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The most widely applied feedback controller is PID. This controller gains its popularity because of the ease of design through loop shaping, since PID can be analyzed in the frequency domain. However, PID is limited by linearity. Reset control is a nonlinear addition to PID control. Through linearization techniques it can be designed by analyzing the frequency domain. Through numerous numerical, analytical and practical experiments it has been shown that reset control can outperformPID. However, when practically implementing reset control, especially in motion stages, one aspect can cause severe performance degradation. Research is underrepresented in this field. Quantization can be described as discretization in the amplitude. This thesis aims to reduce the quantization induced performance degradation. Two methods are proposed: reset band and time regularization. Numerical analysis and practical experiments have been performed in order to analyze the performance degradation and proposed methods. Through the numerical analysis in matlab simulink of a mass system the performance degradation has clearly been addressed. Based on the new understanding tuning rules have been provided for both proposed methods. A preliminary sensitivity analysis shows the robustness of both methods. Both proposed methods show enhanced performance. In numerical analysis it was shown that the reset band solution and time regularization can achieve an improvement of up to 10 dB. It was shown through experiments on a high level motion stage that several dB improvement is feasible. For the reset band at a specifically detrimental frequency the error was reduced from 200 nm to 70 nm. The reset band shows an improvement of several dB. In one setup, the performance enhancement spanned a wide frequency range. Overall it is concluded that for quantization induced performance degradation both proposed methods clearly show improvement. Two novel applications of existing methods have shown an increase in performance. New tuning guidelines have been provided.

CLOC

Mechanical Engineering | Mechatronic System Design (MSD)

Advisors/Committee Members: Hassan HosseinNia, S. (mentor), Saikumar, Niranjan (graduation committee), Delft University of Technology (degree granting institution).

▼ PID is the most commonly used technique in industrial motion control. It consists of three components - lead, lag and low pass filter (LPF). PID, being a linear control method is inherently bounded by waterbed effect due to which there exists a trade-off between precision, tracking, and stability. Reset control is a nonlinear technique which shows promise in overcoming certain limitations. Despite the promise shown, the use of reset elements other than integrator within the framework of PID for improved performance has not been well investigated. This thesis work focuses on implementing reset in lead part and in LPF in order to reduce the severity of the waterbed effect in PID. Three controllers have been developed that provide improvements in bandwidth, precision, and tracking. The controllers were implemented in a Lorentz-actuated nanometer precision stage and the performance has been validated in both time and frequency domain. Advisors/Committee Members: Hossein Nia Kani, Hassan (mentor), Saikumar, Niranjan (graduation committee), Delft University of Technology (degree granting institution).

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Floor vibrations are a common problem in high tech engineering where good tracking, precision and bandwidth have utmost importance. They are mainly present at low frequencies, and they need to be suppressed. PID control is the go-to controller in the industry because of its ease of design, simple implementation and good performance. However, PID is subjected to the fundamental limitations of linear control theory - the waterbed effect and bode's gain-phase relationship. Therefore, it is not possible to improve one performance criterion, like stability, without negatively influencing the other. The need for overcoming the fundamental limitations of linear control initiates research towards nonlinear controllers. Reset control is a type of nonlinear controller as a solution to overcome the limitations of a linear control. It reduces phase lag within the system, gives the advantage to reach higher bandwidth and results in lower overshoot or a faster settling time compared to linear controllers. However, using reset control comes with a price of unwanted dynamics due to the higher order harmonics. The main focus of this thesis is to improve disturbance rejection performance against floor vibrations by attenuating the power of high order harmonics. This problem has been tackled within the thesis, and a band-pass reset control is proposed. Proposed reset controller applies reset only within the frequency range where floor vibrations are present, and it uses integrator as a reset variable. Results show reset controller that has a broadband phase compensation, like CgLp, is more advantageous towards phase lag reduction methods. CgLp is a reset element, which is an abbreviation of Constant-Gain Lead Phase. It gives broadband phase compensation within the desired range of frequencies by using generalized first order reset element. Also, CgLp controller achieved disturbance rejection performance of PIsuperscript{2}D with the phase behavior of Clegg.

