# Top PDF Fuzzy PID control of a two-link flexible manipulator ### Fuzzy PID control of a two-link flexible manipulator

In addition, it is well known that the fuzzy PID control technique combining the traditional PID control with the fuzzy control algorithm can adaptively adjust the PID parameters online by using the fuzzy logic. For this reason, the fuzzy PID control technique can effectively improve the control accuracy and is extensively used in processes where systems dynamics is either very complex or exhibit a highly nonlinear characteristic [20, 21]. In , experiments are carried out to evaluate the effectiveness of the fuzzy PID control method applied for hydraulic systems. In [23-25], fuzzy PID controllers which can adaptively adjust controller parameters on-line are designed to control SRM (Switched Reluctance Motor) system, HVAC (heating, ventilating and air-conditioning) system, and APS (atmospheric pressure simulator) system. These references listed here are merely part of applications of fuzzy PID controllers. However, little research has been done to explore how this control method applied into the vibration control of flexible manipulator systems. In this paper, we focus on the vibration control of a two-link flexible manipulator system using fuzzy PID controllers. According to the time varying feature of the system, a fuzzy PID controller, which can tune control gains online accommodating to the variation of the system is developed to depress the vibration of flexible links. ### Optimal Design of Fractional Sliding Mode Control Based on Multi-Objective Genetic Algorithm for a Two-Link Flexible Manipulator

According to Fig. 1, X 0 OY 0 is the fixed coor- dinate system, and X 1 OY 1 and X 2 OY 2 are the mov- ing coordinate systems attached to the joints cor- responding to the rigid and flexible links, respec- tively. In addition, θ 1 and θ 2 are the rotation angles of each of the links with respect to the X axis of their previous coordinate system, and w(x, t) is the elastic transverse displacement of the flexible member. Since the bending motions of a beam do not impose significant axial vibrations, axial de- formations were not included in our study. Two perpendicular pairs of unit vectors (i 1 , j 1 ) and (i 2 , j 2 ) attached to the moving coordinates of the links are shown in Fig. 1. The position vectors of the points on the Two-Link are R 1 and R 2 , dynamic equations of motion are concluded. Selecting the n first modes as the assumed-modes for the dis- cretization procedure, the following centralized model is acquired for the system: ### Neural Network Controller Based on PID Controller for Two links- Robotic Manipulator Control

used neural networks application for mobile robot control on predetermined trajectory of the road , Ya-Chen , et al used an Fuzzy neural adaptive controller to multiple-link robot control , Devendra P, et al used the proportional plus derivative (PD) control with the PD controller gain parameters optimized via Genetic Algorithm (GA) And Fuzzy Logic for control of Two link- robot , Z.G. Zhang, et al report on the design and stability analysis of a simple quadruped running controller that can autonomously generate steady running with ### Dynamic Characterization Of A Single-Link Flexible Manipulator System

Before proceeding a mathematical model that involves in several effects which include damping, inertia and payload, it is important to recognize the flexible nature and dynamic behaviour of the system. A good control algorithm needs to be designed after obtaining an appropriate model. There are various approaches have been used in order to solve problems regarding on the flexible nature behaviour. The modelling approaches can be divided into two main categories which are: ### Fuzzy Torque Control of the Bionic Flexible Manipulator Actuated by Pneumatic Muscle Actuators

The joint robot, which has the advantages of simple structure, small occupied space, large relative work- ing space, etc., is one of the most widely used robots [23, 24]. Generally speaking, the arrangement of joints actuated by a humanoid arm can be divided into two categories: PMA serial mechanism and PMA parallel mechanism. For example, the study of the 7-DOF manip- ulator actuated by PMA was implemented  from the perspective of functional bionics, and the PMA actuated antagonistic bionic joint was designed ; a 3-DOF parallel robot platform based on PMA was proposed , and a 10-DOF robot arm driven by PMA group was designed . The humanoid shoulder joint is usually designed as a series of rotating joints in order to realize the bionic structure. However, the analysis of this design is not based on the basic structure of the joint. The move- ment of the human shoulder can be divided into two parts: (a) the movement of the upper body and scapula; and (b) the movement of the humerus and scapula. ### Two-Link Flexible Manipulator Control Using Sliding Mode Control Based Linear Matrix Inequality

