S. Hassan HosseinNia

S. Hassan HosseinNia, Inés Tejado, Blas M Vinagre

Reset control is introduced to overcome limitations of linear control. A reset controller includes a linear controller which resets some of states to zero when their input is zero or certain non-zero values. This paper studies the application of the fractional-order Clegg integrator (FCI) and compares its performance with both the commonly used first order reset element (FORE) and traditional Clegg integrator (CI). Moreover, stability of reset control systems is generalized for the fractional-order case. Two examples are given to illustrate the application of the stability theorem.

S. Hassan HosseinNia, Ines Tejado, Blas M. Vinagre

No mixed research of hybrid and fractional-order systems into a cohesive and multifaceted whole can be found in the literature. This paper focuses on such a synergistic approach of the theories of both branches, which is believed to give additional flexibility and help the system designer. It is part II of two companion papers and focuses on fractional-order hybrid control. Specifically, two types of such techniques are reviewed, including robust control of switching systems and different strategies of reset control. Simulations and experimental results are given to show the effectiveness of the proposed strategies. Part I will introduce the fundamentals of fractional-order hybrid systems, in particular, modelling and stability of two kinds of such systems, i.e., fractional-order switching and reset control systems.

S. Hassan HosseinNia, Ines Tejado, Blas M. Vinagre

No mixed research of hybrid and fractional-order systems into a cohesive and multifaceted whole can be found in the literature. This paper focuses on such a synergistic approach of the theories of both branches, which is believed to give additional flexibility and help to the system designer. It is part I of two companion papers and introduces the fundamentals of fractional-order hybrid systems, in particular, modeling and stability analysis of two kinds of such systems, i.e., fractional-order switching and reset control systems. Some examples are given to illustrate the applicability and effectiveness of the developed theory. Part II will focus on fractional-order hybrid control.

S. Hassan HosseinNia, Inés Tejado, Blas M. Vinagre

This paper deals with hybrid systems (HS) with fractional order dynamics and their stability. The stability of two particular types of fractional order hybrid systems (FOHS), i.e., switching and reset control systems, is studied. Common Lyapunov method, as well as its frequency domain equivalence, are generalized for the former systems and, for the latter, H$_β$-condition is used --frequency domain equivalence of Lyapunov-like method for reset control systems. The applicability and efficiency of the proposed methods are shown by some illustrative examples.

Bas Kieft, S. Hassan HosseinNia, Niranjan Saikumar

Reset control is known to be able to outperform PID and the like linear controllers. However, in motion control systems, quantization can cause severe performance degradation. This paper shows the application of time regularization to mitigate this practical issue in reset control systems. Numerical simulations have been conducted in order to analyze the cause of the quantization induced performance degradation and the effectiveness of time regularization to mitigate this degradation; with tuning guidelines for the time regularization parameter also provided. Moreover, a robustness analysis is performed. The solution is also tested experimentally on a high precision motion system for validation. It is estimated by numerical simulations that time regularization can reduce quantization induced performance degradation by almost 10 dB. Experiments have similarly shown a reduction of several dB for the high precision motion stage.

Bas Kieft, S. Hassan HosseinNia, Niranjan Saikumar

Reset control has emerged as a viable alternative to popular PID, capable of outperforming and overcoming the linear limitations. However, in motion control systems, quantization can cause severe performance degradation. This paper investigates this degradation in practical systems and re-purposes the reset band condition in order to mitigate the same. Numerical simulations have been conducted on a mass based positioning system to analyze the cause of the quantization induced performance degradation. Moreover, a performance and robustness analysis was performed with the proposed solution. Finally, novel tuning guidelines are provided for estimating the required reset band parameter. Additionally, practical experiments have been conducted on a high precision motion system for validation. The experiments show by example that the reset band can reduce the error in the problematic region by up to 285% and hence shows the need and effectiveness of the proposed solution.

Karst Brummelhuis, Niranjan Saikumar, Jan-Willem van Wingerden et al.

This paper presents a novel adaptive feedforward controller design for reset control systems. The combination of feedforward and reset feedback control promises high performance as the feedforward guarantees reference tracking, while the non-linear feedback element rejects disturbances. To overcome inevitable model mismatches, the feedforward controller adapts to increase precision in reference tracking. Where linear existing adaptive feedforward controllers do not guarantee convergence in the presence of reset, this work presents a novel adaptive law based on converging and diverging regions of adaptation to achieve good tracking. Experimental results demonstrate the claimed advantage of the novel method.

R. N. Buitenhuis, N. Saikumar, S. H. HosseinNia

The ever-increasing industry desire for improved performance makes linear controller design run into fundamental limitations. Nonlinear control methods such as Reset Control (RC) are needed to overcome these. RC is a promising candidate since, unlike other nonlinear methods, it easily integrates into the industry-preferred PID design framework. Thus far, RC has been analysed in the frequency domain either through describing function analysis or by direct closed-loop numerical computation. The former computes a simplified closed-loop RC response by assuming a sufficient low-pass behaviour. In doing so it ignores all harmonics, which literature has found to cause significant modelling prediction errors. The latter gives a precise solution, but by its direct closed-loop computation does not clearly show how open-loop RC design translates to closed-loop performance. The main contribution of this work is aimed at overcoming these limitations by considering an alternative approach for modelling RC using state-dependent impulse inputs. This permits accurately computing closed-loop RC behaviour starting from the underlying linear system, improving system understanding. A frequency-domain description for closed-loop RC is obtained, which is solved analytically by using several well-defined assumptions. This analytical solution is verified using a simulated high-precision stage, critically examining sources of modelling errors. The accuracy of the proposed method is further substantiated using controllers designed for various specifications.

Niranjan Saikumar, Kars Heinen, S. Hassan HosseinNia

The ever-growing demands on speed and precision from the precision motion industry have pushed control requirements to reach the limitations of linear control theory. Nonlinear controllers like reset provide a viable alternative since they can be easily integrated into the existing linear controller structure and designed using industry-preferred loop-shaping techniques. However, currently, loop-shaping is achieved using the describing function (DF) and performance analysed using linear control sensitivity functions not applicable for reset control systems, resulting in a significant deviation between expected and practical results. We overcome this major bottleneck to the wider adaptation of reset control with two contributions in this paper. First, we present the extension of frequency-domain tools for reset controllers in the form of higher-order sinusoidal-input describing functions (HOSIDFs) providing greater insight into their behaviour. Second, we propose a novel method which uses the DF and HOSIDFs of the open-loop reset control system for the estimation of the closed-loop sensitivity functions, establishing for the first time - the relation between open-loop and closed-loop behaviour of reset control systems in the frequency domain. The accuracy of the proposed solution is verified in both simulation and practice on a precision positioning stage and these results are further analysed to obtain insights into the tuning considerations for reset controllers.

H. Delavari, R. Ghaderi, N. A. Ranjbar et al.

A Fractional adaptive PID (FPID) controller for a robot manipulator will be proposed. The PID parameters have been optimized by Genetic algorithm. The proposed controller is found robust by means of simulation in a tracking job. The validity of the proposed controller is shown by simulation of two-link robot manipulator. The result then is compared with integer type adaptive PID controller. It is found that when error signals in the learning stage are bounded, the trajectory of the robot converges to the desired one asymptotically.