Control design and comprehensive stability analysis of acrobots based on Lyapunov functions
- 81 Downloads
A design method for controllers and a comprehensive stability analysis for an acrobat based on Lyapunov functions are presented. Three control laws based on three Lyapunov functions are designed to increase the energy so as to move the acrobot into the unstable inverted equilibrium position, and solve the problem of posture and energy. The concept of a non-smooth Lyapunov function is employed to analyze the stability of the whole system. The validity of this strategy is demonstrated by simulations.
Key wordsstability Lyapunov function acrobot fuzzy control
Unable to display preview. Download preview PDF.
- Oriolo G, Nakamura Y. Control of mechanical systems with second-order nonholonomic constraints: underactuated manipulators[A]. Proc 30th IEEE Conf on Decision and Control[C]. 1991. 2398–2403.Google Scholar
- Hauser J, Murray R M. Nonlinear controllers for non-integrable systems: the acrobot example[A]. Proc of American Control Conference[C]. 1990. 669–671.Google Scholar
- Spong M W. The swing up control problem for the acrobot[J]. IEEE Trans Control Systems, 1995, 15: 49–55.Google Scholar
- Bortoff S A, Spong M W. Pseudolinearization of acrobot using spline functions[A]. Proc 31st IEEE Conf on Decision and Control[C]. 1992. 593–598.Google Scholar
- She Jinhua, Ohyama Y, Hirano K, et al. Motion control of acrobot using time-state control form[A]. Proc IASTED International Conference on Control and Applications[C]. 1998. 171–174.Google Scholar
- Smith M H, Lee M A, Uliea M, et al. Design limitation of PD versus fuzzy controllers for the acrobot[A]. Proc IEEE Int Conf on Robotics and Automation[C]. 1997. 1130–1135.Google Scholar
- Miyazaki M, Sampei M, Koga M, et al. A control of underactuated hopping gait systems: acrobot example [A]. Proc 39th IEEE Conference on Decision and Control[C]. 2000. 4797–4802.Google Scholar
- Schultz D G, Melsa J L. State Functions and Linear Control Systems[M]. McGraw-Hill Book Company, 1967.Google Scholar
- Yamada K, Yuzawa A. Approximate feedback linearization for nonlinear systems and its application to the acrobot[A]. Proc 2002 American Control Conference [C]. 2002. 1672–1677.Google Scholar