improve the performance of the system that is actually non-linear. Consequently, when the dynamics of the system is moving away from the operating point, then the performance of the controller can be reduced and the system can easily become unstable. It’s due to availability of the control system only works properly in the nearest area of the operating point. The control of Proportional Integral Derivative (PID) is one of control methods that commonly used in industrial applications. However, PID controller becomes unstable when the system parameters changes and external disturbances exist. Moreover, it’s not capable to drive states of the system to turn into its steady state with fast action . In the class of nonlinear control, Variable Control Structure (VCS) via Sliding Mode Control (SMC) with specific characteristics is one of suitable answers for the problems of nonlinear systems. The main benefit of a control system using SMC is its insensitivity (robust) to parameter changes and disturbances. Moreover, SMC also be able to stabilize nonlinear system that can not be stabilized by using continuous state feedback control by using stability analysis . The use of SMC method is expected to improve quality of the control algorithm with fast dynamic response, insensitive to parameter variations and disturbances, simple in control method, and can be implemented quite easy. Main factor affecting the performance of SMC are parameters of the sliding surface . ### Two-link robot manipulator using fractional order PID controllers  optimized by evolutionary algorithms

The application and operation of FOPID controllers to control the actual and practical two- link robot is studied in this paper. According to the non-linearity of the robot system, the design of such controllers for non-linear systems without use of optimization algorithms and using only trial and error, experimental, and conventional methods is very difficult or nearly impossible. So, in the controller design process, controller parameters Fig. 9. Comparison the performance of PSO, GA, ### Mathematical Modelling, Stability Analysis and Control of Flexible Double Link Robotic Manipulator: A Simulation Approach

Abstract: In present work the various aspects on mathematical modelling, stability and control strategies of flexible double link manipulator have been investigated. A mathematical model of flexible double link manipulator has been developed using lagrangian method. This mathematical model has been characterized using classical and modern control theories. Their time domain and frequency domain analysis has been carried out and our study show that the mathematical model of flexible manipulator is highly unstable. Different control strategies such as PID, LQR and State feedback controller have been implemented for controlling the tip position of flexible double link manipulator using MATLAB programming. State feedback controller uses pole placement approach, while the linear quadratic regulator is obtained by resolving the Riccati equation. The best control strategy for controlling the tip position of flexible double link manipulator is obtained by implementation of LQR controller. Finally, this study proven that LQR control method is the best method as compare to PID and State feedback controller for controlling the flexible link robotic manipulator. ### Novel Adaptive PID Control of Flexible Joint Robot Manipulator withBounded Disturbances

Abstract: - A novel robust adaptive PID control scheme is proposed with known upper bound of the external disturbances, to solve the dynamic coupling and strong nonlinearity problems in flexible joint robot manipulator control. Invoking the proposed controller, the bounded external disturbances can be compensated and the global asymptotical stability with respect to the manipulator positions and velocities is able to be guaranteed. The designed control law can enlarge the tolerable external disturbances, enhance the accuracy of trajectory tracking error, and improve the dynamic performance of the manipulator systems. The stability and convergence properties of the closed-loop system are analytically proved using Lyapunov stability theory and Barbalat's lemma. Simulation for the proposed control system is performed for a two-degree of freedom flexible joint robot, each joint modeled by two-equations of second order to illustrate its viability, and advantages. ### Sampled-Data Sliding Mode Control Design of Single- Link Flexible Joint Robotic Manipulator

To design sliding mode controller for the flexible joint manipulator, state variables of each joint, velocities, acceleration and jerks of the link must be known . Since last two decades, dynamic modeling and non-linear control of robotic manipulators (flexible) is the area of research which received notable consideration. To design a control topology that is efficient and robust, the first and fundamental step is to develop an accurate dynamic model of a flexible joint robot. In industrial and space applications, we need the controller that can reduce the disturbance effects and can cope with modeling ### Development of a software for simulating active force control schemes of a two-link planar manipulator

