State feedback based fractional order control scheme for linear servo cart system

Fractional order control schemes are being actively investigated for various systems. Fractional order concept is incorporated in integral (I), proportional integral (PI), proportional derivative (PD) or proportional integral derivative (PID) controller to investigate the performance of different state variables of the system. These techniques are often used for the purpose of technology transfer but very scanty research has so far been conducted using state space approach. The current investigation is initiated to observe the effect of fractional order controller using state space approach for the system's performance while tracking the position and regulating the speed of a linear servo cart system. Integer order controller based on proportional derivative (PD) approach is also shown for comparison. Simulation responses are presented and analyzed, in this investigation. The superiority of state space approach based fractional order controller is shown in the results. The paper contains a literature review on several control techniques used to control position and speed of a servo-cart system. An over view of mathematical modeling of servo cart system and a description of a proposed fractional controller is presented in this paper. A brief description of integer order control scheme is also presented. Simulated results are compared and discussed for both fractional order controller and integer order controller at the end of this paper

Optimum Weight Selection Based LQR Formulation for the Design of Fractional Order PI{\lambda}D{\mu} Controllers to Handle a Class of Fractional Order Systems

A weighted summation of Integral of Time Multiplied Absolute Error (ITAE) and Integral of Squared Controller Output (ISCO) minimization based time domain optimal tuning of fractional-order (FO) PID or PI{\lambda}D{\mu} controller is proposed in this paper with a Linear Quadratic Regulator (LQR) based technique that minimizes the change in trajectories of the state variables and the control signal. A class of fractional order systems having single non-integer order element which show highly sluggish and oscillatory open loop responses have been tuned with an LQR based FOPID controller. The proposed controller design methodology is compared with the existing time domain optimal tuning techniques with respect to change in the trajectory of state variables, tracking performance for change in set-point, magnitude of control signal and also the capability of load disturbance suppression. A real coded genetic algorithm (GA) has been used for the optimal choice of weighting matrices while designing the quadratic regulator by minimizing the time domain integral performance index. Credible simulation studies have been presented to justify the proposition.Comment: 6 pages, 5 figure

Multi-objective Active Control Policy Design for Commensurate and Incommensurate Fractional Order Chaotic Financial Systems

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.In this paper, an active control policy design for a fractional order (FO) financial system is attempted, considering multiple conflicting objectives. An active control template as a nonlinear state feedback mechanism is developed and the controller gains are chosen within a multi-objective optimization (MOO) framework to satisfy the conditions of asymptotic stability, derived analytically. The MOO gives a set of solutions on the Pareto optimal front for the multiple conflicting objectives that are considered. It is shown that there is a trade-off between the multiple design objectives and a better performance in one objective can only be obtained at the cost of performance deterioration in the other objectives. The multi-objective controller design has been compared using three different MOO techniques viz. Non Dominated Sorting Genetic Algorithm-II (NSGA-II), epsilon variable Multi-Objective Genetic Algorithm (ev-MOGA), and Multi Objective Evolutionary Algorithm with Decomposition (MOEA/D). The robustness of the same control policy designed with the nominal system settings have been investigated also for gradual decrease in the commensurate and incommensurate fractional orders of the financial system