Design and Implementation of Sliding Mode Algorithm: Applied to Robot Manipulator-A Review

Please download to get full document.

View again

of 18
25 views
PDF
All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.
Document Description
Refer to the research, review of sliding mode controller is introduced and application to robot manipulator has proposed in order to design high performance nonlinear controller in the presence of uncertainties. Regarding to the positive points in sliding mode controller, fuzzy logic controller and adaptive method, the output in most of research have improved. Each method by adding to the previous algorithm has covered negative points. Obviously robot manipulator is nonlinear, and a number of parameters are uncertain, this research focuses on comparison between sliding mode algorithm which analyzed by many researcher. Sliding mode controller (SMC) is one of the nonlinear robust controllers which it can be used in uncertainty nonlinear dynamic systems. This nonlinear controller has two challenges namely nonlinear dynamic equivalent part and chattering phenomenon. A review of sliding mode controller for robot manipulator will be investigated in this research.
Document Share
Documents Related
Document Transcript
  • 1. Farzin Piltan, N. Sulaiman, Mehdi Rashidi, Zahra Tajpeikar & Payman Ferdosali International Journal of Robotics and Automation (IJRA), Volume (2) : Issue (5) : 2011 265 Design and Implementation of Sliding Mode Algorithm: Applied to Robot Manipulator-A Review Farzin Piltan SSP.ROBOTIC@yahoo.com Department of Electrical and Electronic Engineering, Faculty of Engineering, Universiti Putra Malaysia 43400 Serdang, Selangor, Malaysia N. Sulaiman nasri@eng.upm.edu.my Department of Electrical and Electronic Engineering, Faculty of Engineering, Universiti Putra Malaysia 43400 Serdang, Selangor, Malaysia Mehdi Rashidi SSP.ROBOTIC@yahoo.com Industrial Electrical and Electronic Engineering SanatkadeheSabze Pasargad. CO (S.S.P. Co), NO:16 , PO.Code 71347-66773, Fourth floor Dena Apr , Seven Tir Ave , Shiraz , Iran Zahra Tajpaikar SSP.ROBOTIC@yahoo.com Industrial Electrical and Electronic Engineering SanatkadeheSabze Pasargad. CO (S.S.P. Co), NO:16 , PO.Code 71347-66773, Fourth floor Dena Apr , Seven Tir Ave , Shiraz , Iran Payman Ferdosali SSP.ROBOTIC@yahoo.com Industrial Electrical and Electronic Engineering SanatkadeheSabze Pasargad. CO (S.S.P. Co), NO:16 , PO.Code 71347-66773, Fourth floor Dena Apr , Seven Tir Ave , Shiraz , Iran Abstract Refer to the research, review of sliding mode controller is introduced and application to robot manipulator has proposed in order to design high performance nonlinear controller in the presence of uncertainties. Regarding to the positive points in sliding mode controller, fuzzy logic controller and adaptive method, the output in most of research have improved. Each method by adding to the previous algorithm has covered negative points. Obviously robot manipulator is nonlinear, and a number of parameters are uncertain, this research focuses on comparison between sliding mode algorithm which analyzed by many researcher. Sliding mode controller (SMC) is one of the nonlinear robust controllers which it can be used in uncertainty nonlinear dynamic systems. This nonlinear controller has two challenges namely nonlinear dynamic equivalent part and chattering phenomenon. A review of sliding mode controller for robot manipulator will be investigated in this research. Keywords: Robotic System, Nonlinear System, Robust Controller, Sliding Mode Controller. 1. INTRODUCTION There are a lot of control methodologies that can be used for control of robot manipulators. These range of various controllers applied from linear to nonlinear, to lots of non-classical non-linear and adaptive non- classical non-linear. In this paper an attempted has been made to do a review of sliding mode control (SMC) for robotics manipulator.
  • 2. Farzin Piltan, N. Sulaiman, Mehdi Rashidi, Zahra Tajpeikar & Payman Ferdosali International Journal of Robotics and Automation (IJRA), Volume (2) : Issue (5) : 2011 266 Non linear control methodologies are more general because they can be used in linear and non linear systems. These controllers can solve different problems such as, invariance to system uncertainties, and resistance to the external disturbance. The most common non linear methodologies that have been proposed to solve the control problem consist of the following methodologies: feedback linearization control methodology, passivity-based control methodology, sliding mode control methodology, robust Lyapunov-based control methodology, adaptive control methodology, and artificial intelligence- based methodology [2]. Sliding mode controller (SMC) is a powerful nonlinear controller which has been analysed by many researchers especially in recent years. This theory was first proposed in the early 1950 by Emelyanov and several co-workers and has been extensively developed since then with the invention of high speed control devices [19, 21]. The main reason to select this controller in wide range area is have acceptable control performance and solve two most important challenging topics in control which names, stability and robustness [2; 17; 62]. However, this controller used in wide range but, pure sliding mode controller has following disadvantages. Firstly, chattering problem; which can caused the