Title:Some Studies on Two-degree-of-freedom Inversion-based Adaptive Control for Time-delay Systems
Volume: 18
Author(s): Santanu Mallick*Ujjwal Mondal
Affiliation:
- Department of Applied Electronics & Instrumentation Engineering, Bankura Unnayani Institute of Engineering,
Bankura, 722146, India
Keywords:
Feedforward control, model reference adaptive control, non-minimum phase, proportional integral derivative, pole placement method, two-degree-of-freedom.
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 twodegree-
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.
