Multirate control and multiscale monitoring of chemical processes

Multirate (MR) systems arise due to the limitations on the output sampling rates and input adjustment rates of the physical variables. They are inherently more complex and challenging than single-rate (SR) systems and yet, practically important.; The concept of ‘lifting’, is used in this thesis to analyze multirate systems. It is shown that lifting techniques can give rise to intersample ripples in the closed-loop outputs of the MR system. These ripples can be eliminated if the lifted controller satisfies certain gain constraints or by incorporating an integrator at the input rate.; Due to the limitation on the sampling rates, control of multirate systems can be limited by the slowest available measurement, defined here as slow single rate (SSR) control. A natural problem of interest is to explore the benefits that lifted MR control systems can offer over SSR control systems. In this thesis, we address the performance issue: what are the upper and lower bounds on the performance of multirate systems? We also answer the question: can we get better performance with fast single-rate control (FSR) (sampling at faster rates )? The main contribution of this thesis is a proof that the optimal performance of MR systems is bounded above by that of SSR systems and bounded below by that of FSR systems, with the continuous-time LQR cost function and the generalized $H2$-norm as the benchmarks. In the presence of a model-plant mismatch, the sensitivity of the performance benefits is analyzed for first-order SISO systems.; Multirate representations of data are a special case of a more general class of representations, known as multiscale representations, which can capture the inherent different/multiple time-frequency scales. These representations are obtained by employing wavelet transforms.; The last part of this thesis focusses on monitoring of multiscale systems using a combination of wavelet transformation with PCA, known as Multiscale PCA (MSPCA). It is shown that MSPCA has several advantages over conventional PCA both in the theoretical and practical aspects. MSPCA provides an enhanced sensitivity towards and discrimination between detection of incipient and abrupt faults. Application of MSPCA to sheet-break diagnosis using data from a major pulp and paper mill is presented to highlight the potential of this technique.