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 SlidingModeControl (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 .
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 twolink robot manipulator is shown in figure 1.
This paper evaluates a new and simple controller design method based on QFT (quantitative feedback theory) for a two-linkmanipulator whose first link is rigid and the second is flexible. A piezoelectric patch is attached to the surface of the flexiblelink for vibration suppression of it. This system is modeled as a nonlinear multi-input multi- output (MIMO) control systems whose inputs are two motor torques which are applied on the joints and a voltage which is applied on the piezoelectric patch. To control the manipulator’s end point position, motion of the manipulator is divided to two rigid and flexible parts. To control both parts, nonlinear equations of the motion is replaced by a family of uncertain linear time-invariant equivalent systems using Rafeeyan-Sobhani’s method(RS method) which results in three decoupled transfer functions established in the Laplace domain. Then the QFT method is used to design a diagonal matrix as the prefilter of the system an another diagonal matrix as the system controller. Results demonstrate the remarkable performance of the proposed controllers in reduction of residual vibration of elastic link and tracking a circular trajectory by the manipulator end point.
Traditionally, robotic manipulators have been designed and built heavy and bulky for high structural stiffness; but it resulted in drawbacks such as high power consumption, low motion speed, high manufacturing cost etc. Modern industrial robots are designed with flexible joints. This has the advantage of increased payload capacity, cheaper construction and faster movement. However, the consequence of making mechanically flexible constructions resulted in new and complicated problems in modeling, identification and control. Moreover joint flexibility causes significant vibration at the end points. Research on the dynamic modeling and control of flexible robots has received increased attention in the last few decades. A first step towards designing an efficient control strategy for manipulators with flexible joints must be aimed at developing dynamic models that can characterize the flexibility of the joints accurately. The controller design that minimizes the effects of the flexible displacements in lightweight robots is highly demanded in many industrial and space applications that require accurate trajectory control. In control applications of robot, manipulators with flexible arms are targeted either to reach a target position or to follow a prescribed trajectory. In the first case to reach a target position, a short settling time is desired while a large robot arm displacement is planned in the second case to follow a prescribed trajectory. In both cases, strong control actions are applied to the robot arm, and, as a result, undesired behaviors could appear if vibrations induced in the robot arm are not considered. The control issue of the flexible joint is to design the controller so that link of robot can reach a desired position or track a prescribed trajectory precisely with minimum vibration to the link. In order to achieve these objectives, various methods using different technique have been proposed such as follow: linear quadratic regulation (LQR) control , adaptive output- feedback controller based on a backstepping design –
For this purpose, different techniques have been suggested for last two decades. For example, linear quadratic regulation (LQR) control technique is widely used for such control , another technique which is vastly used is adaptive output feedback controller based on a back stepping -. In the case of nonlinear control, feedback linearization is the most renowned technique that is used for robotic manipulators . The integral control technique described in  and , robust control that uses PD control and H∞ control, PD fuzzy and optimal control and slidingmodecontrol . In , an adaptive second order terminal slidingmode controller for robotic manipulators is proposed.
Studies on fractional calculations are very widespread in the field of automatic control, and some of them are: Fractional systems in the context of feedback control (Zinober 1989), fractional PID controller (Hamamci 2007), and issues related to parameters selection using the Ziegler-Nichols method rules (Valério & da Costa 2006). Das and Pan (2014) designed a fractional-order PID controller for an automatic voltage regulator system to measure objectives such as the set-point tracking, load disturbance, and noise rejection controller effort, in the Pa- reto optimal solution. Pan et al. (2015) proposed an active control policy design for a fractional order financial system, which considers multiple conflicting objectives as a nonlinear state feed- back mechanism. Pan and Das (2015) designed a fractional-order PID controller for load-frequen- cy control of two interconnected power systems. They developed multi-objective optimization frameworks based on the NSGAII and chaotic optimization to tune the gains and the fraction- al differ-integral orders of the PID controllers. Their results showed that the fractional PID con- troller system which optimized evolutionary al- gorithms could rapidly follow the desired output with higher precision and robustness.
