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부족구동 역학 시스템의 비선형 적응제어
- Alternative Title
- Mun-Soo Park
- Author(s)
- 박문수
- Alternative Author(s)
- Mun-Soo Park
- Advisor
- 홍석교
- Department
- 일반대학원 전자공학과
- Publisher
- The Graduate School, Ajou University
- Publication Year
- 2007-08
- Language
- eng
- Keyword
- Underactuated mechanical system; semi-global stabilization; trajectory tracking; backstepping technique; sliding mode control; partial feedback linearization; fuzzy adaptive trajectory tracking; fuzzy uncertainty observer
- Alternative Abstract
- This dissertation is devoted to a nonlinear adaptive stabilization and tracking control of a class of underactuated mechanical systems. Underactuated systems are mechanical control systems with fewer controls than the number of configuration variables. Control of underactuated systems has been one of the active research fields due to their broad range of applications in robotics, aerospace vehicles, and marine vehicle. For example, underactuated systems in real-life include flexible-link robots, mobile robots, walking robots, robots on mobile platforms, cars, locomotive systems, snake-type and swimming robots, acrobatic robots, aircraft, spacecraft, helicopters, satellites, surface vessels, and underwater vehicles. Recent survey shows that the control of general underactuated mechanical systems is still one of the major open problems. The objective of this dissertation is to develop several methods for the configuration stabilization and trajectory tracking of a class of underacuated mechanical systems. The configuration stabilization is addressed for non-minimum phase underactuated systems (e.g., inverted pendulum) having unstable zero dynamics. In this dissertation, the scope of configuration stabilization is focused on the global or semi-global stabilization as well as orbital stabilization (i.e., stabilization of limit cycle). On the other hand, the trajectory tracking is considered for both minimum and non-minimum phase underactuated systems. For minimum phase underactuated systems, decoupling control based on collocated partial feedback linearization is adopted, which includes additive variable structure control law (VSC) for the asymptotical stabilization of unactuated subsystems. On the other hand, a novel partial feedback linearization (so called ”Lagrangian preserving partial feedback linearization”) is developed and utilized for the decoupling control of non-minimum phase underacuated systems. In addition, an adaptive schem based on fuzzy systems is proposed, to cope with systems uncertainties including system parameter uncertainties, external disturbances, and actuator nonlinarities for more practical issues. The main results of this dissertation are summaried as follows. First, semi-global and orbital stabilizations are presented by using backstepping technique, sliding mode control (SMC), and a novel partial feedback linearization. In backstepping based approach, we define an error state that utilizes momentum conjugate to unactuated variables which make it easy to apply standard backstepping approach. In stability analysis for the whole systesm, a condition that ensures semi-global and almost global domain of attraction is provided. In SMC based approach, we firstly decompose an underacuated mechanical system into actuated and unactuated subsystems, followed by a design of individual control law for each subsystem. Semi-global stabilizations of equilibrium and relative equilibrium point, as well as orbital stabilization around equilibrium are demonstrated through an illustrative numerical example. In a novel partial feedback linearization based approach, we define a weakly (or marginally) minimum phase output of a non-minimum phase underactuated mechanical system. For this new output, partially feedback linearizing control is designed, which renders the integral of closed-loop zero dynamics be an energy-like function having Lagrangian form. This energy-like function has its maximum value at equilibrium point and differs from a Lyapunov function in the sense that it is not positive or negative definite. Then, two methods for the asymptotic stabilization of equilibrium are propsed; the first method utilizes a nonlinear dissipation control in such a way that the energy-like function converges to its maximum value (energy-maximizing control); second method considers a modified version of the energy-like function as a Lyapunov fucntion. Second, trajectory tracking of underactuated mechanical systems is based on the decoupling control and partial feedback linearization. For minimum pahse systems (e.g., overhead cranes), we adopt collocated partial feedback linearization and employ a nonlinear dissipation control law to guarantee the asymptotic stability of unactuated subsystem. To demonstrate the proposed method, we perform numerical simulations and experiments for an overhead crane without hoisting motion. For non-minimum phase systems (e.g., inverted pendulum), we utilize the Lagrangian preserving partial feedback linearization and design trajectory tracking control law for the redefined output. By introducing a nonlinear dissipation control, asymptotic and bounded trajectory trakcing is accomplished. Finally, fuzzy based adaptive scheme to deal with systems uncertainties is proposed, where fuzzy system is utilized to estimate two lumped uncertainties for each actuated and unactuated subsystem. In this scheme, we treat uncertainties as a lumped one which is coupled with each other. Thus, we can estimate both uncertainties for actuated subsystem and unactuated subsystem with one uncertainty observer for the unactuated subsystem.
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- Graduate School of Ajou University > Department of Electronic Engineering > 3. Theses(Master)
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