Mechatronic System Design

Advisors/Committee Members: Hossein Nia Kani, Hassan (mentor), Saikumar, Niranjan (mentor), Delft University of Technology (degree granting institution).

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Reset control is a "simple" nonlinear control strategy that has the potential of being widely adopted and improving the performance of systems traditionally controlled with PIDs. Lack of suitable methods for proving stability, that are in line with the current industrial practice, hampers the wider acceptance of reset control. In this thesis, novel sufficient conditions for stability of reset control systems, that can be evaluated using measured frequency response function of a system to be controlled, are derived using the hybrid passivity and finite-gain framework. A method for analysing the hybrid passivity and finite-gain parameters of reset systems, that can be extended to other classes of nonlinear systems, is developed. Additionally, a variant of the “Constant in Gain Lead in Phase” reset element, that facilitates the use of the proposed method for the stability analysis, is introduced. Stability of several precision positioning systems with reset controllers, designed for different objectives, is studied to demonstrate the applicability of the proposed hybrid passivity and finite-gain approach for the stability analysis of reset control systems. Guidelines for design of reset systems such that their stability can be concluded using the hybrid passivity and finite gain method are shown. This thesis presents a new view on the stability of reset systems and addresses the need for frequency-domain tools for stability analysis of nonlinear control systems in precision mechatronics applications.

Mechanical Engineering | Systems and Control

Advisors/Committee Members: Steur, Erik (mentor), Hossein Nia Kani, Hassan (mentor), Saikumar, Niranjan (mentor), De Schutter, Bart (graduation committee), Delft University of Technology (degree granting institution).

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The ever-increasing industry desire for improved performance makes linear controller design run into its fundamental limitations. A nonlinear controller, such as Reset Control (RC), is needed to overcome these. RC is promising since, unlike other nonlinear methods, it easily integrates into the PID design framework preferred by industry. Thus far, closed-loop behaviour of RC has been analysed in the frequency domain either through Describing Function analysis or by direct closed-loop numerical computation. The former method computes a simplified closed-loop RC response by ignoring all harmonics, an approach which literature has found to inflict significant modelling errors. The latter method gives an accurate solution but does not provide understanding of how open-loop RC design affects closed-loop performance. No methods link these aspects, which impairs RC design and tuning. The main contribution of this work is aimed at providing this link, while achieving an accurate closed-loop RC model. A novel approach for modelling RC is considered, which uses state-dependent impulse inputs. This approach is shown to permit an accurate computation of closed-loop RC behaviour starting from an open-loop model, thus linking both aspects, enhancing system understanding. A frequency-domain description for closed-loop RC is obtained, as needed for the PID design framework, which is solved for analytically by inserting several well-defined assumptions. This 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.

Mechanical Engineering | Systems and Control

Advisors/Committee Members: Hossein Nia Kani, S.H. (mentor), Saikumar, Niranjan (graduation committee), Verhaegen, M.H.G. (mentor), Kok, Manon (graduation committee), Delft University of Technology (degree granting institution).

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PID is the most popular controller in the industry. PID controllers are linear, and thus have fundamental limitations, such that certain performance criteria cannot be achieved. To overcome these limitations, nonlinear reset control can be used. Reset control can achieve less overshoot and a faster response time than linear controllers. However, the resetting mechanism has a jump function which causes jumps in the control input, which can result in limit cycles. Linear filters and controllers are designed in the industry using loop shaping, which is done in the frequency domain. In this study it is investigated how to analyse reset systems in the frequency domain. A reset system is nonlinear, so transfer functions needs to be approximated by describing functions. The sinusoidal input describing function considers only the first harmonic of the output and therefore does not capture all the dynamics of the element. The effects of the higher order harmonics are important in precision systems, since unwanted dynamics should not be excited nor should performance be affected. In this thesis, the higher order sinusoidal input describing functions (HOSIDF) are derived analytically. The HOSIDF shows the magnitude and phase response per harmonic, such that stability and performance analysis can be improved. Because the HOSIDF shows multiple responses, it is not trivial how to do loop shaping. The information from the HOSIDF is combined, creating a combined magnitude and combined phase response. It is seen that the combined magnitude looks promising, but the combined phase has jumps. It is concluded that the combined magnitude and combined phase are not mature enough to rely on during loop shaping and further work in this direction is required.

