A fractional representation approach to the robust regulation problem for MIMO systems

The aim of this paper is in developing unifying frequency domain theory for robust regulation of MIMO systems. The main theoretical results achieved are a new formulation of the internal model principle, solvability conditions for the robust regulation problem, and a parametrization of all robustly regulating controllers. The main results are formulated with minimal assumptions and without using coprime factorizations thus guaranteeing applicability with a very general class of systems. In addition to theoretical results, the design of robust controllers is addressed. The results are illustrated by two examples involving a delay and a heat equation.Comment: 23 pages, 3 figures, submitted to International Journal of Robust and Nonlinear Contro

Parameterization of Stabilizing Linear Coherent Quantum Controllers

This paper is concerned with application of the classical Youla-Ku\v{c}era parameterization to finding a set of linear coherent quantum controllers that stabilize a linear quantum plant. The plant and controller are assumed to represent open quantum harmonic oscillators modelled by linear quantum stochastic differential equations. The interconnections between the plant and the controller are assumed to be established through quantum bosonic fields. In this framework, conditions for the stabilization of a given linear quantum plant via linear coherent quantum feedback are addressed using a stable factorization approach. The class of stabilizing quantum controllers is parameterized in the frequency domain. Also, this approach is used in order to formulate coherent quantum weighted $H_2$ and $H_\infty$ control problems for linear quantum systems in the frequency domain. Finally, a projected gradient descent scheme is proposed to solve the coherent quantum weighted $H_2$ control problem.Comment: 11 pages, 4 figures, a version of this paper is to appear in the Proceedings of the 10th Asian Control Conference, Kota Kinabalu, Malaysia, 31 May - 3 June, 201

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

A fractional representation approach to the robust regulation problem for SISO systems

The purpose of this article is to develop a new approach to the robust regulation problem for plants which do not necessarily admit coprime factorizations. The approach is purely algebraic and allows us dealing with a very general class of systems in a unique simple framework. We formulate the famous internal model principle in a form suitable for plants defined by fractional representations which are not necessarily coprime factorizations. By using the internal model principle, we are able to give necessary and sufficient solvability conditions for the robust regulation problem and to parameterize all robustly regulating controllers.Comment: 13 pages, 1 figure, to appear in Systems & Control Letter

Hybrid Systems and Control With Fractional Dynamics (II): Control

No mixed research of hybrid and fractional-order systems into a cohesive and multifaceted whole can be found in the literature. This paper focuses on such a synergistic approach of the theories of both branches, which is believed to give additional flexibility and help the system designer. It is part II of two companion papers and focuses on fractional-order hybrid control. Specifically, two types of such techniques are reviewed, including robust control of switching systems and different strategies of reset control. Simulations and experimental results are given to show the effectiveness of the proposed strategies. Part I will introduce the fundamentals of fractional-order hybrid systems, in particular, modelling and stability of two kinds of such systems, i.e., fractional-order switching and reset control systems.Comment: 2014 International Conference on Fractional Differentiation and its Application, Ital

Equilibrium transition study for a hybrid MAV

Wind tunnel testing was performed on a VTOL aircraft in order to characterize longitudinal flight behavior during an equilibrium transition between vertical and horizontal flight modes. Trim values for airspeed, pitch, motor speed and elevator position were determined. Data was collected by independently varying the trim parameters, and stability and control derivatives were identified as functions of the trim pitch angle. A linear fractional representation model was then proposed, along with several methods to improve longitudinal control of the aircraft

Sound and Automated Synthesis of Digital Stabilizing Controllers for Continuous Plants

Modern control is implemented with digital microcontrollers, embedded within a dynamical plant that represents physical components. We present a new algorithm based on counter-example guided inductive synthesis that automates the design of digital controllers that are correct by construction. The synthesis result is sound with respect to the complete range of approximations, including time discretization, quantization effects, and finite-precision arithmetic and its rounding errors. We have implemented our new algorithm in a tool called DSSynth, and are able to automatically generate stable controllers for a set of intricate plant models taken from the literature within minutes.Comment: 10 page