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

Basic Properties and Stability of Fractional-Order Reset Control Systems

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.Comment: The 12th European Control Conference (ECC13), Switzerland, 201

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.Comment: European Control Conference 201

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.Comment: American Control Conference 201

Absorption of light through isolated and coupled resonances in horizontal InP nanowire arrays

We have studied the interaction of light with two types of closely related nanostructures: a single horizontal InP nanowire and an infinite periodic array of such nanowires. The study has been done theoretically by calculating the absorption cross section of the nanowires via a semi analytical method, the Mie theory, and two numerical methods, the scattering matrix method (SMM) and the finite element method (FEM) to perform electromagnetic modeling. The absorption spectra obtained by the Mie theory show strong polarization dependency. Also, we have noticed that the peaks in the spectra red shift by increasing the radius of the nanowires. To study this redshift, we assumed that the nanowires can be seen as optical waveguides that can capture the light in certain eigenmodes much like a whispering gallery mode. Due to this, a semi analytical eigenfunction method has been employed to investigate the eigenmodes in the nanowire. The results show that the eigenmodes are the origin of the Mie resonances and redshift by increasing the radius of the nanowire. By moving to study the optical response of the periodic array consisting of infinitely many nanowires, an additional set of optical resonances is introduced to the absorption in the nanowires. These resonances are due to Bragg grating condition for constructive interference of scattered light between neighboring nanowires, and these resonances depend on the period of the structure. These new resonances are called lattice resonance throughout this thesis. We show that for specific combination of the period of the array and the radius of the constituent nanowires, the lattice resonances couple with the single nanowire resonances. This coupling can boost the absorption in the array by a factor of 18 compared to that in single nanowires. Through such resonant absorption, the nanowires can absorb 200 times stronger than the same amount of InP material in bulk form.Objects with dimensions in the order of nanometer (1 millionth fraction of 1mm), have special characteristics that enable them with the potential to be applied in a variety of technologies, including solar cells and LEDs. Light behaves differently when it interacts with special materials with such small dimensions. In the current work, we try to explain this interaction between light and these objects called nano-structures, specifically an infinitely long single indium phosphide (InP) nanowire and an infinite periodic array of such nanowires. Essentially, a nanowire is a one dimensional nano-structure with the length from a few tens of nanometers to several micrometers and the radius around 50-100 nanometers (1000 times thinner than a human hair). InP is a semiconductor with electrical conductivity between that of insulators (e.g. glass) and metals (e.g. copper). Furthermore, semiconductors can absorb the energy of the light and convert it to electricity in opto-electronics devices such as photovoltaic cells and photo-detectors. This study has been done theoretically via semi analytical methods for simple systems like a single nanowire and via numerical methods for more complicated systems like the array of nanowires. The calculations show that the absorption mechanism of light in the single nanowire depends on the radius of the nanowire. Due to the small size of the nanowire, part of the light is captured inside the nanowire where it is absorbed and part of it leaks out from the nanowire. Then, in the periodic array, this leaked light can interact with the neighboring nanowires and change the absorption pattern. Therefore, the absorption in the periodic array not only depends on the radius of the nanowires but also on the period of the structure, that is, on the distance between the nanowires. We show that for specific combinations of the period of the array and the radius of the constituent nanowires, the leaked light from a single nanowire interferes constructively inside the neighboring nanowires. This constructive interference can boost the absorption up to 18 times in contrast to that in a single nanowire. Through such resonant absorption, the nanowires can absorb 200 times stronger than the same amount of InP material in bulk form. The direct consequence of this is achieving higher efficiency of photo-devices exploiting the interaction of light and semiconductor nanowires. A higher efficiency facilitates lower utility of the material and a potentially lower cost

Hybrid Systems and Control With Fractional Dynamics (I): Modeling and Analysis

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.Comment: 2014 International Conference on Fractional Differentiation and its Application, Ital

'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