Systems and Control

Advisors/Committee Members: Hossein Nia Kani, Hassan (mentor), Saikumar, Niranjan (mentor), van Wingerden, Jan-Willem (mentor), Delft University of Technology (degree granting institution).

▼ Computer vision has been on the rise over the last decades. The applications of computer vision are mostly found within the domain of robotics and Unmanned Aerial Vehicle's. The use of computer visions in precision industry is new and offers both opportunities and challenges. In high performance precision systems the demands on sensors is set high in terms of precision, delay and sample rate. In previous work a computer vision sensor was developed for the control of a microscopy stage. This development opened a path for computer vision sensors in precision systems. However, the limitations of computer vision sensors are challenging in the domain of control. A computer vision sensor needs to process an image before it can estimate the position of an object. This processing requires time which introduces a time delay into the control system. Due to the nature of the computer vision algorithm and computing devices, the delay in the sensor is time varying. Furthermore, since a controller typically requires a tenfold sample rate of the control bandwidth the limited frame rate of computer vision sensors imposes additional challenges. In previous work, the delay and limited sample rate of the computer vision sensor limited the control bandwidth of a microscopy to 0.87Hz in translational range. Since high performance precision systems require higher bandwidths a new computer vision sensor is developed in this thesis. An existing microscopy stage is used to test the performance of a computer vision sensor. Ground vibrations in a laboratory environment have a peak value at 10Hz which defines the target bandwidth. In order to reach this target bandwidth a new computer vision sensor is proposed. The sensor uses a cost-effective camera and a computer to run the computer vision algorithm. By decreasing the delay from 60ms to 10ms a control bandwidth of 7Hz, using PID, is obtained in this work. Since the target bandwidth is 10Hz time delay compensation is considered to improve the performance. By implementing a Filtered Smith Predictor the target bandwidth of 10Hz is reached. The maximum control bandwidth of the controller, 15Hz, was derived in order to inspect the limit of computer vision sensors in precision systems. Advisors/Committee Members: Hossein Nia Kani, Hassan (mentor), Saikumar, Niranjan (mentor), van Wingerden, Jan-Willem (mentor), Delft University of Technology (degree granting institution).

▼ Reset controllers can outperform PID controllers and may introduce phase advantage compared to linear PID control. However, in general, reset controllers do not have the same steady state properties as linear controllers, like removing steady state errors. In case of model mismatches and disturbances, this may cause limit cycles (persisting oscillations) in the closed response when (constant) references are tracked. The occurrence of these limit cycles is very unwanted in mechatronic precision systems, since the response does not converge to the desired set-point. To avoid / remove limit cycles in the response, some reset control methods are currently available. Examples are PI+CI controllers, reset controllers that reset to non-zero values and reset controllers with (adaptive) feedforward. Although the existing methods can be used to overcome the limit cycle problem, they are often dependent on the model of the system or are a trade-off between linear and nonlinear control. Hence, the existing methods are not very robust in general or do not use the full advantage of reset control. In this thesis, a simple and robust fixed instant adaptive reset controller is developed for a minimum phase SISO system that can be stabilized by standard PID control. The presented adaptive reset algorithm detects if a limit cycle is present and adapts the after reset value in an iterative way until the limit cycle is removed. Although no mathematical proof is given, the idea behind the presented method is explained. Simulations and measurements are performed to show that the algorithm is able to get rid of limit cycles caused by model mismatches and constant input disturbances. Furthermore, it is shown that the adaptive algorithm can be applied to zero-crossing reset as well. Advisors/Committee Members: Hossein Nia Kani, Hassan (mentor), Saikumar, Niranjan (mentor), van Wingerden, Jan-Willem (graduation committee), Delft University of Technology (degree granting institution).

