[16] has proposed a link-space pressure feedback controller for Stewart type hydraulic **manipulator**. However, this approach lacks stability proofs that are important from both theoretical and implementations points of view. [17] has developed a generalized predictive **control** algorithm for hydraulic **control** system but the limitation of this approach is that it relies heavily on online parameter estimation and consequently , is computationally expensive. [18] on the other hand, have adopted a Lyapunov based Model-based Adaptive **Control** for hydraulic **manipulator**. Even though the technique possesses mathematical stability proof but it needs persistent excitation and pressure feedback. A strategy based on Backstepping approach has been developed by [19] to provide necessary position tracking for the hydraulic **robot**. However, the proposed strategy also relies on online computation for converting into task-space coordinates. Furthermore, it is said to be sensitive to sensor noise, hence high-quality measurements are needed. To overcome this drawback is by introducing heuristic limitation of time derivatives in the **control** law so that the influence of sensor noise in the simulations reduces significantly, but may deteriorate the **control** performance.

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ISMC is equal to the order of the original system, rather than reduced by the number of dimension of the **control** input. Moreover, by using this approach, the robustness of the system can be guaranteed throughout the entire response of the system starting from the initial time instance.

maintenance cost with high power-to-weight ratio. The hydraulic actuator system also has the ability to produce a very large force and torque in any system[5]. Some of the examples of hydraulic actuator system application that require large force and torque are electro-hydraulic positioning system, industrial hydraulic machines[6], **robot** manipulators [7] and hydraulic elevators[8]. Due to high precision position controllers, hydraulic actuator systems are applied in specialized manufacturing equipment or test equipment such as simple shear apparatus utilized for soil testing[9]. Although there are a number of advantages for applications that utilize hydraulic actuator systems, there are some weaknesses that complicate the development of hydraulic actuator system controller as the system is a highly nonlinear system. Aside from the nonlinear behaviour, the hydraulic actuator system also suffers from a large extent of model uncertainties. The uncertainties can be classified into two main groups which are parametric uncertainties and uncertain nonlinearities. Examples of parametric uncertainties are large variations in load and hydraulic parameters such as bulk modulus due to component wear or temperature change. Meanwhile, external disturbance, leakage and friction are called uncertain nonlinearities[10]. These uncertainties can cause the hydraulic actuator system controller to be unstable or to have degradation in its performance.

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Abstract β In this paper, controlling a rigid **robot** **manipulator** driven by hydraulic system is considered. Due to changing of inertia moment of the **manipulator** as well as the effect of fiction of hydraulic system, the dynamics of the **robot** arm is highly nonlinear. Therefore **sliding** **mode** **control** method is applied. **Sliding** **mode** **control** is a robust **control** method. It provides a symmetric approach to the problem of maintaining stability and consistent performance in the face of modeling imprecision. Numerical simulations and experiment results of the **control** system are presented. The results show the extremely good robustness of the proposed method.

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Whenever, fast and high-precision position **control** is required for a system which has high nonlinearity and unknown parameters, and also, suffers from uncertainties and disturbances, such as **robot** manipulators, in that case, necessity of designing a developed controller that is robust and has self-learning ability is appeared. For this purpose, an efficient combination of **sliding** **mode** **control**, PID **control** and neural network **control** for position tracking of **robot** manipulators driven by permanent magnet DC motors was addressed in the third case. SMC is robust against uncertainties, but it is extremely dependent on model and uses unnecessary high **control** gain; So, NN **control** approach is employed to approximate major part of the model. A PID part was added to make the response faster, and to assure the reaching of **sliding** surface during initial period of weight adaptations. Moreover, four practical aspects of **robot** **manipulator** **control** such as actuator dynamics, restriction on input armature voltage of actuators due to saturation of them, friction and uncertainties were considered. In spite of these features, the controller was designed based on Lyapunov stability theory and it could carry out the position **control** with fast transient and high-precision response, successfully. Finally, two-step simulation was performed and its results confirmed the success of presented approach. However, the presented design was performed in the joint space of **robot** **manipulator** and kinematic uncertainty was not considered. For the future work, one can expand this method to work space design with uncertain kinematics.

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Before designing a controller, the system model should be defined firstly. In reality, most systems are nonlinear, and the model is imprecise, with actual uncertainty[1][2]. From a **control** point of view, modeling inaccuracies can be classified into two major kinds: 1. Structured (or parametric) uncertainties, and 2. Unstructured uncertainties (or unmodelled dynamics)[3]. For any practical design, the system model must be explicitly defined[4][5]. For the class of systems to which it applies, **sliding** controller design provides a systematic approach to the problem of maintaining stability and consistent performance in the face of modeling imprecision[6]. It has been widely used in **manipulator**, ground and submarine operation vehicles, automotive transmission systems and engines, high-capacity motors and power **control** systems[7][8].

