Robust stability and stabilization of fractional order linear systems with positive real uncertainty

This paper investigates the robust stability and stabilization of fractional order linear systems with positive real uncertainty. Firstly, sufficient conditions for the asymptotical stability of such uncertain fractional order systems are presented. Secondly, the existence conditions and design methods of the state feedback controller, static output feedback controller and observer-based controller for asymptotically stabilizing such uncertain fractional order systems are derived. The results are obtained in terms of linear matrix inequalities. Finally, some numerical examples are given to validate the proposed theoretical results.     

Homomorphism types and some of their applications in model theory and algebraic linguistics

A strategy of shifting by multiple scanning which can lead to near optimum results for the bandwidth minimization (BM) problem for sparse symmetric matrices is presented. An algorithm is described, and the comparisons of results and timings with other algorithms is given. The optimum results are estimated and further refinements of the algorithms are recommended.     

Bandwidth and transient analysis of bilayer organic photodetectors

Utilization of organic photodetectors (OPDs) and their applications for assembling on flexible and curved substrates have increased in recent years. However, organic semiconductors suffer from low carrier mobility that demands an optimized design and precise modeling for their applications. The OPDs frequency bandwidth is one of the most important criteria that needs to be investigated carefully. In this paper a comprehensive physical time-domain framework is introduced for bandwidth calculations as well as other several evaluation criteria. This model is verified by experimental measurements. According to the results, increasing the reverse bias voltage boosts the bandwidth of OPD owing to the increase of the carrier mobility. Based on the introduced simulation approach, the trade-off between the bandwidth and the responsivity has been investigated and an efficient design method is also proposed which could effectively improve the OPD performance.     

Performance analysis of fractional order fuzzy PID controllers applied to a robotic manipulator

A two-link robotic manipulator is a Multi-Input Multi-Output (MIMO), highly nonlinear and coupled system. Therefore, designing an efficient controller for this system is a challenging task for the control engineers. In this paper, the Fractional Order Fuzzy Proportional-Integral-Derivative (FOFPID) controller for a two-link planar rigid robotic manipulator for trajectory tracking problem is investigated. Robustness testing of FOFPID controller for model uncertainties, disturbance rejection and noise suppression is also investigated. To study the effectiveness of FOFPID controller, its performance is compared with other three controllers namely Fuzzy PID (FPID), Fractional Order PID (FOPID) and conventional PID. For tuning of parameters of all the controllers, Cuckoo Search Algorithm (CSA) optimization technique was used. Two performance indices namely Integral of Absolute Error (IAE) and Integral of Absolute Change in Controller Output (IACCO) having equal weightage for both the links are considered for minimization. Numerical simulation results clearly indicate the superiority of FOFPID controller over the other controllers for trajectory tracking, model uncertainties, disturbance rejection and noise suppression.     

Fractional Order Linear Variable Differential Transformer: Design and analysis

Linear Variable Differential Transformer (LVDT) is the most preferred displacement measurement transducer used in industries because of its simple design and proven reliability. The major challenge faced in LVDT is linearity in limited stroke range. In this paper, a fractional order model of LVDT is developed and its characteristics like sensitivity, nonlinearity and stroke range are analysed by considering fractional behaviour only in self-inductance, mutual inductance and both. The results presented in this paper shows that Fractional Order Linear Variable Differential Transformer (FOLVDT) provides high sensitivity with reduced nonlinearity compared to the conventional LVDT. The results also demonstrate that the FOLVDT can be operated for increased stroke range without compromising on sensitivity and linearity.     

Oxidative pyrolysis of kraft lignin in a bubbling fluidized bed reactor with air

Fast pyrolysis of kraft lignin with partial (air) oxidation was studied in a bubbling fluidized bed reactor at reaction temperatures of 773 and 823 K. The bio-oil vapors were fractionated using a series of three condensers maintained at desired temperatures, providing a dry bio-oil with less than 1% water and over 96% of the total bio-oil energy.Oxygen feed was varied to study its effect on yield, composition, and energy recovery in the gas, char and oil products. The addition of oxygen to the pyrolysis process increased the production of gases such as CO and CO₂. It also changed the dry bio-oil properties, reducing its heating value, increasing its oxygen content, reducing its average molecular weight and tar concentration, while increasing its phenolics concentration. The lower reaction temperature of 773 K was preferred for both dry bio-oil yield and quality.Autothermal operation of the pyrolysis process was achieved with an oxygen feed of 72 or 54 g per kg of biomass at the reaction temperatures of 773 and 823 K, respectively. Autothermal operation reduced both yield and total energy content of the dry bio-oil, with relative reductions of 24 and 20% for the yield, 28 and 23% for the energy content, at 773 and 823 K.     

Analytical fractional PID controller design based on Bode’s ideal transfer function plus time delay

In this paper, a fractional order PID controller cascaded with a fractional filter is proposed for higher order processes. In this analytical design methodology, one or two reduced fractional orders plus time delay models are used to represent higher order system transfer functions. The controller parameters are determined so as to meet certain frequency domain specifications. A unity feedback reference model is employed where Bode’s ideal loop transfer function plus time delay of the fractional order model is placed in the forward path. The addition of this time delay provides the exact determination of frequency domain specifications if the system either intrinsically owns a time delay or a time delay is injected by its reduced order model. The proposed methodology is compared with two other related methodologies and it has been observed that the proposed controller performs much better than the others. Moreover, some empirical formulas for time domain characteristics of the reference model are numerically derived in terms of certain frequency domain specifications and time delay of the fractional reduced order model. The accuracy of these formulas is tested by simulations. The iso-damping, noise attenuation and load disturbance suppression performances of the proposed controller are also considered and compared with those of other related controllers.     

Dustiness Quantification of Powders by the Fractional Release Rate

The handling of dispersed solids may lead to undesirable release of dust particles. Size and quantity of the particles transferred into the gas with time depend on the binding and separating forces in the powder. These in turn are determined by characteristic parameters of the powder and of the process. Analogous to the well‐known “fractional collection efficiency” describing the dust separation, a newly defined “fractional release rate” to quantify the release of dust is introduced. The application is demonstrated by an example and the way to further development of this innovative approach is demonstrated.     

Model-free adaptive fractional order control of stable linear time-varying systems

This paper presents a new model-free adaptive fractional order control approach for linear time-varying systems. An online algorithm is proposed to determine some frequency characteristics using a selective filtering and to design a fractional PID controller based on the numerical optimization of the frequency-domain criterion. When the system parameters are time-varying, the controller is updated to keep the same desired performances. The main advantage of the proposed approach is that the controller design depends only on the measured input and output signals of the process. The effectiveness of the proposed method is assessed through a numerical example.