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The application of actively controlled micrometer precision positioning stages in products that are accessible to start-ups, individual consumers or third world countries is currently limited by their price and size. To solve this problem, the use of low-cost and compact components in stages is investigated. Earlier research done in the MSD group already showed that relatively low-cost sensor concepts and mechanical designs can be applied to significantly reduce the price of stages, while still achieving sub-micrometer precision. In this research, the applicability of the Arduino Due micro-controller (€40) and amplifiers based on Pulse Width Modulation (PWM, €6) in precision stages is investigated. The use of cheap components doesn’t come without its drawbacks. To name a few examples, the Analog-to-Digital Converter (ADC) in the Arduino doesn’t have the resolution of higher quality components, PWM adds frequency content to the output of the amplifier and the Arduino processor isn’t as fast. In this research project, an extensive theoretical analysis is done to reveal how the components affect the overall performance of the stage, which can then be used to optimize system parameters to circumvent the performance losses that are inevitable with cheap components. This way much of the overall system performance can be maintained. The theory is experimentally validated and the Arduino and PWM based amplifiers are successfully implemented into a working prototype with a precision of 1.5μm.

Mechatronic System Design

Advisors/Committee Members: Spronck, Jo (mentor), Saikumar, Niranjan (graduation committee), Vdovine, Gleb (graduation committee), Delft University of Technology (degree granting institution).

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The PID controller is one of the most used controllers in the industry. However, fundamental limitations due to linearity restrict its performances when higher bandwidth, stability, and precision are required simultaneously in today’s high-tech industry. Reset control is a promising nonlinear control strategy which can overcome these limitations. But it also brings new problems. High order harmonics are introduced into the system because of non-linearity which lead to unwanted dynamics and deterioration of performances. So it is necessary to reduce them as much as possible. It is found that the sequence of different parts of a reset controller has effects on the magnitude of high order harmonics. Through high order sinusoidal input describing functions (HOSIDOFs) tool, the optimal sequence of the open loop in which the magnitude of high order harmonics is minimum is achieved for a general reset controller. The superiority of the suggested sequence in the closed-loop system is validated through both simulation and experiments at a Lorentz-actuated precision positioning stage.

Mechatronic System Design

Advisors/Committee Members: Hassan HosseinNia, S. (graduation committee), Ahmadi Dastjerdi, Ali (mentor), Saikumar, Niranjan (graduation committee), Delft University of Technology (degree granting institution).

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The high-tech industry is pushing the motion system technology towards faster, more precise and more robust system. One of the keys to this growing demand is the advancement of motion control. To this day, Proportional-Integral-Derivative (PID) has been the workhorse for the industry system control. This is because PID is simple to design and implement and adapt to industrial loopshaping method. Nevertheless, PID suffers fundamental limitations of linear control. To deal with this, a nonlinear control should be utilized. Reset control is a nonlinear control that is still easy but can overcome the limitation of linear control and more importantly, loop shaping method can be used to reset control by using describing function analysis which is pseudo-approximation of nonlinear system that based on the first harmonic. However, reset control also introduces higher order harmonics into the system that can negatively affect system performance. This is because these harmonics may cause some unwanted dynamics present in system response. Describing function which is the common tool to analyze and design reset control is not accurate enough since higher order harmonics are not considered. Recently, a tool to visualize higher order harmonics in frequency domain is developed. This open the possibilities to study the behavior of higher order harmonics and its effect to system performance. This thesis focuses on a performance analysis and tuning of a novel reset element called ’Constant in Gain, Lead in Phase’(CgLp). It is shown by the literature that reset control is often utilized to provide phase lag reduction but CgLp has shown the use of reset control to provide phase compensation and this improves system performance. Since its introduction, no guidelines available in the literature to design and tune CgLp. Looking at its potential to be industry standard for motion control, finding guidelines to tune CgLp is an important step to achieve this goal. To do the optimal tuning of reset element, higher order harmonics should be considered so that the effect of unwanted response can be minimized while maintaining the advantage of reset control. Therefore, the work in this thesis is performed by doing performance analysis of CgLp through describing function and HOSIDF. It is shown that while there is an improvement in tracking and steady state precision performance by using CgLp compared to normal PID, there is deterioration of the performance although describing function predicted an improvement. This is because there is a trade-off between improvement by CgLp and the rise of higher order harmonics gain. In this work, the higher order harmonics was considered at the bandwidth frequency and normalized over its first harmonic. It was observed that the optimal performance is achieved when the highest gain value of normalized 3rd harmonic is around half of maximum possible value of normalized 3rd harmonic.