Abstract. The paper describes the development of a software in the form of an interactive computer program that integrates a number of robotic control schemes with the active force control (AFC) strategy as the key element of the robotic system that assumes a rigid two-link planar configuration. The various AFC schemes are employed in conjunction with a number of conventional and intelligent techniques embedded in the main control loop to approximate the estimated inertia matrix of the robot arm. The schemes have been individually developed and rigorously experimented through simulation studies. The results of these studies clearly indicate that the AFC technique provides a practical solution to enhance the robustness of the robotic system even in the wake of uncertainties, disturbances and varied loading conditions. Thus, it is deemed useful to develop software that can integrate a number of individual AFC schemes into a single program using a graphic user interface (GUI) technique. In this manner, the user can effectively select and execute any scheme by the manipulation of a few keystrokes or buttons of the input devices. This resulted in a program that is user friendly, readily accessible, flexible and proved very convenient. On top of that, the graphical results can be observed and analysed on-line while the program is running. By using MATLAB and its GUI facility, all the AFC schemes already described in the previous works such as the AFC with crude approximation method, AFC and Iterative Learning (AFCAIL), AFC and Neural Network (AFCANN), AFC and Fuzzy Logic (AFCAFL), and AFC and Genetic Algorithm (AFCAGA) schemes were linked into a single menu-driven program where each of the scheme can be easily selected and executed by the user. A classic proportional-derivative (PD) control scheme was also included in the program for the purpose of benchmarking. ### Dynamic Analysis of Flexible-Link Planar Parallel Manipulator with Platform Rigidity Considerations

Abstract: This paper presents dynamic analysis studies of planar parallel flexible 3-RRR manipulator with and without considering the flexibility of mobile platform. Initially, by treating all the members of the manipulator as flexible, the joint displacements, reaction forces and stresses are obtained during a specified trajectory tracking in Cartesian space. A comparative study is conducted with manipulator configuration having rigid mobile platform using coupled dynamics of limbs and kinematic constraints of mobile platform. Dynamic response of flexible manipulator is validated using ANSYS simulations for two different cases of trajectories. The results show a remarkable effect of flexibility of mobile platform on the overall dynamic response. After validation of the model, the inverse dynamic analysis data is used to create the system dynamics by employing generalized regression neural network (GRNN) model and the forward dynamic solutions of the flexible manipulator are predicted instantaneously. This study is useful for the real time implementation of motion control of flexible manipulators with complex dynamic model of manipulators. ### System Identification and Intelligent Control of Flexible Manipulator System

Position control of flexible manipulator system is normally accompanied with tip vibration that results in degradation of performance. This paper investigates an active control strategy by applying classical PID controller to suppress unwanted vibration of flexible manipulator in presence of disturbances. The parameters of PID controller are tuned by genetic algorithm (GA) and particle swarm optimization (PSO) in the intelligent (self-tuning) manner. The results of these two optimization methods are compared toward vibration control capability, moreover; modeling of flexible manipulator is conducted by applying system identification method in which autoregressive with exogenous input (ARX) model is intended as linear model. This research can be regarded as guidance for further elaborate research on implementing optimization method particularly integrated with PID controller for flexible manipulator system modeled by system identification approach. ### Reduced Model Based Control of Two Link Flexible Space Robot

Model based control schemes use the inverse dynamics of the robot arm to produce the main torque compo- nent necessary for trajectory tracking. For model-based controller one is required to know the model pa- rameters accurately. This is a very difficult task especially if the manipulator is flexible. So a reduced model based controller has been developed, which requires only the information of space robot base velocity and link parameters. The flexible link is modeled as Euler Bernoulli beam. To simplify the analysis we have con- sidered Jacobian of rigid manipulator. Bond graph modeling is used to model the dynamics of the system and to devise the control strategy. The scheme has been verified using simulation for two links flexible space manipulator. ### Studies on Trajectory Tracking of Two Link Planar Manipulator

Literature survey was conducted to obtain some insights into various factors relating to modelling of planar manipulators for various industrial applications. In this work several aspects regarding the kinematics, workspace, Jacobian analysis and dynamic identification of a two-link planar manipulator are studied and presented. De Luca and Siciliano  presented the kinematic and dynamic issues of planar link manipulator. William  described automatic Control Systems, analysis and design of serial manipulators. Kwanho  explained the adaptive control of tip point in a serial link robot. Nagrath and Gopal  explained various issues like kinematics, dynamics, control theories for different serial manipulators. Tokhi and Azad  discussed the kinematic and modelling of flexible manipulators. Finally the proposed control method is applied for the flexible manipulator to illustrate the results. Ata  presented the review on various optimal trajectory planning control techniques for serial manipulators. Islam and Liu  proposed a sliding mode control technique to serial manipulator and studied the. Kumara et al.  explained trajectory tracking control of kinematically redundant robot manipulators using neural network. Moldoveanu et al.  explained a trajectory control of a two-link robot manipulator using variable structure theory. Wang and Deng et al.  explained the design of articulated inspection arm with an embedded camera and interchangeable tools. Zhu et al.  presented the structure of a serial link robot with 8 degrees of freedom with a 3-axes wrist carrying camera. Ionescu  described an approach of measurement using a calibrated Cr252 neutron source deployed by in-vessel remote handling boom and mascot manipulator for J0ET vacuum vessel. Monochrome CCD cameras were used as image sensors. Karagulle and Malgaca  proposed the effect of flexibility on the trajectory of a planar two-link manipulator is studied using integrated computer-aided design procedures. Nageshrao et al.  explained the passivity based control method. Detailed algorithm was proposed and implemented for 2- DOF manipulator. Ayala and Coelho  illustrated an algorithm to test the PID tuning by using a two degree of freedom robot manipulator. ### Design and Implementation of Fuzzy PID Controller for Single Link Flexible Joint Robotic System using FPGA

