Sliding Mode Based Robust Control Design Framework for Underactuated Mechanical Systems


Underactuated mechanical systems have increasing number of practical applications, theoretical importance as nonlinear benchmark systems, and obvious advantages such as low cost and low weight. However, complex nonlinear behavior makes the control design problem a difficult task and the presence of uncertainties makes it further challenging. Hence, enhanced performance and robustness to uncertainties become critical issues in designing control for these systems. Increasing practical applications and theoretical importance, make the design of a comprehensive robust control framework for underactuated mechanical systems an important problem. The explicit consideration of uncertainties in the design framework and its capabilities to effectively control the highly nonlinear dynamics will enhance the advantages of these systems. SMC techniques remain the only nonlinear control techniques that can better achieves these objectives. In this research work, the author proposes a sliding mode based robust control design framework for underactuated mechanical systems. The framework is comprehensive applicable to classes of systems in a unified but simply-to-apply way. The framework is built on three sliding mode design solutions to the problem. First, a standard SMC design is proposed for underactuated mechanical systems. The control laws take explicitly into account both the matched and unmatched uncertainties. Generic expressions for the sliding mode dynamics are derived. Analytic expressions for the sliding parameters are also given which characterize the desired performance. The main results are general and based on the EulerLagrange representation of these systems. Moreover, the discontinuous terms explicitly embedded in the control for the rejection of matched and unmatched uncertainties provide a better insight and understanding into the complex nature of uncertainties in these systems. Second, to address the chattering associated with standard SMC, the author proposes the use of super-twisting algorithm for underactuated mechanical systems. This treatment is based on linear sliding mode surfaces and use some the results derived for the standard SMC.

Third, novel nonlinear sliding manifolds based on the Lagrangian zero dynamics are proposed for underactuated mechanical systems. The application of smooth higher order sliding mode control is proposed to enforce sliding mode in the manifold that guarantees stability of the overall dynamics of the system. The relative degree of these systems, in general, is not 1, and hence, leaving the designer with the choice of using higher order sliding mode control. The proposed design framework remarkably simplifies the control design problem of underactuated mechanical systems. Finally, the nature of dynamics and singularities are hurdles in the global convergence of some underactuated mechanical systems. To overcome these hurdles, the author address the swingup control problems of these systems in a classical way and demonstrate successful swingup and balancing using the proposed higher order sliding mode control.

The proposed control design framework is validated for the following benchmark underactuated mechanical systems and achieve enhanced performance with the added advantage of remarkable robustness to uncertainties.

  1. The Inertia-Wheel Pendulum
  2. The Translational Oscillator with Rotational Actuator
  3. The Acrobot
  4. The Furuta Pendulum
  5. The Overhead Crane
  6. The Cart-Pole System
  7. The Pendubot
  8. The Beam-and-Ball System

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