• Proceedings of the Korean Society of Precision Engineering Conference
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• 2000.11a
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• pp.647-652
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• 2000

This paper presents a study on the position tracking control of robot system on the uncertain elastic base. The elastic base is modeled as a virtual robot which has passive joints and the control strategy is using approximate Jacobian operators. Jacobian operators represent the overall robot system including base movement. However, because we don't know the base movement we can't estimate the jacobian operators directly. The control algorithm is proposed which uses only Jacobian operators of a real robot as approximate Jacobian operators. The measured errors from external sensor are compensated by approximate Jacobian operators. The simulation results of a single-axis robot system show that the control strategy can be used for position tracking.

• International Journal of Control, Automation, and Systems
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• v.6 no.1
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• pp.101-108
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• 2008

The transposed Jacobian is proposed to transform the control space from task space to joint space, in this paper. Instead of inverse Jacobian, the transposed Jacobian is preferred to avoid singularity problem, short real time calculations and its generality to apply for rectangular Jacobian. On-line Jacobian identification is proposed to cancel parametric errors produced by D-H parameters of manipulator. To identify Jacobian, the joint angles and the end-effector position are measured when tracking a desired trajectory in task space. Stability of control system is analyzed. The control system is simulated for position control of a two-link manipulator driven by permanent magnet dc motors. Simulation results are shown to compare the roles of inverse Jacobian and transposed Jacobian for transforming the control space.

• Journal of the Korean Society for Precision Engineering
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• v.18 no.10
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• pp.45-52
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• 2001

This paper presents a study on the position tracking control of a robot system on the uncertain elastic base. The elastic bathe is a nonholonomic system but it can be changed into holonomic system, which is much easier to analyze, by modeling an elastic base as a virtual robot that has passive joints. Also, Jacobian operators, which represent the overall robot system including base movement, are defined and applied to the changed model. However, because base movements are not known, the exact Jacobian operators can＇t be estimated. The control algorithm proposed is that uses only Jacobians of a real robot as approximate Jacobian operators. Therefore the approximate Jacobian operators compensate the measured errors from external sensors. The proposed control strategy is evaluated by the simulation and experiment of a single-axis robot system on the elastic base.

• Journal of the Korean Society for Precision Engineering
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• v.20 no.2
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• pp.112-119
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• 2003

Generally, PID controller is not suitable to control multi variable system because it is very difficult to tune the PID gains. However, this paper shows that it is not hard to tune the PID gains if we can find a Jacobian matrix of the system. The Jacobian matrix expresses the ratio of output variations according to input variations. It is possible to adjust the input values in order to reduce the output error using the Jacobian. When the colt function is composed of error related terms, the gradient approach can tune the PID gains to minimize the function. In simulation, a hydrofoil catamaran with two inputs and two outputs is applied as a multi variable system. We can easily get the multi variable PID controller by the proposed teaming method. When the controller is compared with LQR controller, the performance is as good as that of LQR controller with a modeling equation.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.23 no.4
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• pp.337-344
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• 2014

While implicit integration methods such as Newton's method have excellent stability for the analysis of stiff and constrained mechanical systems, they have the drawback that the evaluation and LU-factorization of the system Jacobian matrix required at every time step are time-consuming. This paper proposes a Jacobian update-free Newton's method in order to overcome these defects. Because the motions of all bodies in a vehicle model are limited with respect to the chassis body, the equations are formulated with respect to the moving chassis-body reference frame instead of the fixed inertial reference frame. This makes the system Jacobian remain nearly constant, and thus allows the Newton's method to be free from the Jacobian update. Consequently, the proposed method significantly decreases the computational cost of the vehicle dynamic simulation. This paper provides detailed generalized formulation procedures for the equations of motion, constraint equations, and generalized forces of the proposed method.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.799-802
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• 1997

This paper deals with a new method to derive the Generalized Jacobian Matrix of a space robot. In a conventional method to derive the Generalized Jacobian Matrix, generalized coordinates select Joint angles and a space robot body's position and attitude angle. But, in this paper, we select position and attitude angle of the end-effector or the handled floating object as generalized coordinates. Then, we can derive the Generalized Jacobian Matrix of the system which consists of several space robots and a handled floating object. Moreover control methods operated by only one space robot can be easily extended to the cases of cooperation task by several space robots. Computer simulations show that the Generalized Jacobian Matrix derived here is effective.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.12
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• pp.1966-1973
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• 2001

The Jacobian matrix of the equations of motion of a system using velocity transformation technique is derived via variation methods to apply the implicit integration algorithm, DASSL. The concept of generalized coordinate partitioning is used to parameterize the constraint set with independent generalized coordinates. DASSL is applied to determine independent generalized coordinates and velocities. Dependent generalized coordinates, velocities, accelerations and Lagrange multipliers are explicitly retained in the formulation to satisfy all of the governing kinematic and dynamic equations. The derived Jacobian matrix of a system is proved to be valid and accurate both analytically and through solution of numerical examples.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.9
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• pp.1081-1087
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• 1999

Load Flow calulation methods can usually be divided into Gauss-Seidel method, Newton-Raphson method and decoupled method. Load flow calculation is a basic on-line or off-line process for power system planning. operation, control and state analysis. These days Newton-Raphson method is mainly used since it shows remarkable convergence characteristics. It, however, needs considerable calculation time in construction and calculation of inverse Jacobian matrix. In addition to that, Newton-Raphson method tends to fail to converge when system loading is heavy and system has a large R/X ratio. In this paper, matrix equation is used to make algebraic expression and then to slove load flow equation and to modify above defects. And it preserve P-Q bus part of Jacobian matrix to shorten computing time. Application of mentioned algorithm to 14 bus, 39 bus, 118 bus systems led to identical results and the same numbers of iteration obtained by Newton-Raphson method. The effect of computing time reduction showed about 28% , 30% , at each case of 39 bus, 118 bus system.

• Proceedings of the KIEE Conference
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• 1998.11a
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• pp.311-315
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• 1998

Load Flow calculation methods can usually be divided into Gauss-Seidel method, Newton-Raphson method and decoupled method. Load flow calculation is a basic on-line or off-line process for power system planning, operation, control and state analysis. These days Newton-Raphson method is mainly used since it shows remarkable convergence characteristics. It, however, needs considerable calculation time in construction and calculation of inverse Jacobian matrix. In addition to that, Newton-Raphson method tends to fail to converge when system loading is heavy and system has a large R/X ratio. In this paper, matrix equation is used to make algebraic expression and then to solve load flow equation and to modify above defects. And it preserve certain part of Jacobian matrix to shorten the time of calculation. Application of mentioned algorithm to 14 bus, 39 bus, 118 bus systems led to identical result and the number of iteration got by Newton-Raphson method. The effect of time reduction showed about 28%, 30%, at each case of 39 bus, 118 bus system.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.66 no.5
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• pp.819-832
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• 2017

We propose a new switching control scheme for a ball and beam system by utilizing two linearization methods. First, the Jacobian linearization is applied and state observer is developed afterward. Then, motivated [6], the approximate input-output linearization is carried out, and after that, the Jacobian linearization is applied along with the design of state observer. Since the second approach requires two linearizations, it is called a two-step linearization method. The state observer is needed for the estimation of the velocities of ball and motor movement. Since the Jacobian linearization based controller tends to provide faster response at the initial time, and after that, the two-step linearization based controller tends to provide better response in terms of output overshoot and convergence to the origin, it is natural to give a switching control scheme to provide the best overall control response. The validity of our control scheme is shown in both simulation and experimental results.