arXiv subjects

S. Hassan HosseinNia

Publications and source records attributed to S. Hassan HosseinNia.

At least 37 records · Page 2Linked to original sources

arXiv2021

Stacking Integrators Without Sacrificing the Overshoot in Reset Control Systems

According to the well-known loop-shaping control design approach, the steady-state precision of control systems can be improved by stacking integrators. However, due to the waterbed effect in linear control systems, such an action will worsen the transient response by increasing overshoot and creating wind-up problems. This paper presents a new architecture for rest control systems that can significantly decrease the overshoot and create a no-overshoot performance even in presence of stacked integrators. The steady-state analysis of the proposed system will also show that improved precision expected due to stacked integrators can be achieved as well. A numerical simulation study is presented to verify the results and the tuning guide presented.

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arXiv2020

Closed-Loop Frequency Analysis of Reset Control Systems

This paper introduces a closed-loop frequency analysis tool for reset control systems. To begin with sufficient conditions for the existence of the steady-state response for a closed-loop system with a reset element and driven by periodic references are provided. It is then shown that, under specific conditions, such a steady-state response for periodic inputs is periodic with the same period as the input. Furthermore, a framework to obtain the steady-state response and to define a notion of closed-loop frequency response, including high order harmonics, is presented. Finally, pseudo-sensitivities for reset control systems are defined. These simplify the analysis of this class of systems and allow a direct software implementation of the analysis tool. To show the effectiveness of the proposed analysis method the position control problem for a precision positioning stage is studied. In particular, comparison with the results achieved using methods based on the Describing Function shows that the proposed method achieves superior closed-loop performance.

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arXiv2020

Adaptive Feedforward Control For Reset Feedback Control Systems -- Application in Precision Motion Control

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.

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arXiv2020

Reset band for mitigatation of quantization induced performance degradation

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.

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arXiv2020

Time regularization as a solution to mitigate quantization induced performance degradation

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.

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arXiv2020

Fractional-Order Single State Reset Element

This paper proposes a fractional-order reset element whose architecture allows for the suppression of nonlinear effects for a range of frequencies. Suppressing the nonlinear effects of a reset element for the desired frequency range while maintaining it for the rest is beneficial, especially when it is used in the framework of a "Constant in gain, Lead in phase" (CgLp) filter. CgLp is a newly introduced nonlinear filter, bound to circumvent the well-known linear control limitation -- the waterbed effect. The ideal behaviour of such a filter in the frequency domain is unity gain while providing a phase lead for a broad range of frequencies. However, CgLp's ideal behaviour is based on the describing function, which is a first-order approximation that neglects the effects of the higher-order harmonics in the output of the filter. Although CgLp is fundamentally a nonlinear filter, its nonlinearity is not required for all frequencies. Thus, it is shown in this paper that using the proposed reset element architecture, CgLp gets closer to its ideal behaviour for a range of frequencies, and its performance will be improved accordingly.

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arXiv2020

Band-Passing Nonlinearity in Reset Elements

This paper addresses nonlinearity in reset elements and their effects. Reset elements are known for having less phase lag compared to their linear counterparts; however, they are nonlinear elements and produce higher-order harmonics. This paper investigates the higher-order harmonics for reset elements with one resetting state and proposes an architecture and a method of design which allows for band-passing the nonlinearity and its effects, namely, higher-order harmonics and phase advantage. The nonlinearity of reset elements is not entirely useful for all frequencies, e.g., they are useful for reducing phase lag at cross-over frequency region; however, higher-order harmonics can compromise tracking and disturbance rejection performance at lower frequencies. Using proposed "phase shaping" method, one can selectively suppress nonlinearity of a single-state reset element in a desired range of frequencies and allow the nonlinearity to provide its phase benefit in a different desired range of frequencies. This can be especially useful for the reset elements in the framework of "Constant in gain, Lead in phase" (CgLp) filter, which is a newly introduced nonlinear filter, bound to circumvent the well-known linear control limitation -- the waterbed effect.

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arXiv2020

Loop-shaping for reset control systems -- A higher-order sinusoidal-input describing functions approach

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.