progress on their active control has already been made. For PMSM drives containing a single torsion vibration mode, SMC has been applied in an outer loop by Dodds and Vittek, 2007, and directly by Hace, et. al., 2005. The control system offered here, however, is unique in requiring no tuning when commissioning and yielding a closed loop step response with a prescribed settling time using the formula of Dodds, 2008. 1.2. Introduction to SlidingModeControl: Slidingmodecontrol (Utkin, 1992) is well known to achieve robustness. Fig. 1 shows the general block diagram for a single input, single output (SISO) plant. Here, x ÎÂ n , is the state vector, where n is the order of the plant, and
In space exploration for instance, robot is required to be light in weight due to the space and weight restriction issues. The advantages of using a lighter weight manipulator as against the rigid linkmanipulator include: higher manipulation speed, less power consumption, they require less material for their construction, they required smaller actuator, and they are easily maneuverable and can easily be transported anywhere . By making the weight of the manipulator to be lighter has resulted in the flexibility of the manipulator that makes the modeling of such a system to become very cumbersome. The dynamic behaviour of such a system is usually described by partial differential equation that is characterized by infinite dimensional distributed parameters with non- minimum phase property . This complex model that is generated by such a flexible system is often truncated to reduce the complexity that it will pose on the controller design. Truncating such model in order to simplify the controller design process will affect the performance of the model based controller in real time operation because; the unmodelled part of the system that creates a ripple effect on any small error in the control system which will result in the collapse of such a system.
Direct current (DC) motors are used frequently because of their features such as cost, ease of control, long life and quiet operation. DC motors for robotics, defense industry and automotive applications etc. are used in many fields [1-10]. In recent years, sensorless control methods have been used in the control of dc motors [11-15]. During the control of most systems, there is only parameter information and partial status over the measured outputs, which usually limits the performance of the system.In order to recover unknown situations and parameters, powerful observers with high estimation accuracy are required. Many effective technologies and methods have been developed to solve case and parameter estimation problems.
Wang and Gao  have reported inverse dynamics model-basedcontrol for flexible-link robots, based on modal analysis, i.e., on the assumption that the deforma- tion of the flexible-link can be written as a finite series expansion containing the elementary vibration modes. Leahy et al.  worked on robust model basedcontrol. They also discussed an experimental case. Fawaz et al.  developed a model based real-time virtual simulator of industrial robot in order to detect eventual external collision. The method concerns a model based fault de- tection and isolation used to determine any lock of mo- tion from an actuated robot joint after contact with static obstacles. Tso et al.  worked on a model-basedcontrol scheme for robot manipulators employing a variable structure control law in which the actuator dynamics is taken into consideration. Zhu et al.  attached an addi- tional model-based parallel-compensator to the conven- tional model-based computed torque controller which is in the form of a serial compensator to enhance the ro- bustness of robot manipulatorcontrol. Qu et al.  have discussed robust control of robots by the computed torque law with respect to unknown dynamics by judi- ciously choosing the feedback gains and the estimates of the nonlinear dynamics. The choices for the constant gains depend only on the coefficients of a polynomial bound of the unknown dynamics. Khosla and Kanade  presented the experimental results of the real-time per- formance of model-basedcontrol algorithms. The com- puted-torque scheme which utilizes the complete dy- namics model of the manipulator is compared with the independent joint control scheme which assumes a de- coupled and linear model of the manipulator dynamics. Pathak et al.  worked on a scheme for robust trajec- tory control of space robot and this work presents a re- duced modal based controller for trajectory control of flexible space robot in work space. Berger et al.  carried out the application of bond graph modeling to robots. Special emphasis is placed on adjusting the exact bond graph to allow for valid numerical solutions.
