Optimal H2 order-one reduction by solving eigenproblems for polynomial equations

A method is given for solving an optimal H2 approximation problem for SISO linear time-invariant stable systems. The method, based on constructive algebra, guarantees that the global optimum is found; it does not involve any gradient-based search, and hence avoids the usual problems of local minima. We examine mostly the case when the model order is reduced by one, and when the original system has distinct poles. This case exhibits special structure which allows us to provide a complete solution. The problem is converted into linear algebra by exhibiting a finite-dimensional basis for a certain space, and can then be solved by eigenvalue calculations, following the methods developed by Stetter and Moeller. The use of Buchberger's algorithm is avoided by writing the first-order optimality conditions in a special form, from which a Groebner basis is immediately available. Compared with our previous work the method presented here has much smaller time and memory requirements, and can therefore be applied to systems of significantly higher McMillan degree. In addition, some hypotheses which were required in the previous work have been removed. Some examples are included.

CLADP - THE CAMBRIDGE LINEAR ANALYSIS AND DESIGN PROGRAMS USER REFERENCE MANUAL (4TH ISSUE: APRIL 1983).

CLADP is an engineering software program developed at Cambridge University for the interactive computer aided design of feedback control systems. CLADP contains a wide range of tools for the analysis of complex systems, and the assessment of their performance when feedback control is applied, thus enabling control systems to be designed to meet difficult performance objectives. The range of tools within CLADP include the latest techniques in the field whose central theme is the extension of classical frequency domain concepts (well known and well proven for single loop systems) to multivariable or multiloop systems, and by making extensive use of graphical presentation information is provided in a readily understood form.

CLADP: THE CAMBRIDGE LINEAR ANALYSIS AND DESIGN PROGRAMS.

An interactive software facility for designing multivariable control systems is described. The paper discusses the desirable characteristics of such a facility, the particular capabilities of CLADP and the numerical algorithms which lie behind them.

Bypass transition to sustained thermoacoustic oscillations in a linearly stable rijke tube

In this paper we examine triggering in a simple linearly-stable thermoacoustic system using techniques from flow instability and optimal control. Firstly, for a noiseless system, we find the initial states that have highest energy growth over given times and from given energies. Secondly, by varying the initial energy, we find the lowest energy that just triggers to a stable periodic solution. We show that the corresponding initial state grows first towards an unstable periodic solution and, from there, to the stable periodic solution. This exploits linear transient growth, which arises due to nonnormality in the governing equations and is directly analogous to bypass transition to turbulence. Thirdly, we introduce noise that has similar spectral characteristics to this initial state. We show that, when triggering from low noise levels, the system grows to high amplitude self-sustained oscillations by first growing towards the unstable periodic solution of the noiseless system. This helps to explain the experimental observation that linearly-stable systems can trigger to self-sustained oscillations even with low background noise. © 2010 by University of Cambridge. Published by the American Institute of Aeronautics and Astronautics, Inc.

Surface excavation with model predictive control

This paper describes the application of variable-horizon model predictive control to trajectory generation in surface excavation. A nonlinear dynamic model of a surface mining machine digging in oil sand is developed as a test platform. This model is then stabilised with an inner-loop controller before being linearised to generate a prediction model. The linear model is used to design a predictive controller for trajectory generation. A variable horizon formulation is augmented with extra terms in the cost function to allow more control over digging, whilst still preserving the guarantee of finite-time completion. Simulations show the generation of realistic trajectories, motivating new applications of variable horizon MPC for autonomy that go beyond the realm of vehicle path planning. ©2010 IEEE.

Some biocybernetic aspects in gene expression and regulatory control

In eucaryotes, gene expression and control is a complex nonlinear process, where there are many control mechanisms and ways, both physic, chemical and informational control. By the exploration from the angle of biocybernetics, the authors suggest that gene expression is a co-control process. In this process, physic, chemical and informational feedback controls are associated and influential each other, and are cross and co-functional. The physic, chemical and informational control ways composed an order non-linear feedback control system in eucaryotes.

Hybrid model predictive control applied to switching control of burner load for a compact marine boi

This paper discusses the application of hybrid model predictive control to control switching between different burner modes in a novel compact marine boiler design. A further purpose of the present work is to point out problems with finite horizon model predictive control applied to systems for which the optimal solution is a limit cycle. Regarding the marine boiler control the aim is to find an optimal control strategy which minimizes a trade-off between deviations in boiler pressure and water level from their respective setpoints while limiting burner switches.The approach taken is based on the Mixed Logic Dynamical framework. The whole boiler systems is modelled in this framework and a model predictive controller is designed. However to facilitate on-line implementation only a small part of the search tree in the mixed integer optimization is evaluated to find out whether a switch should occur or not. The strategy is verified on a simulation model of the compact marine boiler for control of low/high burner load switches. It is shown that even though performance is adequate for some disturbance levels it becomes deteriorated when the optimal solution is a limit cycle. Copyright © 2007 International Federation of Automatic Control All Rights Reserved.

