title: Multi-objective LQR with optimum weight selection to design FOPID controllers for delayed fractional order processes.
abstract: An optimal trade-off design for fractional order (FO)-PID controller is proposed with a Linear Quadratic Regulator (LQR) based technique using two conflicting time domain objectives. A class of delayed FO systems with single non-integer order element, exhibiting both sluggish and oscillatory open loop responses, have been controlled here. The FO time delay processes are handled within a multi-objective optimization (MOO) formalism of LQR based FOPID design. A comparison is made between two contemporary approaches of stabilizing time-delay systems withinLQR. The MOO control design methodology yields the Pareto optimal trade-off solutions between the tracking performance and total variation (TV) of the control signal. Tuning rules are formed for the optimal LQR-FOPID controller parameters, using median of the non-dominated Pareto solutions to handle delayed FO processes.
authors.affiliation: School of Electronics and Computer Science, University of Southampton, Southampton SO17 1BJ, United Kingdom; Department of Power Engineering, Jadavpur University, Salt Lake Campus, LB-8, Sector 3, Kolkata 700098, India. Electronic address: s.das@soton.ac.uk.
authors.forename: Saptarshi
authors.initials: S
authors.lastname: Das
authors.affiliation: Department of Power Engineering, Jadavpur University, Salt Lake Campus, LB-8, Sector 3, Kolkata 700098, India; Department of Earth Science and Engineering, Imperial College London, Exhibition Road, London SW7 2AZ, United Kingdom. Electronic address: i.pan11@imperial.ac.uk.
authors.forename: Indranil
authors.initials: I
authors.lastname: Pan
authors.affiliation: Reactor Control Division, Bhabha Atomic Research Centre, Mumbai 400085, India. Electronic address: shantanu@barc.gov.in.
authors.forename: Shantanu
authors.initials: S
authors.lastname: Das
keywords: Fractional order PID controller; Integral performance index; LQR weighting matrices; Multi-objective control; Non-Integer Order Plus Time Delay (NIOPTD) process