In this paper, a new adaptive control method is proposed for direct matrix converters. The proposed method uses interval type-2 fuzzy logic integrated with slidingmodecontrol. Employing the slidingmodecontrol in matrix converters leads to an efficient choice of switching combinations and a reliable reference tracking. The main problem of the slidingmodecontrol is the chattering phenomenon that degrades the controller performance through injecting high-frequency variations in the controller variables. The proposed method incorporates the interval type-2 fuzzy with the slidingmodecontrol to mitigate the chattering problem. The slidingmode switch surface can be adjusted adaptively according to the system state and the proposed fuzzy compensation based on the Lyapunov stability theorem, so that the control system has the characteristics of low chattering effect and appropriate operation quality. Comprehensive evaluations of the waveforms are conducted for the new matrix converter through various simulations. Simulation results verify the effectiveness of the proposed adaptive control method for matrix converter in various conditions, and its superiority in chattering suppression in comparison to the conventional slidingmodecontrol and the boundary layer method.
Slidingmodecontrol (SMC) for variable structure systems (VSS) is well applied as a robust approach for control of dynamic systems with uncertainties for its various features such as fast response, good transient performance, and robust to system uncertainties and external disturbances. SMC for VSS was first proposed and elaborated in the early 1950s in the former Soviet Union by Emelyanov and several co-researchers (Emelyanov, 1967, Itkis, 1976 and Utkin, 1977). From then on, SMC has been expanded into a general design method being examined for a wide spectrum of system types including nonlinear systems, multi-input/multi-output systems, discrete time models, large scale and infinite dimensional systems, and stochastic systems. And today, research and development continue to apply SMC to a wide variety of modern but complex engineering systems to achieve high quality products and specified operational performance (Hung, et al, 1993).
Essentially, in coupling the controllers we are using our experience and intuition to redesign the fuzzy controller. Figure 1.a shows the proposed coupled fuzzy controller and the rule base and the membership functions for the shoulder are shown in Figure 1.b and Table 1, and the elbow link rule base is formulated to include the acceleration information from the shoulder link endpoint. The number of rules for the 2 nd link with 7 fuzzy sets
Flexible manipulators have been expressively useful machines in many industrial applications in a wide range. They are developed to undertake most industrial applications that could not be easily solve by heavy rigid robots. This is due to their advantages such as; low electric power consumption, light weight and cheap as compare to the heavy rigid industrial robots. However on the other hand they are associated with some disadvantage which makes their control a challenging and difficult task, some of which are; high oscillation and vibration as a result of rigid body motion at the motor hub angle and the flexible (elastic) motions, also the systems are high order systems and the existence of non-minimum phase dynamic between the applied torque and the tip position . These problems become more difficult especially when there is an increased in the payload . Another well-known problem is the presence of multiple modes which results in generating resonant frequencies close to or at the desire natural frequencies. To overcome this problem, a multi-modecontrol scheme that can add damping and suppress the vibration close to or at natural frequencies is suggested in .
In this work, a PD-type fuzzy logic controller (PDFLC) have been designed with hub angel error and its derivative as inputs of the controller, it was implemented using MATLAB fuzzy tool box to achieve twocontrol purposes namely input tracking and tip deflection regulation. The results shows that the controller successfully achieved both the tracking and regulation control, it also the advantage of the propose control in handling various payload. This control is applicable to many industrial flexible manipulators system, In order to test the robustness of the controller different values of payload are tested and the results shows small changes in the overshot, rise time and settling time as compared to the result with no payload, which shows that the controller is robust to some extend with external changes with zero steady state error. Some limitations of this control scheme it is difficult to design the rule base and the simulation time takes longer time (delay) but this is as a result of using many membership functions and many rule bases. The control gives better result with high number of membership function as when design with less number of membership function. The propose control scheme can be improved by introducing another controller to improve the tracking performance such as integral control in the outer loop.
