• Journal of Institute of Control, Robotics and Systems
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• v.14 no.12
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• pp.1270-1277
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• 2008

A Haar wavelet based numerical method for solving singularly perturbed linear time invariant system is presented in this paper. The reduced pure slow and pure fast subsystems are obtained by decoupling the singularly perturbed system and differential matrix equations are converted into algebraic Sylvester matrix equations via Haar wavelet technique. The operational matrix of integration and its inverse matrix are utilized to reduce the computational time to the solution of algebraic matrix equations. Finally a numerical example is given to demonstrate the validity and applicability of the proposed method.

• International Journal of Control, Automation, and Systems
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• v.5 no.5
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• pp.547-558
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• 2007

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.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.32 no.5
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• pp.58-64
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• 2004

A new method to obtain approximate solutions by placing the only poles of the slow subsystem for the two-time-scale aircraft dynamic systems. The two kinds of approximate solutions are obtained by a matrix block diagonalization. One is called the uncorrected solution, and the other is called the corrected solution. The former has an error of $O({\varepsilon})$, and the latter has an error of $O({\varepsilon}^2)$. Of course, both solutions are robust enough even though they are reduced solutions. The excellence of the proposed method is illustrated by an numerical example of an aircraft longitudinal dynamics.