George Halikias

Optimal design of PID controllers using the QFT method

An optimisation algorithm is proposed for designing PID controllers, which minimises the asymptotic open-loop gain of a system, subject to appropriate robust stability and performance QFT constraints. The algorithm is simple and can be used to automate the loop-shaping step of the QFT design procedure. The effectiveness of the method is illustrated with an example

Optimal loop-shaping for systems with large parameter uncertainty via linear programming

This paper describes an optimization method for designing feedback systems subject to large parameter uncertainty. Following the design philosophy of the Quantitative Feedback Theory (Horowitz and Sidi 1972, 1978) the objective is to minimize the magnitude of the open loop L(jω) at high frequencies subject to: (a) low and intermediate-frequency bounds capturing the closed-loop robust-performance objectives; (b) a universal-frequency bound on L(jω) which limits the effects of disturbances; and (c) realization constraints on L(s) in the form of Bodes integral. This last relation is discretized at a number of frequencies and defines, together with (a) and (b), the overall set of linear constraints in a resulting linear programming optimization problem.

Measuring Change Risk for Organisational Decision Making through a Hierarchical Model Process Approach

Project Management has long established the need for risk management techniques to be utilised in the succinct identification and mitigation of associated risks in projects. Such techniques aim at the reconciliation of countervailing project activities to reduce scope creep, increase the probability of on-time and within-budget delivery. Uncontrolled changes, regardless of size and complexity, can develop risks to projects and affect project success or even an organisation’s project delivery coherence. Ideally, a change or consequence based upon a decision should have a fairly high level of predictability and thus a low level of a potential risk materializing, which would significantly undo the decision taken. This paper proposes a novel modeling process approach; CRAM (Change Risk Assessment Model), which could significantly contribute to the missing formality of business models especially in the change risk assessment area.

State-space algorithm for the computation of superoptimal matrix interpolating functions

A state-space algorithm is studied which generates the (unique) superoptimal Nehari extension of a general rational matrix

A controller degree bound for H∞-optimal control problems of the second kind

. The procedure is to use a set of all-pass transformations to sequentially minimize each frequency-dependent singular value (of the interpolating function) in a dimension peeling algorithm. These all-pass transformations are determined by the maximal Schmidt pairs of a sequence of Hankel operators. The process terminates when the original problem is reduced to one of rank one; at this stage all the available degrees of freedom have been exhausted. The work is an extension of that by Young (1986) and gives a ‘concrete’ state-space implementation of his operator-theoretic arguments. In addition, bounds are given on the minimum achievable values for s1 ∞ (E) = supωeRSi (E(jω)), i = 1, 2,..., rank (G0), and also the McMillan degree of the final superoptimal extension. Here Si.(.) denotes the ith singular value of a (frequency-dependent) matrix, and the numbering is taken to be in decrea...

Modelling and H∞ control of a single-link flexible manipulator

The aim of this paper is to present further results on the cancellation phenomena which occur in H∞-optimal control problems which may be embedded in the generalized regulator configuration illustrated in Fig. 1. This is a continuation of the work in [6]. In this paper we concentrate on problems of the second kind which are characterized by the assumption that one of the off-diagonal blocks P12(s) or P21(s) is non-square. To fix ideas, we assume that P21(s) is square while P12(s) is tall. We also assume that P12(jω) and P21(jω) have full rank for all ω. If the McMillan degree of P(s) in Fig. 1 is n, we show that there is always an H∞-optimal controller requiring no more than 2n-1 states. Space limitations make it impossible to present proofs of the main steps in the argument.

Supply-chain modelling and control under proportional inventory-replenishment policies

Abstract The aim of this study is to investigate motion in the horizontal and the vertical planes of a single-link flexible manipulator. The manipulator is modelled including gravity terms, and it is verified experimentally that the horizontal and the vertical motions are decoupled for a cylindrically symmetrical link and payload. The mathematical model is used to design a mixed-sensitivity H∞ contrlllerr. The sensitivity weighting function is used to obtain the required disturbance rejection properties, including zero sensitivity to a force disturbance in the steady state (i. e. integral action control). The control sensitivity weighting function is chosen to guarantee stability despite variation in the payload mass. The controller is compared experimentally with a proportional-plus-integral controller with velocity feedback and shown to give improved vibration control performance in the vertical plane.

A state-space algorithm for the superoptimal Hankel-Norm approximation problem

A novel state-space model of a multi-node supply chain is presented, controlled via local proportional inventory-replenishment policies. The model is driven by a stochastic sequence representing customer demand. The model is analysed under stationarity conditions and a simple recursive scheme is developed for updating its covariance matrix. This allows us to characterise the ‘bullwhip effect’ (demand amplification) in the chain and to solve an optimisation problem for a three-node model involving the minimisation of inventory subject to a probabilistic constraint on downstream demand. Finally, issues related to estimation schemes based on local historical data are briefly discussed.

H/sub /spl infin// robust-performance control of decoupled active suspension systems based on LMI method

It has been demonstrated by N. T. Young [NATO ASI Series F34, Springer-Verlag, Berlin, New York, 1987] that given a stable matrix-valued function

An affine parametrization of all one-block H ∞ -optimal matrix interpolating functions

G_0 (s)