The study of fault tolerant control (FTC) has received much attention in the last decade. Many different schemes have been proposed, ranging from active to passive control methods , with applications running the gamut from large scale petrochemical plants to automotive and aerospace systems . The work in , , ,  provides an excellent literature review on the different schemes used for FTC including different applications; however, research into FTC has been significantly driven by problems encountered in the safety critical aerospace industry. This is due to the practical requirement for increasing safety as well as lowering operational costs. Many different FTC methods, specific to aircraft applications, have been proposed including linear approaches (e.g. H ∞ , LQG , model-following , multiple model , model predictive control ), and nonlinear approaches (e.g. nonlinear dynamic inversion , backstepping , neural networks , slidingmode ). Some of these methods have attracted the attention of industry and have been further tested and evaluated in order to assess their potential for future applications and implementations on aircraft (see for example the European study on state-of-the-art FTC by the GARTEUR AG-16 group  and the recent ADDSAFE project ). However many of these proposed FTC schemes are based on linear plant representations and are therefore only valid in the vicinity of the designed trim point. Therefore, one of the main challenges for practical implementation, especially for aircraft, is to ensure good performance for a wide range of operating conditions. Some of the linearbased designs can be extended to handle variations in operating conditions (see for example, gain scheduling and linear parameter varying (LPV) schemes , ), but direct nonlinear methods such as nonlinear dynamic inversion (NDI) and backstepping provide equally viable alternatives – with many benefits compared to the extended linear cases. One obvious benefit is the direct exploitation of the well known aircraft equations of motion, which provide good and consistent performance throughout the flight envelope.
Researchers considered different control methods to improve the performance in flexible joint/link robotic systems. Modelling of flexible joint manipulators using singular perturbation method was first proposed by Khorosani and Kokotovic in 1985 . Spong used perturbation method for dynamic modelling and control of manipulator with joint flexibility . Singular perturbation is a unique systematic and mathematical tool for dealing with such flexibilities. This technique allows one to extract the slow and fast dynamics and formulate a separate control strategy for each subsystem. Thikhonov theorem  provides stability guarantees for the combined system. Among other methods, Lew introduced a simple robust control strategy for internal damping of mechanical vibrations for a manipulator with compliant (non-mobile) base .
Abstract—This paper studies the application of the slidingmodecontrol method to reduce the vibration of flexible structure with piezoelectric actuators and strain gage transducer in practical complex environment. The state- space dynamic model of the system was derived by using finite element method and experimental modal test. The structure is subjected to arbitrary, unmeasurable disturbance forces. Taking into account the uncertain random disturbance and measurement noise, Kalman filter is chosen as the state estimator to obtain the modal coordinates and modal velocities for the modal space control. A slidingmode controller is adopted due to its distinguished robustness property of insensitiveness to parameter uncertainties and external disturbances. The sliding surface is determined by using optimization method, and the sliding controller is designed by applying Lyapunov direct method. That is, along the switching surface, the cost function of the states is minimized. A real-time control system was built using dSPACE DS1103 platform, and vibration control tests were performed to experimentally verify the performances of the proposed controller. The results of experiment show the controller can effectively attenuate elastic vibration of the structure.
DC motors have been dominating the field of adjustable speed drives for a long time because of excellent operational properties and control characteristics. In this section different slidingmodecontrol strategies are formulated for different objectives e.g. speed control, torque control and position control.
This paper presents a Gaussian radial basis function neural network based on slidingmodecontrol for trajectory tracking and vibration control of a flexible joint manipulator. To study the effectiveness of the controllers, designed controller is developed for tip angular position control of a flexible joint manipulator. The adaptation laws of designed controller are obtained based on slidingmodecontrol methodology without calculating the Jacobian of the flexible joint system. Also in this study, the anti-control is applied to reduce the deflection angle of flexible joint system. To achieve this goal, the chaos dynamic must be created in the flexible joint system. So, the flexible joint system has been synchronized to chaotic gyroscope system. In this study, control and anti-control concepts are applied to achieve the high quality performance of flexible joint system. It is tried to design a controller which is capable to satisfy the control and anti- control aims. The performances of the proposed control are examined in terms of input tracking capability, level of vibration reduction and time response specifications. Finally, the efficacy of the proposed method is validated through experimentation on QUANSER’s flexible-joint manipulator.