Mechanical Engineering

Advisors/Committee Members: Hossein Nia Kani, Hassan (mentor), Saikumar, Niranjan (mentor), Spronck, Jo (graduation committee), Goosen, Hans (graduation committee), Delft University of Technology (degree granting institution).

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Stringent control demands from the high-tech mechatronics industry have warranted the need to explore potentially advantageous non-linear controllers. Variable Fractional Order (VFO) calculus provides one such avenue to build non-linear PID-like controllers. VFO calculus is the generalization of integer order differentiation and integration, where, in addition to the possibility of orders being real or even complex, the orders can vary as a function of a variable like time, temperature, etc. However, in this nascent field of VFO control, the focus has mainly been on controller tuning by time domain optimization of the performance for certain specific trajectories or cost functions. On the other hand, Frequency domain tools allow for analysis and tuning of controllers for performance over a wide range of exogenous inputs. For smooth adoption into industry, it is important to develop a frequency domain framework for working with VFO control. Describing function (DF) analysis is a method to obtain an approximate Frequency Response Function (FRF)-like function for non-linear systems. In this thesis, DF analysis is used for developing VFO PID controllers in the frequency domain from an industry compatibility point of view and the closed loop performance of these controllers in controlling a precision positioning stage is examined.

Mechanical Engineering | Systems and Control

Advisors/Committee Members: van Wingerden, Jan-Willem (graduation committee), Giordano, Giulia (mentor), Hossein Nia Kani, Hassan (mentor), Saikumar, Niranjan (mentor), Delft University of Technology (degree granting institution).

▼ In high-tech industry (sub)nanometre precision motion control is essential. For example wafer scanners, used for production of integrated circuits, have to provide (sub)nanometre precision positioning whilst satisfying challenging requirements on speed at the same time. It is in demanding cases like this that different requirements begin to conflict with each other. A fundamental trade-off between robustness and performance exists as an inevitable result of the waterbed effect in linear control. PID controllers, which have been an industry-standard for many years, do not satisfy the ever increasing demands. In this MSc thesis a novel reset control synthesis method is proposed: CRONE reset control, which combines a robust fractional CRONE controller (Commande Robuste d’Ordre Non-Entier) with non-linear reset control to overcome waterbed effect. In CRONE control, robustness is achieved against gain deviations by creation of constant phase behaviour around bandwidth with the use of fractional operators. The use of fractional operators also introduces more freedom in shaping the open- loop frequency response, allowing fractional factors in Bode’s gain-phase relation. However, waterbed effect remains, which motivates introduction of non-linear reset control in the CRONE design. In reset control, controller states are reset when the error between output- and reference- signal is zero. In frequency domain, using describing function analysis it is predicted that reset filters generate less phase lag for similar gain behaviour. For instance, a reset integrator gives a phase lag of about 38 degrees, which is 52 degrees less compared to the linear integrator. This allows for relief from Bode’s gain-phase relation, breaking aforementioned trade-offs. In the new controller design, reset phase advantage is approximated using describing function analysis and used to achieve better open-loop shape. New design rules for CRONE reset control have been developed in this thesis. Three different reset control strategies have been investigated: integrator reset, lag reset and lead- lag/lag-lead reset. For these controllers, a two-degree-of-freedom non-linearity tuning CRONE reset control structure has been developed. This control structure has been implemented digitally within a MATLAB/Simulink environment on a Lorentz-actuated (dual) precision stage via a real-time dSPACE DS1103 controller interface. For the implemented controllers sufficient quadratic stability has been shown using the Hβ-condition. It has been shown that simulated frequency responses using describing function correspond well to experimental identified frequency responses. Moreover, frequency domain measurements have shown that better performance for CRONE reset control can be achieved for same phase margin compared to linear CRONE. Relief from both waterbed effect and Bode’s gain-phase relation has been accomplished. Furthermore, for the same bandwidth, average noise reduction between 1.79dB and 3.93dB has been attained at a number of distinct… Advisors/Committee Members: Saikumar, Niranjan (mentor), Hossein Nia Kani, Hassan (mentor), Baldi, Simone (mentor), van Wingerden, Jan-Willem (graduation committee), Delft University of Technology (degree granting institution).

