On the effects of time-delay on precision degradation in fixed point transformation-based adaptive control

Redjimi, Hemza; Tar, József K.

doi:10.1109/nc.2017.8263267

Cited by 20 publications

(4 citation statements)

References 20 publications

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“…Schematic structure of the "Fixed Point Transformation-based Adaptive Controller" after [19] (the adaptive deformation can be realized by the use of various fixed point transformations, and the system's response r can be an arbitrary order time-derivative of the generalized coordinates of the controlled system)…”

Section: Delay1mentioning

confidence: 99%

On the Implementation of Fixed Point Iteration-based Adaptive Receding Horizon Control for Multiple Degree of Freedom, Higher Order Dynamical Systems

Khan¹,

Tar²

2019

ACTA POLYTECH HUNG

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Based on the observation that it is very difficult to combine the mathematical frameworks of the prevailing Lyapunov function-based adaptive controllers and the traditional, optimal control-based "Model Predictive Controllers (MPC)", a novel adaptive solution was introduced to improve the operation of the "Receding Horizon Controllers (RHC)". Because at the local optima the gradient of the auxiliary function is zero, Lagrange's original "Reduced Gradient Method (RGM)" was replaced by a "Fixed Point Iteration (FPI)"-based algorithm that directly drove this gradient toward zero. According to "Banach's Fixed Point Theorem" the convergence of the method was guaranteed by a contractive function that generated the iterative sequence. The greatest modeling burden in this approach was the need for the calculation of the Jacobian of the problem, i.e. the gradient of the gradient of the auxiliary function. In the first simulations only a single "Degree of Freedom (DoF)" 2 nd order nonlinear system, a van der Pol oscillator was investigated. The attempts that were made to evade the calculation of the Jacobian were finished with the conclusion that at least a rough numerical approximation of this Jacobian generally must be utilized. Though the MPC approach allows the use a great variety of cost functions and dynamical models, mathematically well established results are available only for quadratic cost functions and "Linear Time-invariant (LTI)" models. For other cost functions and models careful numerical analysis is needed. In this paper the use of non-quadratic cost functions is numerically investigated in the FPI-based adaptive RHC control of 2 DoF 2 nd order nonlinear system that consists of two, nonlinearly coupled van der Pol oscillators, is considered. To guarantee lucid calculations simple functions are introduced that map the active parts of the horizon under consideration to the elements of the gradient of the auxiliary function that are calculated analytically. For the calculation of the Jacobian only a rough numerical estimation is applied. The simulation results reveal certain limitations of the suggested method.

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Section: Delay1mentioning

confidence: 99%

On the Implementation of Fixed Point Iteration-based Adaptive Receding Horizon Control for Multiple Degree of Freedom, Higher Order Dynamical Systems

Khan¹,

Tar²

2019

ACTA POLYTECH HUNG

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“…(A combination with the Lyapunov function-based adaptive approach would be far less plausible and simple.) In [49] the applicability of this approach was introduced into the control of systems with time-delay. The possibility of fractional order kinematic trajectory tracking prescription in the FPI-based adaptive control was studied, too [63].…”

Section: Robotics and Automation Engineering Journalmentioning

confidence: 99%

On the Alternatives of Lyapunov’s Direct Method in Adaptive Control Design

Tar

2018

RAEJ

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“…On the other hand, the delays introduced by the same sensors entail a degradation of the control actuation. As a consequence, the reduction of the gain of the controller is required not only to reduce the delay effect and its propagation through time, but also to avoid the instability of the control system [ 30 ]. To alleviate these effects, different denoising and delay correction approaches can be considered: (i) from the denoising filter-based solutions [ 31 , 32 ] to the data-based denoising techniques such as Principal Component Analysis [ 33 ] and Denoising Autoencoders (DAE) [ 34 ], and (ii) from forecasting algorithms and controllers to the application of ANNs [ 35 ].…”

Section: Introductionmentioning

confidence: 99%

Industrial Control under Non-Ideal Measurements: Data-Based Signal Processing as an Alternative to Controller Retuning

Pisa

Morell

Vilanova

et al. 2021

Sensors

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Industrial environments are characterised by the non-lineal and highly complex processes they perform. Different control strategies are considered to assure that these processes are correctly performed. Nevertheless, these strategies are sensible to noise-corrupted and delayed measurements. For that reason, denoising techniques and delay correction methodologies should be considered but, most of these techniques require a complex design and optimisation process as a function of the scenario where they are applied. To alleviate this, a complete data-based approach devoted to denoising and correcting the delay of measurements is proposed here with a two-fold objective: simplify the solution design process and achieve its decoupling from the considered control strategy as well as from the scenario. Here it corresponds to a Wastewater Treatment Plant (WWTP). However, the proposed solution can be adopted at any industrial environment since neither an optimization nor a design focused on the scenario is required, only pairs of input and output data. Results show that a minimum Root Mean Squared Error (RMSE) improvement of a 63.87% is achieved when the new proposed data-based denoising approach is considered. In addition, the whole system performance show that similar and even better results are obtained when compared to scenario-optimised methodologies.

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On the effects of time-delay on precision degradation in fixed point transformation-based adaptive control

Cited by 20 publications

References 20 publications

On the Implementation of Fixed Point Iteration-based Adaptive Receding Horizon Control for Multiple Degree of Freedom, Higher Order Dynamical Systems

On the Implementation of Fixed Point Iteration-based Adaptive Receding Horizon Control for Multiple Degree of Freedom, Higher Order Dynamical Systems

On the Alternatives of Lyapunov’s Direct Method in Adaptive Control Design

Industrial Control under Non-Ideal Measurements: Data-Based Signal Processing as an Alternative to Controller Retuning

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