high frequency oscillation of the controllers output. Secondly, sensitivity; this controller is very sensitive to the noise when the input signals very close to the zero. Last but not the least, nonlinear equivalent dynamic formulation; which this problem is very important to have a good performance and it is difficult to calculation because it is depending on the nonlinear dynamic equation [63, 25]. Chattering phenomenon can cause some problems such as saturation and heat for mechanical parts of robot manipulators or drivers. To reduce or eliminate the chattering, various papers have been reported by many researchers and classified in two most important methods, namely, boundary layer saturation method and estimated uncertainties method [2, 19, 21-23, 27, 51, 53, 56]. In recent years, artificial intelligence theory has been used in sliding mode control systems. Neural network, fuzzy logic, and neuro-fuzzy are synergically combined with sliding mode controller and used in nonlinear, time variant, and uncertainty plant (e.g., robot manipulator). The strategies for robotics are classified in two main groups: classical and non-classical methods, where the classical methods use the mathematical models to control systems and non-classical methods use the artificial intelligence theory such as fuzzy logic, neural networks and/or neuro-fuzzy. After the invention of fuzzy logic theory in 1965 by Zadeh, this theory was used in wide range applications. Fuzzy logic controller (FLC) is one of the most important applications in fuzzy logic theory. This controller can be used to control of nonlinear, uncertain systems and transfer expert knowledge to mathematical formulation. However pure FLC works in many areas but, it cannot guarantee the basic requirement of stability and acceptable performance [53]. Some researchers applied fuzzy logic methodology in sliding mode controllers (FSMC) to reduce the chattering and equivalent problems in pure sliding mode controller so called fuzzy sliding mode controller [41, 46, 61] and the other researchers applied sliding mode methodology in fuzzy logic controller (SMFC) to improve the stability of system that is most important challenge in pure FLC [4, 23, 48-50]. Fuzzy sliding mode controller (FSMC) is a sliding mode controller which combined to fuzzy logic system (FLS) to reduce or eliminate the high frequency oscillation (chattering), to compensate the unknown system dynamics, and also to adjustment of the linear sliding surface slope. H.Temeltas [46] has proposed FSMC to achieving robust tracking of nonlinear systems. C. L. Hwang et al. [8] have proposed a fuzzy model based sliding mode control based on N fuzzy based linear state-space. A multi-input multi-output FSMC to reduce the chattering and constructed to approximate the unknown system has been presented for a robot manipulator [42]. Sliding mode fuzzy controller (SMFC) is a fuzzy logic controller based on sliding mode methodology to reduce the fuzzy rules and to refine the stability of close loop system. Research on SMFC is significantly growing as their applications, for instance, in control robot manipulator which, have been reported in [4, 23, 48-50]. H.K.Lee et al. [52] have presented self tuning SMFC to reduce the fuzzy rules, increase the stability and to automatically adjusted control parameters. Palm R [23] has proposed SMFC to increase the robustness and trajectory disturbance.
  • 3. Farzin Piltan, N. Sulaiman, Mehdi Rashidi, Zahra Tajpeikar & Payman Ferdosali International Journal of Robotics and Automation (IJRA), Volume (2) : Issue (5) : 2011 267 Another method to intelligent control of robot manipulator is Artificial Neural Networks (ANNS) or Neural networks (NNs). It is a parametric nonlinear function and the parameters are the weights of the NNs. It can be used in two areas in robotics, namely, control robot manipulator and identification. Neural networks control is very effective tool to control robot manipulator when robot manipulators have uncertainty in dynamic part. With this method, researcher can design approximate for an unknown dynamical system only by knowing the input-output data of systems (i.e., training data) [24-25]. Adaptive control used in systems whose dynamic parameters are varying and need to be training on line. In general states adaptive control classified in two main groups: traditional adaptive method and fuzzy adaptive method, that traditional adaptive method need to have some information about dynamic plant and some dynamic parameters must be known but fuzzy adaptive method can training the variation of parameters by expert knowledge. Combined adaptive method to artificial sliding mode controllers can help to controllers to have better performance by online tuning the nonlinear and time variant parameters. F Y Hsu et al. [54] have presented adaptive fuzzy sliding mode control, which can update fuzzy rules to compensate nonlinear parameters and guarantee the stability robot manipulator controller. Y.C. Hsueh et al. [43] have presented self tuning sliding mode controller which can resolve the chattering problem without to use of saturation function. This paper is organized as follows. In section 2, main subject of sliding mode controller and formulation are presented. This section covered the following details, classical sliding mode control, classical sliding for robotic manipulators, equivalent control and chatter free sliding control. A review of the fuzzy logic system and application to sliding mode controller is presented and introduces the description and analysis of adaptive artificial sliding mode controller is presented in section 3. In section 4, the conclusion is presented. 