Symbolic Representation for Analog Realization of A Family of Fractional Order Controller Structures via Continued Fraction Expansion

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.This paper uses the Continued Fraction Expansion (CFE) method for analog realization of fractional order differ-integrator and few special classes of fractional order (FO) controllers viz. Fractional Order Proportional-Integral-Derivative (FOPID) controller, FO[PD] controller and FO lead-lag compensator. Contemporary researchers have given several formulations for rational approximation of fractional order elements. However, approximation of the controllers studied in this paper, due to having fractional power of a rational transfer function, is not available in analog domain; although its digital realization already exists. This motivates us for applying CFE based analog realization technique for complicated FO controller structures to get equivalent rational transfer functions in terms of the controller tuning parameters. The symbolic expressions for rationalized transfer function in terms of the controller tuning parameters are especially important as ready references, without the need of running CFE algorithm every time and also helps in the synthesis of analog circuits for such FO controllers

Effect of Random Parameter Switching on Commensurate Fractional Order Chaotic Systems

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.The paper explores the effect of random parameter switching in a fractional order (FO) unified chaotic system which captures the dynamics of three popular sub-classes of chaotic systems i.e. Lorenz, Lu and Chen's family of attractors. The disappearance of chaos in such systems which rapidly switch from one family to the other has been investigated here for the commensurate FO scenario. Our simulation study show that a noise-like random variation in the key parameter of the unified chaotic system along with a gradual decrease in the commensurate FO is capable of suppressing the chaotic fluctuations much earlier than that with the fixed parameter one. The chaotic time series produced by such random parameter switching in nonlinear dynamical systems have been characterized using the largest Lyapunov exponent (LLE) and Shannon entropy. The effect of choosing different simulation techniques for random parameter FO switched chaotic systems have also been explored through two frequency domain and three time domain methods. Such a noise-like random switching mechanism could be useful for stabilization and control of chaotic oscillation in many real-world applications

Intelligent optimisation of analogue circuits using particle swarm optimisation, genetic programming and genetic folding

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University London.This research presents various intelligent optimisation methods which are: genetic algorithm (GA), particle swarm optimisation (PSO), artificial bee colony algorithm (ABCA), firefly algorithm (FA) and bacterial foraging optimisation (BFO). It attempts to minimise analogue electronic filter and amplifier circuits, taking a cascode amplifier design as a case study, and utilising the above-mentioned intelligent optimisation algorithms with the aim of determining the best among them to be used. Small signal analysis (SSA) conversion of the cascode circuit is performed while mesh analysis is applied to transform the circuit to matrices form. Computer programmes are developed in Matlab using the above mentioned intelligent optimisation algorithms to minimise the cascode amplifier circuit. The objective function is based on input resistance, output resistance, power consumption, gain, upperfrequency band and lower frequency band. The cascode circuit result presented, applied the above-mentioned existing intelligent optimisation algorithms to optimise the same circuit and compared the techniques with the one using Nelder-Mead and the original circuit simulated in PSpice. Four circuit element types (resistors, capacitors, transistors and operational amplifier (op-amp)) are targeted using the optimisation techniques and subsequently compared to the initial circuit. The PSO based optimised result has proven to be best followed by that of GA optimised technique regarding power consumption reduction and frequency response. This work modifies symbolic circuit analysis in Matlab (MSCAM) tool which utilises Netlist from PSpice or from simulation to generate matrices. These matrices are used for optimisation or to compute circuit parameters. The tool is modified to handle both active and passive elements such as inductors, resistors, capacitors, transistors and op-amps. The transistors are transformed into SSA and op-amp use the SSA that is easy to implement in programming. Results are presented to illustrate the potential of the algorithm. Results are compared to PSpice simulation and the approach handled larger matrices dimensions compared to that of existing symbolic circuit analysis in Matlab tool (SCAM). The SCAM formed matrices by adding additional rows and columns due to how the algorithm was developed which takes more computer resources and limit its performance. Next to this, this work attempts to reduce component count in high-pass, low-pass, and all- pass active filters. Also, it uses a lower order filter to realise same results as higher order filter regarding frequency response curve. The optimisers applied are GA, PSO (the best two methods among them) and Nelder-Mead (the worst method) are used subsequently for the filters optimisation. The filters are converted into their SSA while nodal analysis is applied to transform the circuit to matrices form. High-pass, low-pass, and all- pass active filters results are presented to demonstrate the effectiveness of the technique. Results presented have shown that with a computer code, a lower order op-amp filter can be applied to realise the same results as that of a higher order one. Furthermore, PSO can realise the best results regarding frequency response for the three results, followed by GA whereas Nelder- Mead has the worst results. Furthermore, this research introduced genetic folding (GF), MSCAM, and automatically simulated Netlist into existing genetic programming (GP), which is a new contribution in this work, which enhances the development of independent Matlab toolbox for the evolution of passive and active filter circuits. The active filter circuit evolution especially when operational amplifier is involved as a component is of it first kind in circuit evolution. In the work, only one software package is used instead of combining PSpice and Matlab in electronic circuit simulation. This saves the elapsed time for moving the simulation between the two platforms and reduces the cost of subscription. The evolving circuit from GP using Matlab simulation is automatically transformed into a symbolic Netlist also by Matlab simulation. The Netlist is fed into MSCAM; where MSCAM uses it to generate matrices for the simulation. The matrices enhance frequency response analysis of low-pass, high-pass, band-pass, band-stop of active and passive filter circuits. After the circuit evolution using the developed GP, PSO is then applied to optimise some of the circuits. The algorithm is tested with twelve different circuits (five examples of the active filter, four examples of passive filter circuits and three examples of transistor amplifier circuits) and the results presented have shown that the algorithm is efficient regarding design.Tertiary Education Trust Fund (TETFUND) through University of Calabar, Nigeria