Anthony Holohan

l1-Optimal regulation of a pH control plant

Abstract This paper presents an innovative approach to controller design, and applies it to the pH-control problem. The proposed approach uses a robust controller implemented with a full two-degree-of-freedom (2-DoF) structure. The first of “feedback” DoF was designed using a standard μ-synthesis approach. A procedure based on a novel variation of l1-optimal control theory is applied to design the second or “open loop” DoF. This design may be carried out completely independently of the first DoF, provided an appropriate factorization of the feedback controller is used. The approach is illustrated by the design and evaluation of a control system for a laboratory scale pH-control plant. The resulting controller was implemented and tested on the physical plant. It was found that it gave good performance over widely varying conditions. Specifically, the open loop properties of the μ-synthesis feedback controller acting on its own, were improved significantly by the use of a certain class of l1-optimal second DoF controller block. We conclude that the tradeoff between good command tracking and reasonable plant inputs given by a feedback controller can be improved by the use of the proposed approach, a novel variation on l1-optimization applied to the second DoF controller block.

Simplified overflow analysis of an optical burst switch with fibre delay lines

We develop an approximate analytic model of an Optical Burst Switch with share-per-node fibre delay lines and tuneable wavelength converters by employing Equivalent Random Theory, an approach from circuit-switching analysis. Our model is formulated in terms of virtual traffic flows within the switch from which we derive expressions for burst blocking probability, fibre delay line occupancy and mean delay, which we then resolve numerically. Emphasis is on simplicity of the model to achieve good numerical efficiency so that the method can be useful for formulating dimensioning problems for large-scale networks. Solution values from the analysis are compared with discrete-event simulation results.

On inverse problems in 2-norm and infinity-norm controller synthesis

Studies certain inverse problems in the optimal frequency-domain synthesis of robust controllers, in both the 2-norm and the infinity-norm. These inverse problems identify the class of controllers which are optimal for some choice of weights. Their implications for loopshaping are discussed.

Real-time control of electron density in a capacitively coupled plasma

Reactive ion etching (RIE) is sensitive to changes in chamber conditions, such as wall seasoning, which have a deleterious effect on process reproducibility. The application of real time, closed loop control to RIE may reduce this sensitivity and facilitate production with tighter tolerances. The real-time, closed loop control of plasma density with RF power in a capacitively coupled argon plasma using a hairpin resonance probe as a sensor is described. Elementary control analysis shows that an integral controller provides stable and effective set point tracking and disturbance attenuation. The trade off between performance and robustness may be quantified in terms of one parameter, namely the position of the closed loop pole. Experimental results are presented, which are consistent with the theoretical analysis.

Attenuation of wall disturbances in an electron cyclotron resonance oxygen–argon plasma using real time control

Present practice in plasma-assisted semiconductor manufacturing specifies recipes in terms of inputs such as gas flow rates, power and pressure. However, ostensibly identical chambers running identical recipes may produce very different results. Extensive chamber matching, i.e., initial iterative, empirical tuning of the process recipe, which entails time-consuming, ex situ statistical analysis of process metrics such as etch depth, uniformity, anisotropy and selectivity, is required to ensure acceptable results. Once matched, chambers are run open loop and are thus sensitive to disturbances such as actuator drift, wall seasoning and substrate loading, which may impact negatively on process reproducibility. An alternative approach, which may obviate the need for chamber matching and reduce the sensitivity of process metrics to exogenous disturbances, would be to specify a recipe in terms of quantities such as active species densities, and to regulate these in real time by adjusting the inputs with a suita...

PI Controller for Electron Density Control in Low Pressure Plasma

Abstract This paper reports a PID control application for real-time feedback control of electron density, n e , in a low pressure, capacitively coupled plasma chamber. Experimental results are presented which demonstrate that a PI controller enables effective control of electron density when radio frequency power is used as an actuator. A hairpin resonator probe is used to measure the electron density, when the resonator is placed in plasma, its characteristic resonance frequency in vacuum shifts to a higher value. From the frequency shifts, electron density can be easily determined. Actuation and data acquisition are briefly outlined.

Two-degrees-of-freedom compensators for systems with commands bounded in slope

Abstract The design of two-degrees-of-freedom controllers for systems with bounded signals is studied by application of the L\ theory to certain two-degrees-of-freedom structures. It is argued that this gives a natural approach for discrete-time systems with commands bounded in slope. A specific design strategy is proposed and illustrated by way of an example.

A New Algorithm for Robustness Analysis via the Structured Singular Value µ

Abstract In this paper, the problem of computing the structured singular value µ, (or equivalently, the multivariable stability margin k m or the robustness margin r max ) is considered. The problem of computing µ for the completely general case is known to be essentially intractable, being non-convex and NP-complete. Hence, following current practice (Packard and Doyle 1993), one considers computing an upper bound on µ, termed µ co , the computation of which is a convex problem. A key intermediate step is determining if a point belongs to a certain convex set. In this paper, a new algorithm is proposed and its performance compared with several alternatives. The main conclusions are that, when determining if a point belongs to this convex set, algorithms based on the 1-norm are faster than their 2-norm based counterparts, and algorithms based on the dual problem are faster than those based on the primal problem.