2 SLIDING MODE CONTROL (VARIABLE STRUCTURE CONTROL) AND THE ROBOT MANIPULATOR APPLICATIONS Sliding mode controller (SMC) is a powerful nonlinear controller which has been analyzed by many researchers especially in recent years. This theory was first proposed in the early 1950 by Emelyanov and several co-workers and has been extensively developed since then with the invention of high speed control devices [2]. The main reason to opt for this controller is its acceptable control performance in wide range and solves two most important challenging topics in control which names, stability and robustness [7, 17-20]. Sliding mode control theory for control of robot manipulator was first proposed in 1978 by Young to solve the set point problem ( by discontinuous method in the following form [19, 3]; (1) where is sliding surface (switching surface), for n-DOF robot manipulator, is the torque of joint. Sliding mode controller is divided into two main sub controllers: discontinues controller and equivalent controller . Discontinues controller causes an acceptable tracking performance at the expense of very fast switching. In the theory of infinity fast switching can provide a good tracking performance but it also can provide some problems (e.g., system instability and chattering phenomenon). After going toward the sliding surface by discontinues term, equivalent term help to the system dynamics match to the sliding surface[1, 6]. However, this controller used in many applications but, pure sliding mode controller has following challenges: chattering phenomenon, and nonlinear equivalent dynamic formulation [20]. Chattering phenomenon can causes some problems such as saturation and heat the mechanical parts of robot manipulators or drivers that has shown in Figure 2.6. To reduce or eliminate the chattering, various papers have been reported by many researchers which classified into two most important methods: boundary layer saturation method and estimated uncertainties method [1]. In boundary layer saturation method, the basic idea is the discontinuous method replacement by saturation (linear) method with small neighborhood of the switching surface. This replacement caused to
  • 4. Farzin Piltan, N. Sulaiman, Mehdi Rashidi, Zahra Tajpeikar & Payman Ferdosali International Journal of Robotics and Automation (IJRA), Volume (2) : Issue (5) : 2011 268 increase the error performance against with the considerable chattering reduction. Slotine and Sastry have introduced boundary layer method instead of discontinuous method to reduce the chattering[21]. Slotine has presented sliding mode with boundary layer to improve the industry application [22]. R. Palm has presented a fuzzy method to nonlinear approximation instead of linear approximation inside the boundary layer to improve the chattering and control the result performance[23]. Moreover, C. C. Weng and W. S. Yu improved the previous method by using a new method in fuzzy nonlinear approximation inside the boundary layer and adaptive method[24]. As mentioned [24]sliding mode fuzzy controller (SMFC) is fuzzy controller based on sliding mode technique to simple implement, most exceptional stability and robustness. Conversely above method has the following advantages; reducing the number of fuzzy rule base and increasing robustness and stability, the main disadvantage of SMFC is need to define the sliding surface slope coefficient very carefully. To eliminate the above problems control researchers have applied artificial intelligence method (e.g., fuzzy logic) in nonlinear robust controller (e.g., sliding mode controller) besides this technique is very useful in order to implement easily. Estimated uncertainty method used in term of uncertainty estimator to compensation of the system uncertainties. It has been used to solve the chattering phenomenon and also nonlinear equivalent dynamic. If estimator has an acceptable performance to compensate the uncertainties, the chattering is reduced. Research on estimated uncertainty to reduce the chattering is significantly growing as their applications such as industrial automation and robot manipulator. For instance, the applications of artificial intelligence, neural networks and fuzzy logic on estimated uncertainty method have been reported in [25- 28]. Wu et al. [30] have proposed a simple fuzzy estimator controller beside the discontinuous and equivalent control terms to reduce the chattering. Their design had three main parts i.e. equivalent, discontinuous and fuzzy estimator tuning part which has reduced the chattering very well. Elmali et al. [27]and Li and Xu [29]have addressed sliding mode control with perturbation estimation method (SMCPE) to reduce the classical sliding mode chattering. This method was tested for the tracking control of the first two links of a SCARA type HITACHI robot. In this technique, digital controller is used to increase the system’s response quality. Conversely this method has the following advantages; increasing the controller’s response speed and reducing dependence on dynamic system model by on-line control, the main disadvantage are chattering phenomenon and need to improve the performance. Robot manipulators are one of the highly nonlinear and uncertain systems which caused to needed to robust controller. This section provides introducing the formulation of sliding mode controller to robot manipulator based on [1, 6]Consider a nonlinear single input dynamic system of the form [6]: (2) Where u is the vector of control input, is the derivation of , is the state vector, is unknown or uncertainty, and is of known sign function. The control problem is truck to the desired state; , and have an acceptable error which is given by: FIGURE 1: Chattering as a result of imperfect control switching [1]
