This paper deals with the analysis of electrical circuits with classical one-port elements including two novel defined one-port fractional order elements: fractional-order resistive-capacitive RC-α and fractional-order inductive RL-α element. The definitions and analytical relations between current, voltage and power of introduced fractional elements are provided. An example of fractional element realization via ladder electrical circuit composed of classical resistors, capacitors and/or inductors is presented. Several examples are analyzed to illustrate the behavior of electrical circuit with fractional order elements for different values of fractional order α including differentiator/integrator circuits as well as complex circuits without accumulated energy.

This paper presents a new optimization method for PID controller cascaded with a lead-lag compensator (PIDC). Parameters of PIDC controller are obtained by solving the constrained optimization problem. We propose two variants of optimality criterion. First one is defined through the max-min optimization problem wherein objective function is the amplitude frequency response of the PIDC controller. Second one is based on an effective approximation of the minimum value of the amplitude frequency response of PIDC controller. Consequently, the resulting max optimization problem is defined as simplified setup of the first one criterion to obtain computationally less expensive problem. Both variants of optimality criterion result in efficient load disturbance rejection evaluated by the Integrated Absolute Error (IAE). Robustness is ensured by constraining the value of the maximum sensitivity M_s, while efficient noise rejection is guaranteed by the desired value of the sensitivity to measurement noise M_n. Good reference shaping is supported with proper constraints based on the Amplitude Optimum (AO) principle. Numerous batches of processes typically encountered in the industry are used to demonstrate the effectiveness of the proposed design method.

In this paper a closed-loop PD ^α - type iterative learning control (ILC) of fractional order singular time-delay system is considered. In particular, we discuss fractional order linear singular timed-delay systems in state space form. The sufficient conditions for the convergence in time domain of the proposed PD-alpha type ILC for a class of fractional order singular system are given by the corresponding theorem together with its proof. Finally, the validity of the proposed PD ^α ILC scheme for a class of fractional order singular time-delay system is verified by a numerical example.

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This paper will provide some an applications of memristors and mem-systems with a particular focus on electromechanical systems and analogies that holds great promise for advanced modeling and control of complex objects and processes. Also, we present the connection between fractional order differ integral operators and behavior of the mem-systems. Finally, several potential applications of electromechanical analogies of integer and fractional order are discussed.