologies to find the parameters for PID controllers, however currently there is not enough available information regarding the application of optimization methods for nonlinear controllers. The present work describes the application of the maximum descent method to find the gains of IDA-PBC controller for a ball and beam system. The proposed methodology involves implementing a mathematical model to describe the system’s dynamics, the design of a objective function to measure how closely the plant follows the desired behaviour, and finally the evaluation of a set of gains obtained by the numerical method. The dynamic model and the optimization algorithm were implemented in C language in order to reduce the computer time compared to the use of frameworks such as MATLAB. Numerical simulations to validate the effectiveness of the proposed methodology are included.