Multiplexed model predictive control

Most academic control schemes for MIMO systems assume all the control variables are updated simultaneously. MPC outperforms other control strategies through its ability to deal with constraints. This requires on-line optimization, hence computational complexity can become an issue when applying MPC to complex systems with fast response times. The multiplexed MPC scheme described in this paper solves the MPC problem for each subsystem sequentially, and updates subsystem controls as soon as the solution is available, thus distributing the control moves over a complete update cycle. The resulting computational speed-up allows faster response to disturbances, and hence improved performance, despite finding sub-optimal solutions to the original problem. The multiplexed MPC scheme is also closer to industrial practice in many cases. This paper presents initial stability results for two variants of multiplexed MPC, and illustrates the performance benefit by an example. Copyright copy; 2005 IFAC. Copyright © 2005 IFAC.

Mathematical relationships between representations of structure in linear interconnected dynamical systems

A dynamical system can exhibit structure on multiple levels. Different system representations can capture different elements of a dynamical system's structure. We consider LTI input-output dynamical systems and present four representations of structure: complete computational structure, subsystem structure, signal structure, and input output sparsity structure. We then explore some of the mathematical relationships that relate these different representations of structure. In particular, we show that signal and subsystem structure are fundamentally different ways of representing system structure. A signal structure does not always specify a unique subsystem structure nor does subsystem structure always specify a unique signal structure. We illustrate these concepts with a numerical example. © 2011 AACC American Automatic Control Council.

Force ripple compensation in a tubular linear generator for marine renewable generation

Tubular permanent magnet linear generators are a promising generator technology for use in marine renewables. One aspect of their design relates to the conditions necessary for achieving a smooth thrust response from the generator, free from cogging and periodic variations due to spatial harmonics of the flux cutting the generator coils. This paper presents an experimental and finite element study of the sources of thrust ripple in a prototype linear generator for marine generation. A simple self-commutated control scheme is shown, which uses linear Hall-effect sensors and look-up-table based feed-forward compensation to derive the excitation currents required to drive the machine with constant force. Details of the controller's FPGA based implementation are given, including its strategy for detecting sensor failure. © 2011 IEEE.

Multiplexed model predictive control

This paper proposes a form of MPC in which the control variables are moved asynchronously. This contrasts with most MIMO control schemes, which assume that all variables are updated simultaneously. MPC outperforms other control strategies through its ability to deal with constraints. This requires on-line optimization, hence computational complexity can become an issue when applying MPC to complex systems with fast response times. The Multiplexed MPC (MMPC) scheme described in this paper solves the MPC problem for each subsystem sequentially, and updates subsystem controls as soon as the solution is available, thus distributing the control moves over a complete update cycle. The resulting computational speed-up allows faster response to disturbances, which may result in improved performance, despite finding sub-optimal solutions to the original problem. This paper describes nominal and robust MMPC, states some stability results, and demonstrates the effectiveness of MMPC through two examples. © 2011 Elsevier Ltd. All rights reserved.

Bias-free identification of a linear model-predictive steering controller from measured driver steering behavior

Recent developments in modeling driver steering control with preview are reviewed. While some validation with experimental data has been presented, the rigorous application of formal system identification methods has not yet been attempted. This paper describes a steering controller based on linear model-predictive control. An indirect identification method that minimizes steering angle prediction error is developed. Special attention is given to filtering the prediction error so as to avoid identification bias that arises from the closed-loop operation of the driver-vehicle system. The identification procedure is applied to data collected from 14 test drivers performing double lane change maneuvers in an instrumented vehicle. It is found that the identification procedure successfully finds parameter values for the model that give small prediction errors. The procedure is also able to distinguish between the different steering strategies adopted by the test drivers. © 2006 IEEE.

Active control of high-frequency vibration: Optimisation using the hybrid modelling method

This work presents active control of high-frequency vibration using skyhook dampers. The choice of the damper gain and its optimal location is crucial for the effective implementation of active vibration control. In vibration control, certain sensor/actuator locations are preferable for reducing structural vibration while using minimum control effort. In order to perform optimisation on a general built-up structure to control vibration, it is necessary to have a good modelling technique to predict the performance of the controller. The present work exploits the hybrid modelling approach, which combines the finite element method (FEM) and statistical energy analysis (SEA) to provide efficient response predictions at medium to high frequencies. The hybrid method is implemented here for a general network of plates, coupled via springs, to allow study of a variety of generic control design problems. By combining the hybrid method with numerical optimisation using a genetic algorithm, optimal skyhook damper gains and locations are obtained. The optimal controller gain and location found from the hybrid method are compared with results from a deterministic modelling method. Good agreement between the results is observed, whereas results from the hybrid method are found in a significantly reduced amount of time. © 2012 Elsevier Ltd. All rights reserved.