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U-Model-Based Dynamic Inversion Control for a Class of Nonlinear Dynamical Systems

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Iranian Journal of Science and Technology, Transactions A: Science Aims and scope Submit manuscript

Abstract

Different types of techniques such as state-space linearization method and state-dependent parameter method are available for designing a control system of nonlinear plant although a little bit disadvantages generally occur. This paper deals with the adaptive controller which is based on recently developed U-Model-based control that has contributed a generic approach for modeling and controlling of various complicated systems. U-Model works with less number of parameters and variables, resulting a simple model configuration and applied to both linear and nonlinear dynamical systems. The single inverted pendulum on a cart being an unstable, nonlinear system is popularly applied as a benchmark for designing different control methodologies. Here, the control objective of this proposed work is to control the system in such a way that when the cart reaches the desired position, this inverted pendulum is balanced in an upright position with a particular angle, for achieving the aforementioned goal this paper has proposed U-Model dynamic inversion control, U-Model-based Model Reference Adaptive Control technique with Massachusetts Institute of Technology rule, Feedback linearization-based dynamic inversion technique and different Model Reference Adaptive Control methodologies. The novel contribution of the proposed work is to implement U-Model-based dynamic inversion technique where the inversion of the closed loop is performed for the development of the invariant controller, and ultimately, the necessity of solving complex diophantine equation is avoided. The MATLAB Simulink environment is applied for simulation of the proposed technique for determining the system performance.

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Authors and Affiliations

  1. Department of Applied Electronics and Instrumentation Engineering, Bankura Unnayani Institute of Engineering, Bankura, 722146, India

    Santanu Mallick

  2. Instrumentation Engineering, Department of Applied Physics, University of Calcutta, Kolkata, 700009, India

    Ujjwal Mondal

Authors
  1. Santanu Mallick
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  2. Ujjwal Mondal
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Contributions

The submitted paper has expressed U-Model-based Dynamic Inversion, U-Model-based MRAC technique with MIT rule, Feedback linearization-based Dynamic Inversion, MRAC methodology employing MIT rule, MRAC employing Lyapunov stability method and MRAC augmented with PID applied to a single inverted pendulum. In the proposed work paper, the authors have contributed to the implementation of U-Model-based Dynamic Inversion technique where the inversion of closed loop is performed for development of the Invariant controller, and ultimately, the necessity of solving complex Diophantine equation is avoided. Time domain analysis of single inverted pendulum with U-model-based dynamic inversion control is also being shown with proper comparison with U-model-based MRAC technique with MIT rule, DI, MRAC using MIT rule, MRAC using Lyapunov stability method and MRAC augmented with PID. Effectiveness of U-model-based dynamic inversion controller is justified with proper mathematical basis in terms of tracking performance compared to the following control techniques (U-model-based MRAC technique with MIT rule, DI, MRAC using MIT rule, MRAC using Lyapunov stability method and MRAC augmented with PID) for unit step reference input.

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Correspondence to Santanu Mallick.

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Mallick, S., Mondal, U. U-Model-Based Dynamic Inversion Control for a Class of Nonlinear Dynamical Systems. Iran J Sci Technol Trans Sci 46, 475–490 (2022). https://doi.org/10.1007/s40995-022-01261-1

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  • DOI: https://doi.org/10.1007/s40995-022-01261-1

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