Some Studies on Two-degree-of-freedom Inversion-based Adaptive Control for Time-delay Systems

Santanu Mallick; Ujjwal Mondal

doi:10.2174/0123520965245114231005062309

ISSN: 2352-0965
E-ISSN: 2352-0973

Some Studies on Two-degree-of-freedom Inversion-based Adaptive Control for Time-delay Systems
Authors: Santanu Mallick¹ and Ujjwal Mondal²
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¹ Department of Applied Electronics & Instrumentation Engineering, Bankura Unnayani Institute of Engineering, Bankura, 722146, India; ² Instrumentation Engineering, Department of Applied Physics, University of Calcutta, Kolkata, 700009, India
Source: Recent Advances in Electrical & Electronic Engineering, Volume 18, Issue 10, Dec 2025, p. 1879 - 1890
DOI: https://doi.org/10.2174/0123520965245114231005062309
- Received: 03 Mar 2023
- Accepted: 05 Sep 2023
- Available online: 26 May 2025

Abstract

Background

Adaptive controller has contributed to a generic approach for modeling and controlling various complicated systems. In the non-minimum phase (NMP) system, inversion-based feedforward tracking is not achievable, as its inverse transfer model is unstable. To overcome the set point tracking problem of the non-minimum phase system, model reference adaptive control is used as inversion-based feedforward control, and state feedback is used as feedback control in the two-degree-of-freedom (TDOF) structure. Here, the model reference adaptive control (MRAC) scheme is used for obtaining the desired response of the system with a small steady-state error, whereas the state feedback technique provides stabilization of the system. The presence of a delay in the transfer function turns the system into a non-minimum phase system. The time-delay system is widely applied as a benchmark for designing different control methodologies.

Aims

In this study, a two-degree-of-freedom inversion-based model reference adaptive control for a time-delay system was implemented.

Objective

A two-degree-of-freedom inversion-based model reference adaptive control for a class of time-delay systems was implemented so that the system could track the reference input. Moreover, it also provided stability to the given system.

Methods

Different techniques, such as two-degree-of-freedom inversion-based model reference adaptive control, Proportional Integral Derivative (PID) control, and (FOPID) control, were discussed for the stabilization of a class of time-delay systems. Here, an inversion-based model reference adaptive control structure with rules of the Massachusetts Institute of Technology (MIT), along with a state feedback control technique, was applied for the delay system so that the system could track the reference input.

Results

By the analysis of different techniques, it was observed that the combined form of MRAC and state feedback control scheme was able to provide a suitable tracking response. Here, the unit step signal was used as the reference input. In a time-delay system, an initial undershoot was observed; however, using a two-degree-of-freedom inversion-based MRAC technique, the initial undershoot was almost nullified. The two-degree-of-freedom technique was also found to provide a better tracking response compared to PID control and (FOPID) control technique, as also elaborated in this study.

Conclusion

The results of the simulation using MATLAB indicated that the proposed two-degree-of-freedom inversion-based adaptive control technique provides a better tracking response compared to PID control and fractional order PID control. However, for the stabilization of time-delay systems, other methodologies may be implemented.

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/content/journals/raeeng/10.2174/0123520965245114231005062309

Some Studies on Two-degree-of-freedom Inversion-based Adaptive Control for Time-delay Systems

Recent Advances in Electrical & Electronic Engineering 18, 1879 (2025); https://doi.org/10.2174/0123520965245114231005062309

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Article Type: Research Article

Keyword(s): Feedforward control; model reference adaptive control; non-minimum phase; pole placement method; proportional integral derivative; two-degree-of-freedom

Some Studies on Two-degree-of-freedom Inversion-based Adaptive Control for Time-delay Systems

Abstract

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