  • 5. Farzin Piltan, N. Sulaiman, Mehdi Rashidi, Zahra Tajpeikar & Payman Ferdosali International Journal of Robotics and Automation (IJRA), Volume (2) : Issue (5) : 2011 269 (3) A time-varying sliding surface is given by the following equation: (4) where λ is the positive constant. To further penalize tracking error integral part can be used in sliding surface part as follows: (5) The main target in this methodology is kept the sliding surface slope near to the zero. Therefore, one of the common strategies is to find input outside of . (6) where ζ is positive constant and in equation (6) forces tracking trajectories is towards sliding condition as shown in Figure 2. FIGURE 2: Sliding surface [2] If S(0)>0 (7) To eliminate the derivative term, it is used an integral term from t=0 to t= (8)
  • 6. Farzin Piltan, N. Sulaiman, Mehdi Rashidi, Zahra Tajpeikar & Payman Ferdosali International Journal of Robotics and Automation (IJRA), Volume (2) : Issue (5) : 2011 270 Where is the time that trajectories reach to the sliding surface so, suppose S( defined as (9) and (10) Equation (2.41) guarantees time to reach the sliding surface is smaller than since the trajectories are outside of . (11) suppose S is defined as (12) The derivation of S, namely, can be calculated as the following; (13) suppose the second order system is defined as; (14) Where is the dynamic uncertain, and also since , to have the best approximation , is defined as (15) A simple solution to get the sliding condition when the dynamic parameters have uncertainty is the switching control law: (16) where the switching function is defined as (17) and the is the positive constant. Suppose by (16) the following equation can be written as, (18) and if the equation (17) instead of (18) the sliding surface can be calculated as (19) in this method the approximation of is computed as (20) To reduce or eliminate the chattering it is used the boundary layer method; in boundary layer method the basic idea is replace the discontinuous method by saturation (linear) method with small neighborhood of the switching surface. Figure 3 is shown the control law in boundary layer.
  • 7. Farzin Piltan, N. Sulaiman, Mehdi Rashidi, Zahra Tajpeikar & Payman Ferdosali International Journal of Robotics and Automation (IJRA), Volume (2) : Issue (5) : 2011 271 FIGURE 3: Boundary layer applied in discontinuous part [2] (21) Where is the boundary layer thickness. Therefore the saturation function is added to the control law as (22) Where can be defined as (23) Based on above discussion, the control law for a multi degrees of freedom robot manipulator is written as: (24) Where, the model-based component is the nominal dynamics of systems and can be calculate as follows: (25)
  • 8. Farzin Piltan, N. Sulaiman, Mehdi Rashidi, Zahra Tajpeikar & Payman Ferdosali International Journal of Robotics and Automation (IJRA), Volume (2) : Issue (5) : 2011 272 Where τ is vector of actuation torque, M (q) is symmetric and positive define inertia matrix, is matrix of coriolis torques, is matrix of centrifugal torque, is vector of joint velocity that it can give by: and is vector, that it can given by: and is Gravity terms, As mentioned above the kinetic energy matrix in DOF is a matrix that can be calculated by the following matrix [1, 6] (26) The Coriolis matrix (B) is a matrix which calculated as follows; (27) and the Centrifugal matrix (C) is a matrix; (28) And last the Gravity vector (G) is a vector; (29) and is computed as; (30) the control output can be written as; (31) Figure 4 shows the position classical sliding mode control for robot manipulator. By (30) and (31) the sliding mode control of robot manipulator is calculated as; (32)
  • 9. Farzin Piltan, N. Sulaiman, Mehdi Rashidi, Zahra Tajpeikar & Payman Ferdosali International Journal of Robotics and Automation (IJRA), Volume (2) : Issue (5) : 2011 273 3 INTRODUCTION TO FUZZY CONTROL AND ITS APPLICATION TO SMC In recent years, artificial intelligence theory has been used in sliding mode control systems. Neural network, fuzzy logic, and neuro-fuzzy are synergically combined with nonlinear classical controller and used in nonlinear, time variant, and uncert
  • Search Related
    We Need Your Support
    Thank you for visiting our website and your interest in our free products and services. We are nonprofit website to share and download documents. To the running of this website, we need your help to support us.

    Thanks to everyone for your continued support.

    No, Thanks
    SAVE OUR EARTH

    We need your sign to support Project to invent "SMART AND CONTROLLABLE REFLECTIVE BALLOONS" to cover the Sun and Save Our Earth.

    More details...

    Sign Now!

    We are very appreciated for your Prompt Action!

    x