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In this paper, a robust neural network global **sliding** **mode** PID-controller is proposed to **control** a **robot** **manipulator** with parameter variations and external disturbances. The chattering phenomenon is eliminated by substituting a single-input radial-basis-function (RBF) neural network. The weights of hidden layers of the neural network are on-line updated to compensate the system uncertainties. Moreover, a theoretical proof of the stability and the convergence of the proposed scheme are provided.

Abstract. Two-link flexible **manipulator** is a **manipulator** **robot** which at least one of its arms is made of lightweight material and not rigid. Flexible **robot** **manipulator** has some advantages over the rigid **robot** **manipulator**, such as lighter, requires less power and costs, and to result greater payload. However, suitable **control** algorithm to maintain the two-link flexible **robot** **manipulator** in accurate positioning is very challenging. In this study, **sliding** **mode** **control** (SMC) was employed as robust **control** algorithm due to its insensitivity on the system parameter variations and the presence of disturbances when the system states are **sliding** on a **sliding** surface. SMC algorithm was combined with linear matrix inequality (LMI), which aims to reduce the effects of chattering coming from the oscillation of the state during **sliding** on the **sliding** surface. Stability of the **control** algorithm is guaranteed by Lyapunov function candidate. Based on simulation works, SMC based LMI resulted in better performance improvements despite the disturbances with significant chattering reduction. This was evident from the decline of the sum of squared tracking error (SSTE) and the sum of squared of **control** input (SSCI) indexes respectively 25.4% and 19.4%.

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Robotic manipulators are widely being used in industry are highly nonlinear systems which often suffer from unmodeled dynamics and uncertainties. Recently **control** engineers have designed controllers for flexible joint robots but it is still very less as compared to the rigid robots. However, in many applications, the robotic manipulators have some flexible joints as well. At the same time, the flexibility of joints may limits the performance and robustness of the controllers designed for robots or may lead to instability [1]. Also, the flexibility of joints can be considered a step for the flexible **robot** link [2] so to by studying the flexible joint **manipulator** can lead us to the flexible link which helps to have link lighter in weight that ultimately results in fast robotic motions. If the flexibility of joint is modeled by the spring, dynamic model of flexible joints can be obtained. Some advantages of flexible joints robotic manipulators over rigid manipulators are less **control** effort, fast motion, light weight and smaller dimension [3]-[6].

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Robotic manipulators are highly nonlinear, highly time-varying and highly coupled. Moreover, there always exists uncertainty in the system model such as external disturbances, parameter uncertainty, and sensor errors. All kinds of **control** schemes, including the classical **Sliding** **Mode** **Control** (SMC) have been proposed in the field of robotic **control** during the past decades (Guo & Wuo, 2003).

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ISMC is a well investigated **control** method, although practical applications are still limited, particularly in the robotics context. Some of the reasons of this may be the jit- tery nature and aggressiveness in the **control** action of slid- ing **mode** **control**. These type of **control** schemes may pose a risk of damaging the robotic devices if not implemented with care. However, due to better understanding of these schemes and availability of good **control** hardware these methods are getting popularity. Shi et al. (2008) have compared tradi- tional **Sliding** **Mode** **Control** and ISMC through simulation for a two-link rigid **manipulator**. Makoto et al. (2010) have applied the ISMC to a power-assisted **manipulator** with a sin- gle degree of freedom through simulation and experiment. Eker and Akinal (2008) have suggested a similar scheme us- ing an integral **sliding** surface in combination with the con-

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important issue and causes an extremely high estimation of the bounds. To solve this problem, the selection of a desired **sliding** surface and π πππ function play a vital role and if the dynamics of the PUMA arm are derived from the **sliding** surface then the linearisation and decoupling through the use of feedback, not gears, can be realised. In this state, the derivative of the **sliding** surface can help to decouple and linearise the closed-loop PUMA arm that would be expected in CTC. Linearisation and decoupling by the above method can be obtained in spite of the lack of quality of the PUMA arm dynamic model, which is in contrast to the CTC that requires an exact dynamic model of the system. It is a well-known fact that the uncertainties can be very well compensated by an on-line tuning PID-like FLC and **sliding** surface slope tuning. To compensate for the uncertainties fuzzy logic theory is a good candidate, but the design of a FLC with perfect dynamic compensation in the presence of uncertainty is not trivial. Therefore, in this research, uncertainties are estimated by discontinuous feedback **control** and the linear part controller is added to eliminate the chatter. To increase the bounds of uncertainty, fuzzy gains and **sliding** surface slope coefficients will be tuned by an on-line tuning method. The above discussion gives the rational for selecting the proposed methodology in this research.

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In this paper, the modeling and impedance **control** of a exible link **manipulator**, using a **sliding** **mode** **control** technique, have been considered. The pro- posed controller works well in both unconstrained and constrained conditions. One can **control** the behavior of the **manipulator**, in both conditions, using a single controller with a single structure (by only tuning the impedance parameters). The use of the **sliding** **mode** **control** theory provides a suitable domain for future research into issues such as robustness and the eects of various nonlinear eects, actuator dynamics and other uncertainties and external disturbances. These studies should be complemented by experimental results to further validate the proposed **control** method.

