International Journal of Research in Advent Technology, Vol.2, No.6, June 2014 E-ISSN: 2321-9637
Design A Tracking Controller for Single-Link Single Manipulator via DSC Mr.Varun Chauhan1, Mrs. Chintu Rza2, Mrs. Shivani Mehta3 Department Electrical Engineering, D.A.V.I.E.T., Jalandhar, Punjab, India1, 2, 3 Student, Master of Technology, chauhan.varun809@gmail.com1 Assistant Professor, chinturza78@gmail.com2 Assistant Professor, shivanimehta7@gmail.com3 Abstract—The aim of this paper is to design a tracking controller for the single link manipulator. The design technique preferred here dynamic surface control. Dynamic surface control (DSC) is a latest approach based on backstepping, which tackles the problem arising due to repeated differentiations in conventional backstepping. It provides a better approach for the tracking control of single link manipulator. Index Terms—manipulator, dynamic surface control (DSC) 1.
INTRODUCTION
Recent year’sindustrial robot is manufactured in a great quality with a better repeatability, precision and resolution.Robot Robot manipulators are mostly used in the industrial production sector and also have a lot other specialized uses. Manipulators are mostly preferred as a robotic arm. It is a process which performs like arm. It is a combination of series of segments, commonly sliding or jointed which hold firmly and move thingss with a number of degree of freedom. The number of degrees of freedom means the number of independent variables that are necessary to completely detect its configuration in space. The consideration of robot manipulators includes dealing with the locations and orientations of the several segments that make up the manipulators. This module tells the basic concepts that are necessary to justify these locations and orientations of rigid bodies in space and complete coordinate transformations.
In this paper, dynamic surface control (DSC) design is proposed to design a tracking controller for the single link manipulator. Conventional backstepping although systematic, suffers from severe problem of explosion of terms which arises due to repeated differentiations of virtual controllers. Thus, the complexity of controller increases severely limiting the use of backstepping technique to higher order systems. In order to tackle this problem, a new approach called dynamical surface control (DSC) was first introduced by Swaroop et al. [1]] for non-adaptive non systems and further extended xtended by Patric and Hedric [2]] for adaptive systems. In DSC, a first order filtering of the synthetic input is carried out at each level of the traditional backstepping design.
This research paper is organised as follows. In section 2 there is the description of the robot manipulator.In .In Section 4, we design a DSC to design a tracking controller for f the single link manipulator with the known system parameters respectively. 2. ROBOT MANIPULATOR Manipulators are the combination of an assembly of links and joints. The he rigid sections that built the mechanism are called links and the connections between two links are called joints. The instrumentaffixed to the manipulator which interacts with its environment ronment to completejobs is called the end-effector. The end effector is shown in Figure1, link 6
(a)
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International Journal of Research in Advent Technology, Vol.2, No.6, June 2014 E-ISSN: 2321-9637 Where, ,
! ,
,
! !
, ,
"
"
Objective:: To design a controller u so that the output # converges to a desired trajectory #$ sin ) with all other signals remaining bounded. First a dynamic sliding surface * is define * ! $ (5)* ! $ ! $ The synthetic value of virtual control which will make * converge to zero, is given as, ̅ ! * (6) $ On passing ̅ through a first order filter with time constant , one can obtain $ .
(b) Fig.1. (a) Links and joints (b) Robot arms
$
A robot manipulator is an electronically controlled mechanism, consisting of multiple segments, that performs tasks by interacting with its environment. They are also usually referred to as robotic arms. An industrial robot contains robot manipulator, powerr supply, and controllers. Robotic manipulators can be divided into two sections, each with a different function as shown in Figure 1(b). The arm and body of a robot is use to move and locate parts or tools as task demands. demands They are formed from three jointss connected by large links. The wrist is used to orient the parts or tools at the work place.
3.
DSC DESIGN FOR MANIPULTOR
̅ ,
$
$
̅ 0
0
(7)
The controller designed after further formulation is given as: ,-
∗
$
!
* !
,
,
)
(8)
3.2 Simulation Results The value of time constants τ and τ is taken as 0.06 and 0.01 respectively and the surface gains are selected as K 100, K 150 and K 10 . The initial value is taken asx as 0 0.1,x 0 6.28and x 0 0[13].Below Below figures i.e. states s of the system, tracking racking Error, Error tracking of desired trajectory displays the effectiveness of $ simulation result.
3.1Tracking Tracking control of single link manipulator The dynamics of single link manipulator system with actuator is given by [5] (1) (2) Here, is the angle of the manipulator is the load torque, is the friction coefficient, and are the terms related to mass and length. Different parameters is taken as D=1; M=0.01; B=1;
10;
Selecting state variables as one can get, (3) (4)
0.6 and N=10 ,
Fig. 2. States of the system
and ,
,
,
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International Journal of Research in Advent Technology, Vol.2, No.6, June 2014 E-ISSN: 2321-9637 [6] Visioli A. andLegnani Legnani G(2002): G On the trajectory tracking control of industrial SCARA robot manipulators //, Journal of IEEE Transactions on Industrial Electronics. Vol. 49, No.1. P. 224–232. [7] Dixon W. E(2004): Adaptive regulation of amplitude limited robot manipulators with uncertain kinematics and dynamics. Proceedings of American Control Conference P. 3844–3939. [8] EricM and LuW.S. (1996):A (1996): reduced-order adaptive velocity observer server for manipulator control, IEEE EE Transactions on Robotics and Automation, vol.11, no.2, pp. 293-303. 293 [9] Berghuis H and Nijmeijer T (1991): Tracking control of robots using u only position measurement, Proceedings of the 30th Conference on Decision and Control, Brighton, B England, pp.1039-1040. [10] Berghuis H and Nijmeijer T (1994): Robust control of robots via linear l estimated state feedback, IEEE Transactions on Automatic Control, vol. 39, no. 10, pp. 2159-2162. 2159
Fig. 3. Tracking Error
Fig. 4. Tracking of desired trajectory
$
CONCLUSION In this paper, we performed new results to design a tracking controller for or the single link manipulator with the known system parameters respectively. respectively Numerical figures were shown by using MATLAB to illustrate the validity and successful operation of the DSC design. REFERENCES [1] Swaroop, D.; Gerdes, J. C.; Yip, P. P.; and Hedrick,J. K (1997): Dynamic surface control of nonlinear systems, Proc. Amer. Control Conf. Albuquerque, NM, pp. 3028-3034, 3028 Jun. [2] Yip, p.p. and Hedrick, J. K. (1998): Adaptive dynamic surface control: a simplified algorithm for adaptive backstepping control of nonlinear systems, INT. J. Control, vol. 71, No.5, pp. 959-979. [3] Tsai.L-W(1999): Robot Analysis: The Mechanics of Serial and Parallel arallel Manipulators, Manipulators NY, John Wiley & Sons, Inc. [4] Melek.W.W (2010):ME ME 547: Robot Manipulators: Kinematics, Dynamics, and Control.. Waterloo, University of Waterloo. [5] SharmaB.B. andKarI.N (2009): Member IEEE, Contraction Based Adaptive Control of a Class of Nonlinear Systems, American Control Cont Conference, June 10-12 .
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