Abstract
This paper proposes a gain scheduling linear quadratic integral (LQI) servo controller design, which is derived from linear quadratic regulator (LQR) optimal control, for non-singular linear parameter varying (LPV) descriptor systems. It is assumed that state space matrices are non-singular since many mechanical systems do not have any non-singular matrices such as the natural state space forms of robotic manipulator, pendulum and suspension systems. A controller design is difficult for the systems due to rational LPV case. Therefore, the proposed gain scheduling controller is designed without the difficulty. Accordingly, the motion control design is implemented for two-link flexible joint robotic manipulator. Finally, the control system simulation is performed to prove the applicability and performance.
Highlights
Many researchers have recently considered the problem of robust controller design on linear parameter varying or linear time invariant systems in the regular statespace form such as in [1,2,3,4,5,6,7,8,9,10,11,12,13,14], where the systems are common linear parameter varying (LPV) systems
This paper proposes a gain scheduling linear quadratic integral (LQI) servo controller design, which is derived from linear quadratic regulator (LQR) optimal control, for non-singular linear parameter varying (LPV) descriptor systems
The complexity of problem arises because they are multi-input multi-output (MIMO) systems, which are affected by several factors such as payload changing and vibration effects of between links
Summary
Many researchers have recently considered the problem of robust controller design on linear parameter varying or linear time invariant systems in the regular statespace form such as in [1,2,3,4,5,6,7,8,9,10,11,12,13,14], where the systems are common linear parameter varying (LPV) systems. In [35], general H∞ LPV control is designed for the non-singular descriptor flexible robotic manipulator. A gain scheduling Linear Quadratic Integral (LQI) controller has not been tackled for the non-singular descriptor systems in the literature. Natural two-link robotic manipulator model has not any singular matrices, but it and similar mechanical systems can be converted to singular form by LPV conversion methods as in [22, 36, 37], which is not in the focus of paper. Because of avoiding the complexity of rational LPV systems, the proposed controller can be applied to a robotic manipulator system or any non-singular LPV descriptor system without using rational LPV form. From the references and the other literature studies, there is not a gain-scheduling controller LQI design for the LPV descriptor systems without conversion methods
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