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The development of the high-tech industry has pushed the requirements of motion applications to extremes regarding precision, speed and robustness. A clear example is given by the wafer and reticle stages that require rigorous demands like robust nanometer precision and high-speed motion profiles to ensure product quality and production efficiency. Industrial workhorse Proportional Integral Derivative (PID) has been widely used for its simple implementation and good performance. However, PID is insufficient to meet the ever-increasing demands in the high-tech industry due to its inherent constraints of linear controllers such as the waterbed effect. To overcome these fundamental limitations, researchers have turned to nonlinear controllers. Nevertheless, most of the nonlinear controllers are difficult to design and implement and thus are not widely accepted in the industry. Reset control is a nonlinear controller that is easy to implement and design since it maintains compatibility with the PID loop shaping technique using a pseudo-linear analysis tool named describing function method. However, the reset control as a nonlinear controller also introduces high order harmonics to the system that can negatively affect system performance by causing unwanted dynamics. Hence, describing function analysis as a linear approximation approach that only considers first harmonics is not accurate enough. Recently, a theory to analyze high order harmonics of nonlinear system in frequency domain termed higher order sinusoidal describing function has been developed, which enables the possibility to perform more precise analysis on reset systems. The majority of research on reset control has focused on the phase lag reduction but a novel reset element proposed in literature termed ”Constant in gain, Lead in phase” (CgLp) is used to provide broadband phase compensation and has been shown to improve system performance. However, there is no systematic designing and tuning approach in literature such that the full advantage of CgLp elements is extracted. This work focuses on the tuning of the CgLp elements in order to obtain optimal performance. High order harmonics are also considered in the tuning analysis since they are critical to system performance due to the effect of unwanted dynamics. When a group of CgLp elements are designed to provide pre-determined phase compensation at the crossover frequency, it is seen that the optimal tracking precision performance is always obtained with the case that has the highest frequency of third order harmonic peak and has almost the smallest magnitude of high order harmonics at low frequencies. Moreover, the second order CgLp controllers are observed to outperform the first order CgLp controller regarding tracking precision. On the other hand, configurations that have the lowest magnitude of third order harmonic at high frequency are found to have the best noise attenuation performance.

Mechanical Engineering | Mechatronic System Design (MSD)

Advisors/Committee Members: Ahmadi Dastjerdi, Ali (mentor), Saikumar, Niranjan (graduation committee), Hossein Nia Kani, Hassan (mentor), Herder, Just (graduation committee), Delft University of Technology (degree granting institution).

Mechanical Engineering | Systems and Control Advisors/Committee Members: van Wingerden, Jan-Willem (mentor), Hossein Nia Kani, Hassan (mentor), Saikumar, Niranjan (mentor), Delft University of Technology (degree granting institution).