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arXiv2020

Tuning of CgLp based reset controllers: Application in precision positioning systems

This paper presents the tuning of a reset-based element called "Constant in gain and Lead in phase" (CgLp) in order to achieve desired precision performance in tracking and steady state. CgLp has been recently introduced to overcome the inherent linear control limitation - the waterbed effect. The analysis of reset controllers including ones based on CgLp is mainly carried out in the frequency domain using describing function with the assumption that the relatively large magnitude of the first harmonic provides a good approximation. While this is true for several cases, the existence of higher-order harmonics in the output of these elements complicates their analysis and tuning in the control design process for high precision motion applications, where they cannot be neglected. While some numerical observation-based approaches have been considered in literature for the tuning of CgLp elements, a systematic approach based on the analysis of higher-order harmonics is found to be lacking. This paper analyzes the CgLp behaviour from the perspective of first as well as higher-order harmonics and presents simple relations between the tuning parameters and the gain-phase behaviour of all the harmonics, which can be used for better tuning of these elements. The presented relations are used for tuning a controller for a high-precision positioning stage and results used for validation.

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arXiv2020

A Frequency-Domain Stability Method for Reset Systems

Nowadays, the demand for an alternative to linear PID controllers has increased because of the rising expectations of the high-precision industry. The potential of reset controllers to solve this important challenge has been extensively demonstrated in the literature. However, similarly to other non-linear controllers, the stability analysis for these controllers is complex and relies on parametric models of the systems which may hinder the applicability of these controllers in industry. The well-known Hbeta method tries to solve this significant issue. However, assessing the H\b{eta} condition in the frequency-domain is complex, especially for high dimensional plants. In addition, it cannot be used to assess UBIBS stability of reset control systems in the case of reseting to non-zero values. These problems have been solved in this paper for the first order reset elements, and an easy-to-use frequency approach for assessing stability of reset control systems is proposed. The effectiveness of the proposed approach is demonstrated through a practical example.

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arXiv2020

Benefiting from Linear Behaviour of a Nonlinear Reset-based Element at Certain Frequencies

This paper addresses a phenomenon caused by resetting only one of the two states of a so-called second order "Constant in gain Lead in phase" (CgLp) element. CgLp is a recently introduced reset-based nonlinear element, bound to circumvent the well-known linear control limitation -- the waterbed effect. The ideal behaviour of such a filter in the frequency domain is unity gain while providing a phase lead for a broad range of frequencies, which clearly violates the linear Bode's gain phase relationship. However, CgLp's ideal behaviour is based on a describing function, which is a first order approximation that neglects the effects of higher order harmonics in the output of the filter. Consequently, achieving the ideal behaviour is challenging when higher order harmonics are relatively large. It is shown in this paper that by resetting only one of the two states of a second order CgLp, the nonlinear filter will act as a linear one at a certain frequency, provided that some conditions are met. This phenomenon can be used to the benefit of reducing higher order harmonics of CgLp's output and achieving the ideal behaviour and thus better performance in terms of precision.

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arXiv2019

Development of Robust Fractional-Order Reset Control

In this paper, a framework for the combination of robust fractional order CRONE control with non-linear reset is given for both first and second generation CRONE control. General design rules are derived and presented for these CRONE reset controllers. Within this framework, fractional order control allows for better tuning of the open-loop responses on the one hand. On the other, reset control enables a reduction in phase lag and a corresponding increase in phase margin compared to linear control for similar open loop gain profile. Hence, the combination of the two control methods can provide well-tuned open-loop responses that can overcome the fundamental linear control limitation of Bode's gain-phase relationship. Moreover, as established loop-shaping concepts are used in the controller design, CRONE reset can be highly compatible with the industry. The designed CRONE reset controllers are validated on a one degree-of-freedom Lorentz-actuated precision positioning stage. On this setup, CRONE reset control is shown to provide better tracking performance compared to linear CRONE control, which is in agreement with the predicted performance improvement.

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arXiv2019

Complex order control for improved loop-shaping in precision positioning

This paper presents a complex order filter developed and subsequently integrated into a PID-based controller design. The nonlinear filter is designed with reset elements to have describing function based frequency response similar to that of a linear (practically non-implementable) complex order filter. This allows for a design which has a negative gain slope and a corresponding positive phase slope as desired from a loop-shaping controller-design perspective. This approach enables improvement in precision tracking without compromising the bandwidth or stability requirements. The proposed designs are tested on a planar precision positioning stage and performance compared with PID and other state-of-the-art reset based controllers to showcase the advantages of this filter.

