Reduced Order Controller Design for Robust Output Regulation

We study robust output regulation for parabolic partial differential equations and other infinite-dimensional linear systems with analytic semigroups. As our main results we show that robust output tracking and disturbance rejection for our class of systems can be achieved using a finite-dimensional controller and present algorithms for construction of two different internal model based robust controllers. The controller parameters are chosen based on a Galerkin approximation of the original PDE system and employ balanced truncation to reduce the orders of the controllers. In the second part of the paper we design controllers for robust output tracking and disturbance rejection for a 1D reaction-diffusion equation with boundary disturbances, a 2D diffusion-convection equation, and a 1D beam equation with Kelvin-Voigt damping.Comment: Revised version with minor improvements and corrections. 28 pages, 9 figures. Accepted for publication in the IEEE Transactions on Automatic Contro

Research on output feedback control

A summary is presented of the main results obtained during the course of research on output feedback control. The term output feedback is used to denote a controller design approach which does not rely on an observer to estimate the states of the system. Thus, the order of the controller is fixed, and can even be zero order, which amounts to constant gain ouput feedback. The emphasis has been on optimal output feedback. That is, a fixed order controller is designed based on minimizing a suitably chosen quadratic performance index. A number of problem areas that arise in this context have been addressed. These include developing suitable methods for selecting an index of performance, both time domain and frequency domain methods for achieving robustness of the closed loop system, developing canonical forms to achieve a minimal parameterization for the controller, two time scale design formulations for ill-conditioned systems, and the development of convergent numerical algorithms for solving the output feedback problem

Investigation and Feasibility Assessment of TOPAZ-2 Derivations for Space Power Applications

The ability to provide continuous power at significant levels is of utmost importance for many space missions, from simple satellite operations to manned Mars missions. One of the main problems faced in delivering solar or chemical space power in the tens of kW range, is the increasingly massive nature of the power source and the costs associated with its launch, operation and maintenance. A national program had been initiated to study the feasibility of using certain advanced technologies in developing an efficient lightweight space power source. The starting point for these studies has been the Russian TOPAZ-2 space reactor system, with the ultimate goal to aid in the development of a TOPAZ-2 derivative which will be ready for flight by the year 2000. The main objective of this project has been to perform feasibility assessment and trade studies which would allow the development of an advanced space nuclear power system based on the in-core thermionic fuel element technology currently used in the Russian TOPAZ-2 reactor. Two of the important considerations in developing the concept are: (1) compliance of the current TOPAZ-2 and of any advanced designs with U.S. nuclear safety expectations, and (2) compliance of the design with the seven years lifetime requirement. The project was composed of two major phases. The initial phase of the project has concentrated on understanding the TOPAZ-2 thermionic reactor in sufficient detail to allow several follow-on tasks. The primary interest during this first phase has been given on identifying the potential of the TOPAZ-2 design for further improvements. The second phase of the project has focused on the feasibility of a TOPAZ-2 system capable of delivering 30-50 kWe. Towards the elimination of single-point failures in the load voltage regulation system an active voltage regulator has been designed to be used in conjunction with the available shunt load voltage regulator. The possible use of a dual-loop, model-based adaptive control system for load-following in the TOPAZ-2 has also been investigated. The objective of this fault-tolerant, autonomous control system is to deliver the demanded electric power at the desired voltage level, by appropriately manipulating the neutron power through the control drums. As a result, sufficient thermal power is produced to meet the required demand in the presence of dynamically changing system operating conditions and potential sensor failures. The designed controller is proposed for use in combination with the currently available shunt regulators, or as a back-up controller when other means of power system control, including some of the sensors, fail

A decentralized linear quadratic control design method for flexible structures

A decentralized suboptimal linear quadratic control design procedure which combines substructural synthesis, model reduction, decentralized control design, subcontroller synthesis, and controller reduction is proposed for the design of reduced-order controllers for flexible structures. The procedure starts with a definition of the continuum structure to be controlled. An evaluation model of finite dimension is obtained by the finite element method. Then, the finite element model is decomposed into several substructures by using a natural decomposition called substructuring decomposition. Each substructure, at this point, still has too large a dimension and must be reduced to a size that is Riccati-solvable. Model reduction of each substructure can be performed by using any existing model reduction method, e.g., modal truncation, balanced reduction, Krylov model reduction, or mixed-mode method. Then, based on the reduced substructure model, a subcontroller is designed by an LQ optimal control method for each substructure independently. After all subcontrollers are designed, a controller synthesis method called substructural controller synthesis is employed to synthesize all subcontrollers into a global controller. The assembling scheme used is the same as that employed for the structure matrices. Finally, a controller reduction scheme, called the equivalent impulse response energy controller (EIREC) reduction algorithm, is used to reduce the global controller to a reasonable size for implementation. The EIREC reduced controller preserves the impulse response energy of the full-order controller and has the property of matching low-frequency moments and low-frequency power moments. An advantage of the substructural controller synthesis method is that it relieves the computational burden associated with dimensionality. Besides that, the SCS design scheme is also a highly adaptable controller synthesis method for structures with varying configuration, or varying mass and stiffness properties

THE OPTIMAL PROJECTION EQUATIONS FOR FINITE-DIMENSIONAL FIXED-ORDER DYNAMIC COMPENSATION OF INFINITE-DIMENSIONAL SYSTEMS

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/57874/1/OptimalProjInfDiml1986.pd

Unified control/structure design and modeling research

To demonstrate the applicability of the control theory for distributed systems to large flexible space structures, research was focused on a model of a space antenna which consists of a rigid hub, flexible ribs, and a mesh reflecting surface. The space antenna model used is discussed along with the finite element approximation of the distributed model. The basic control problem is to design an optimal or near-optimal compensator to suppress the linear vibrations and rigid-body displacements of the structure. The application of an infinite dimensional Linear Quadratic Gaussian (LQG) control theory to flexible structure is discussed. Two basic approaches for robustness enhancement were investigated: loop transfer recovery and sensitivity optimization. A third approach synthesized from elements of these two basic approaches is currently under development. The control driven finite element approximation of flexible structures is discussed. Three sets of finite element basic vectors for computing functional control gains are compared. The possibility of constructing a finite element scheme to approximate the infinite dimensional Hamiltonian system directly, instead of indirectly is discussed

A classification of techniques for the compensation of time delayed processes. Part 2: Structurally optimised controllers

Following on from Part 1, Part 2 of the paper considers the use of structurally optimised controllers to compensate time delayed processes

Design and laboratory implementation of robust FACTS controller for inter-connected power systems

Imperial Users onl