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In this paper, a nonlinear **sliding** surface has been proposed. It is shown that the error states converge to an arbitrarily small region centred at the origin within a finite time and thereafter asymptotically converge to the equilibrium point. A nonlinear **sliding** **mode** **control** law has been developed using an improved version of the exponential reaching law. The method is applied for **control** of a **robot** **manipulator** system. The residual set defined by the **sliding** **mode** has been determined. The simulation results show that the proposed method has more precise tracking, faster convergence, and stronger robustness against system uncertainty and external disturbances than an existing approach. Due to the smooth **control** signal, the proposed approach reduces the chattering effectively and has a wider range of applications. Future work will focus on application of the results experimentally and in industry.

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The mathematical model of two DOF **robot** **manipulator** is designed in the form of differential equations and then feedback linearization technique is applied to obtain the plant model and two **control** techniques that is adaptive **sliding** **mode** **control** and RBF neural network based **sliding** **mode** **control** have been successfully applied to improve the stability of this system.it is seen that position tracking is instantly and correctly achieved in case of RBF-SMC model, also the system implemented with RBF-SMC is more stable. A comparative study of the parameters for the links of **robot** **manipulator** has been carried out.

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SMC can be construed as a variable structure **control** method due to the behaviour of the **control** input that is able to switch from one continuous function to another based on the current position of the state space. There are two main parts involve in the designing of the SMC (Jezernik et al., 1994). The first part is the design of a **sliding** surface with the state variable of the plant dynamic restricted to another set of equations. The second part deals with the construction of a switched feedback gain in order to drive the plantβs state trajectory to the **sliding** surface. The SMC consists of two main phases. The reaching phase, where the state trajectory of the system is driven from any initial state to reach the switching manifolds, or the predetermined **sliding** surface in finite time. The **sliding**-**mode** phase is where the system is induced or slides into the **sliding** motion on the switching manifolds (Bartoszewicz & Zuk, 2010).

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In recent years, artificial intelligence theory is being applied to SMC. Neural networks (NNs), Fuzzy logic and Neuro-fuzzy are combined with SMC and used in non-linear, time variant and uncertain plant. Some researchers applied fuzzy logic methodology in SMC to reduce the chattering (Barrero et al., 2002) and other researchers have applied **sliding** **mode** methodology in fuzzy logic controller (FLC) to improve the stability of system (Hang et al., 2003; Aloui et al., 2011). In Sun et al. (2011), the authors have addressed the robust trajectory tracking problem for a **robot** **manipulator** in the presence of uncertainties and disturbances. A neural network based **sliding** **mode** adaptive **control** (NNSMAC) which is a combination of **sliding** **mode** technique, neural network approximation and adaptive technique is designed for trajectory tracking of the **robot** **manipulator**. Authors, in Lin and Lenk (2008), Moradi and Malekizade (2013) and Rossomando et al. (2013) developed a design method of recurrent fuzzy neural networks (RFNN) **control** system for MIMO non-linear dynamic system. In (Guoling et al., 2014), the authors have addressed hybrid terminal **sliding** **mode** surfaces and a new fast decoupled terminal **sliding** **mode** **control** (FDTSMC) scheme.

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The changing of system variable (parameters) does not influent the performance of controller (Figure 5). That is shown by the same of time response and steady state error of the system. The change of **control** input value is to keep the system on the steady state condition. If comparing with the previous research, backstepping adaptive **control** has been applied with the same plant [8], the simulation result for the reference position 45 O the system need 2 second to achieve the goal position with 0.5 degree steady state error and still have overshoot. The result of proposed method is better then backstepping adaptive **control** as previous research. Another previous research, Design of Adaptive **Sliding** **Mode** Controller for Robotic Manipulators Tracking **Control** [9] shown that performance is still affected by external disturbance.

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Variable Structure **Control** (VSC) or **Sliding** **Mode** **Control** (SMC) was proposed in the early 1950s (Utkin, 1965), (Emelyanov, 1967), (Itkis, 1976), (Utkin, 1977),(Utkin, 1978). Over the past several decades, increasing attention has been drawn to VSC or SMC and hitherto, significant approaches have been developed world widely (Young, 1977).SMC is one of the well-known robust **control** design methods which only require the upper bounds of the parametric uncertainties and Thus the prescribed specifications would be met through these two designing stages in SMC.

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In this paper, a synergistic combination of Radial Basis Function Neural Network (RBFNN) with fuzzy **sliding** **mode** **control** methodology is proposed. The slope of the **sliding** surface is used to adjust with Fuzzy logic. The weights of the RBFNN are adjusted according to an adaptive algorithm for the purpose of controlling the system states to hit the **sliding** surface and then slide along it. The proposed method and PID **control** are implemented on an industrial **robot** (Manu- tec-r15) and the results obtained from the applications are presented.