Petar D. Mandic

Dominant pole placement with fractional order PID controllers: D-decomposition approach

Dominant pole placement is a useful technique designed to deal with the problem of controlling a high order or time-delay systems with low order controller such as the PID controller. This paper tries to solve this problem by using D-decomposition method. Straightforward analytic procedure makes this method extremely powerful and easy to apply. This technique is applicable to a wide range of transfer functions: with or without time-delay, rational and non-rational ones, and those describing distributed parameter systems. In order to control as many different processes as possible, a fractional order PID controller is introduced, as a generalization of classical PID controller. As a consequence, it provides additional parameters for better adjusting system performances. The design method presented in this paper tunes the parameters of PID and fractional PID controller in order to obtain good load disturbance response with a constraint on the maximum sensitivity and sensitivity to noise measurement. Good set point response is also one of the design goals of this technique. Numerous examples taken from the process industry are given, and D-decomposition approach is compared with other PID optimization methods to show its effectiveness.

Fractional order PD control of Furuta pendulum: D-decomposition approach

This paper deals with stability problem of inverted pendulum controlled by a fractional order PD controller. D-decomposition method for determining stability region in controller parameters space is hereby presented. The D-decomposition problem for linear systems is extended for linear fractional systems and for the case of nonlinear parameters dependence. Some comparisons of fractional and integer order PID controllers are given based on simulation results.

Some electromechanical systems and analogies of mem-systems integer and fractional order

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.

Stabilization of Inverted Pendulum by Fractional Order PD Controller with Experimental Validation: D-decomposition Approach

This paper deals with the stability problem of two types of inverted pendulum controlled by a fractional order PD controller. Rotational inverted pendulum and cart inverted pendulum are under-actuated mechanical systems with two degrees of freedom and one control input. Detailed mathematical models of both pendulums are derived using the Rodriguez method. Fractional order PD controller is introduced for inverted pendulum stabilization. Stability regions in control parameters space are calculated using the D-decomposition approach, based on which tuning of the fractional order controller can be carried out. Numerical simulations and experimental realization are given to demonstrate the effectiveness of the proposed method.

Analysis of electrical circuits including fractional order elements

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.

Multi-mode active vibration control of a nanobeam using a non-square MIMO PID controller

In this paper, we suggest a robust non-square MIMO (4×8) PID controller for the multi-mode active vibration damping of a nanobeam. Nanobeam is modeled by using the nonlocal continuum theory of Eringen to consider the small-scale effects and Euler-Bernoulli beam theory. The problem is analyzed for the free vibration case with Heaviside type disturbance of a nanobeam with and without the controller. The proposed system has four inputs and eight outputs, where by using the static decoupling method, decoupled system of four transfer functions is obtained. The controller parameters dependig on one tuning parmeter are designed to suppress the step disturbance on the input without overshooting. All theoretical results are verified with several numerical examples.

Stabilization of double inverted pendulum system by using a fractional differential compensator

In this paper stability problem of double inverted pendulum controlled by a fractional differential compensator is investigated. Pendubot is an underactuated mechanical system, i.e. it has only one control input and two degrees of freedom. Detailed mathematical model of Pendubot is derived using the Rodriguez method and then fractional order lead compensator is introduced in order to stabilize it around unstable upright position. D-decomposition method is used to solve the problem of asymptotic stability of closed loop system. Stability regions in control parameters space are calculated using this technique, which allows tuning of the fractional differential compensator to be carried out.

PD α -type iterative learning control for fractional-order singular time-delay system

In this paper a closed-loop PDα — 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 PDα ILC scheme for a class of fractional order singular time-delay system is verified by a numerical example.

Fractional-order iterative learning control for singular fractional- order system: (P) - PDa type

Iterative learning control (ILC) is one of the recent topics in control theories and it is suitable for controlling a wider class of mechatronic systems it is especially suitable for the motion control of robotic systems. This paper addresses the problem of application of fractional order ILC for fractional order singular system. Particularly, we study fractional order singular systems in the pseudo-state space. An closed-loop fractional order PDalpha type ILC of the fractional-order singular system is investigated. Also, open-closed loop of the fractional order P-PDa type ILC is considered. Sufficient conditions for the convergence in the time domain of the proposed ILC schemes are given by the corresponding theorems and proved. Finally, numerical simulations show the feasibility and effectiveness of the proposed approach.

Feedback-feedforward iterative learning control for fractional order uncertain time delay system-PD alpha type

A feedback-feedforward PDalpha type iterative learning control (ILC) of fractional order uncertain time delay system is considered. Particularly, we discuss fractional order time delay systems in state space form with uncertain bounded constant time delay. Sufficient conditions for the convergence of a proposed PDalpha type of learning control algorithm for a class of fractional state space time delay system are given in time domain. Finally, a simulation example shows the feasibility and effectiveness of the approach.