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Appears in Collections:Computing Science and Mathematics Journal Articles
Peer Review Status: Refereed
Title: Exponential stabilization of a class of underactuated mechanical systems using dynamic surface control
Author(s): Qaiser, Nadeem
Iqbal, Naeem
Hussain, Amir
Qaiser, Naeem
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Keywords: dynamic surface control
integrator backstepping
nonlinear control
underactuated mechanical systems
Issue Date: Oct-2007
Date Deposited: 27-Aug-2013
Citation: Qaiser N, Iqbal N, Hussain A & Qaiser N (2007) Exponential stabilization of a class of underactuated mechanical systems using dynamic surface control. International Journal of Control, Automation and Systems, 5 (5), pp. 547-558.
Abstract: This paper proposes a simpler solution to the stabilization problem of a special class of nonlinear underactuated mechanical systems which includes widely studied benchmark systems like Inertia Wheel Pendulum, TORA and Acrobot. Complex internal dynamics and lack of exact feedback linearizibility of these systems makes design of control law a challenging task. Stabilization of these systems has been achieved using Energy Shaping and damping injection and Backstepping technique. Former results in hybrid or switching architectures that make stability analysis complicated whereas use of backstepping some times requires closed form explicit solutions of highly nonlinear equations resulting from partial feedback linearization. It also exhibits the phenomenon of explosions of terms resulting in a highly complicated control law. Exploiting recently introduced Dynamic Surface Control technique and using control Lyapunov function method, a novel nonlinear controller design is presented as a solution to these problems. The stability of the closed loop system is analyzed by exploiting its two-time scale nature and applying concepts from Singular Perturbation Theory. The design procedure is shown to be simpler and more intuitive than existing designs. Design has been applied to important benchmark systems belonging to the class demonstrating controller design simplicity. Advantages over conventional Energy Shaping and Backstepping controllers are analyzed theoretically and performance is verified using numerical simulations.
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