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arXiv2019

Reset Control for Vibration Disturbance Rejection

The high tech industry which requires fast stable motion with nanometer precision continues to mainly use PID which is limited by fundamental linear control limitations. Floor vibrations as disturbance significantly affect performance and their rejection is particularly affected by these limitations. Reset control has provided a promising alternative to surpass these, while simultaneously allowing the use of industry standard loop-shaping during design. However, the reset action introduced higher order harmonics can induce unwanted dynamics and negatively influence performance. This paper investigates two reset control strategies namely (1) band-pass phase lag reduction and (2) phase compensation to reduce the negative effects of higher order harmonics. The strategies are tested on a precision positioning stage for vibration rejection and the results show that phase compensation provides better performance compared to other tested strategies.

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arXiv2018

'Constant in gain Lead in phase' element - Application in precision motion control

This work presents a novel 'Constant in gain Lead in phase' (CgLp) element using nonlinear reset technique. PID is the industrial workhorse even to this day in high-tech precision positioning applications. However, Bode's gain phase relationship and waterbed effect fundamentally limit performance of PID and other linear controllers. This paper presents CgLp as a controlled nonlinear element which can be introduced within the framework of PID allowing for wide applicability and overcoming linear control limitations. Design of CgLp with generalized first order reset element (GFORE) and generalized second order reset element (GSORE) (introduced in this work) is presented using describing function analysis. A more detailed analysis of reset elements in frequency domain compared to existing literature is first carried out for this purpose. Finally, CgLp is integrated with PID and tested on one of the DOFs of a planar precision positioning stage. Performance improvement is shown in terms of tracking, steady-state precision and bandwidth.

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arXiv2018

Resetting Disturbance Observers with application in Compensation of bounded nonlinearities like Hysteresis in Piezo-Actuators

This paper presents a novel nonlinear (reset) disturbance observer for dynamic compensation of bounded nonlinearities like hysteresis in piezoelectric actuators. Proposed Resetting Disturbance Observer (RDOB) utilizes a novel Constant-gain Lead-phase (CgLp) element based on the concept of reset control. The fundamental limitations of linear DOB which results in contradictory requirements and in a dependent design between DOB and feedback controller are analysed. Two different configurations of RDOB which attempt to alleviate these problems from different perspectives are presented and an example plant is used to highlight the improvement. Stability criteria are presented for both configurations. Performance improvement seen with both RDOB configurations compared to linear DOB is also verified on a practical piezoelectric setup for hysteresis compensation and results analysed.

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arXiv2018

Beyond the Waterbed Effect: Development of Fractional Order CRONE Control with Non-Linear Reset

In this paper a novel reset control synthesis method is proposed: CRONE reset control, combining a robust fractional CRONE controller with non-linear reset control to overcome waterbed effect. In CRONE control, robustness is achieved by creation of constant phase behaviour around bandwidth with the use of fractional operators, also allowing more freedom in shaping the open-loop frequency response. However, being a linear controller it suffers from the inevitable trade-off between robustness and performance as a result of the waterbed effect. Here reset control is introduced in the CRONE design to overcome the fundamental limitations. In the new controller design, reset phase advantage is approximated using describing function analysis and used to achieve better open-loop shape. Sufficient quadratic stability conditions are shown for the designed CRONE reset controllers and the control design is validated on a Lorentz-actuated nanometre precision stage. It is shown that for similar phase margin, better performance in terms of reference-tracking and noise attenuation can be achieved.

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arXiv2018

No More Differentiator in PID:Development of Nonlinear Lead for Precision Mechatronics

Industrial PID consists of three elements: Lag (integrator), Lead (Differentiator) and Low Pass Filters (LPF). PID being a linear control method is inherently bounded by the waterbed effect due to which there exists a trade-off between precision \& tracking, provided by Lag and LPF on one side and stability \& robustness, provided by Lead on the other side. Nonlinear reset strategies applied in Lag and LPF elements have been very effective in reducing this trade-off. However, there is lack of study in developing a reset Lead element. In this paper, we develop a novel lead element which provides higher precision and stability compared to the linear lead filter and can be used as a replacement for the same. The concept is presented and validated on a Lorentz-actuated nanometer precision stage. Improvements in precision, tracking and bandwidth are shown through two separate designs. Performance is validated in both time and frequency domain to ensure that phase margin achieved on the practical setup matches design theories.

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