We have proposed a simple FPID controller for a single link flexible joint robotic system, error and change of error in the velocity have been used as two inputs for the Fuzzy, Proportion, Derivative controller FPD; error and accelerated rate of error in the link angular displacement have been used as two inputs for the Fuzzy, Proportion, Integral controller FPI. The outputs of the two controllers are added to produce the controller action. For each one of the inputs there are 2 triangular membership functions (triangular membership function is a special case of the trapezoidal function) have been selected, for FPD output there are 2 triangular membership functions and for FPI 3 triangular membership functions have been selected. All these membership functions have been coded in VHDL. ### Vibration Control Comparison Of A Single Link Flexible Manipulator Between Fuzzy Logic Control And Pole Placement Control

In this paper, the flexible manipulator model used for the design of the controller is as described in . The model is made from a piece of a thin aluminum alloy. It has the following parameters and corresponding values used during the experiment; the length of the flexible link is L=0.9 m, young modulus of the system is E=71 ×10^9 N/m^2, width of the link 19.008 mm, thickness of 3.2004 mm, second moment of inertia I=5.1924 m^4, and mass density per unit volume ρ=2710 kg/m^3. A test-rig with U9M4AT type circuit is used with motors’ shaft driving the flexible link at the hub. A motor was chosen for the experiment due to its low inductance and low inertia . The schematic diagram of the single link flexible manipulator system is shown as Figure 1. ### Controlling the non-parametric modeling of Double Link Flexible Robotic Manipulator using Hybrid PID tuned by P-Type ILA

Another type of adaptive controller that is Iterative learning algorithm (ILA) has been implemented in different control scheme in the flexible manipulator system. For example, two phase ILA controllers to carry out the ideal input and output signals of iterative learning control (ILC) where the error is used to calculate the parameters of the PD controller by using standard least squares (LS) algorithm for the single link flexible manipulator (SLFM) . Simulation results showed that the proposed controller is effective in tracking the desired trajectory over interval time. Zhang and Liu employed an adaptive iterative learning control scheme based on Fourier basis function for SLFM . The simulation carried out portrayed that the controller successfully tracks the actual trajectory. Besides, genetic algorithm was applied to tune three combinations of controller for single link flexible manipulator in vertical plane motion that is PID, PID-PID and PID-ILC controller . Simulation demonstrated that the PID-ILC parameter obtained in the optimization outperform other controllers and allow the system to perform well in reducing the vibration at the end-point of the manipulator. However, none of the research based on iterative learning algorithm (ILA) was implemented on DLFRM. ### Sliding Mode Control with RBF Neural Network for Two Link Robot Manipulator

nonlinear dynamics of the manipulator system. ]Robot manipulators are very important in the field of flexible automation as they have been widely used for increasing productivity and reduce losses. A lot of research effort is been made to design their controller. ]Robot manipulators are very important in the field of flexible automation as they have been widely used for increasing productivity and reduce losses. A lot of research effort is been made to design their controller. Neural Networks are being applied in many fields such as learning, pattern recognition, signal processing and system control. The major advantages this parallel structure, learning ability, non- linear function approximation, fault tolerance. This benefits make a wide range of applications.. Robot manipulators are very important in the field of flexible automation as they have been widely used for increasing productivity and reduce losses. A lot of research effort is been made to design their controller. The payload of the robot manipulator varies during its operation and is not known advance. To face such problems, adaptive control strategies for robot manipulators have been developed. Research from the past shows that universal approximation theorems on RBF has shown that any nonlinear function over a compact set with arbitrary accuracy can be approximated by RBF neural network. The RBF network adaptation improves the control performance against large uncertainty of the system. The adaptation law can be derived by Lyapunov method which guarantees the stability of the system. RBF neural networks. A schematic diagram of two link robot manipulator is shown in figure 1. 