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The steady-state input/output structure of the infinite horizon LQ bumpless transfer topologies for strictly proper controllers is analyzed. It is found that in these topologies (1) the steady-state gain of the transfer function from the output of the online controller to that of the offline one is unity/asymptotically unity, and (2) the steady-state gain of the transfer function from the input of the online controller to the output of the offline one is zero/asymptotically zero, for essentially all strictly proper controllers with the input dimension being no less than the output one. These facts (1) reveal the steady-state gain structure of the closed-loop transfer matrix in the standard LQ tracking problems, (2) demonstrate that the LQ bumpless transfer technique solves the ideal bumpless transfer problem for controllers with an integrator in each of their output channels, (3) reveal the structure of unavoidable signal discontinuities in the controller input/output upon transfer between controllers with non-integrating channels, and (4) provide guidance for minimizing the above signal discontinuities and the resulting bumps in the plant output in bumpless transfer synthesis. Copyright © 2009 John Wiley & Sons, Ltd.

The state/output feedback topology required for bumpless transfer under controller uncertainty is considered. A steady-state diagonal dominance condition for a subsystem of this topology is derived, which is shown to be sufficient for the existence of the stabilizing decentralized mismatch compensator parameters. Recent results on the input/output steady-state gain structure of the one-degree-of-freedom and the two-degrees-of-freedom infinite horizon LQ bumpless transfer topologies are used to show that the diagonal dominance condition applies to topologies generated by a broad class of controllers, thus completing the state/output feedback bumpless transfer technique. The topologies are also shown to be robust with respect to uncertainty in the mismatch compensator. Copyright © 2008 John Wiley & Sons, Ltd.

Through the combination of the sequential spectral factorization and the coprime factorization, a k-step ahead MIMO H∞ (cumulative minimax) predictor is derived which is stable for the unstable noise model. This predictor and the modified internal model of the reference signal are embedded into the H∞ optimization framework, yielding a single degree of freedom multi-input–multi-output H∞ predictive controller that provides stochastic disturbance rejection and asymptotic tracking of the reference signals described by the internal model. It is shown that for a plant/disturbance model, that represents a large class of systems, the inclusion of the H∞ predictor into the H∞ control algorithm introduces a performance/robustness tuning knob: an increase of the prediction horizon enforces a more conservative control effort and, correspondingly, results in deterioration of the transient and the steady-state (tracking error variance) performance, but guarantees large robustness margin, while the decrease of the prediction horizon results in a more aggressive control signal and better transient and steady-state performance, but smaller robustness margin. Copyright © 2001 John Wiley & Sons, Ltd.

Does the replacement of the quadratic (H2) predictor by the worst-case (H∞, or cumulative minimax) predictor robustify the predictive control laws? The present work provides a partial answer to this question, positive for the examples considered, representative of three broad classes of systems. The H∞ prediction is demonstrated to be a powerful and convenient tool for frequency shaping of the gain of the closed-loop complementary sensitivity function, capable of robustifying the closed loop for systems with different stability properties. The H∞-optimal k-step ahead predictor is derived for an unstable single-input–single- output CARMA model. A BIBO unstable filter for the disturbance rejection is obtained using the internal model principle and included into the closed loop, and the H∞ predictor is applied to the combination of this filter with the plant. The sum over a finite horizon of the current and the predicted tracking error and control signal power spectral densities (PSDs) is decomposed into two parts, one induced by the worst-case predicted disturbance and the other—by the known future reference input. A two degrees of freedom algorithm, referred to as the multi-step closed-loop polynomial H∞ predictive control law, is obtained that minimizes the peaks of the PSD of the first part and the integral on the unit circle of the PSD of the second. It is demonstrated on several systems that H∞ prediction introduces a very intuitive tuning knob in the form of the prediction horizon capable of setting a trade-off between the steady-state disturbance rejection perfor mance in terms of the output error variance and the closed-loop robustness, however the efficacy of the knob strongly depends on the stability properties of the system and its inverse. The trade-off becomes less pronounced or completely disappears when the H∞ predictor is replaced by the quadratic one. Copyright © 2000 John Wiley & Sons, Ltd.

This paper examines the ability of the H∞ design methodology to provide a solution to a gas- or oil-fired boiler control problem, and addresses the nontrivial application issues of the H∞ design. The H∞ methodology is applied to an experimentally verified heating-cogeneration boiler model which exhibits nonlinearities, instability, time delays, non-minimum phase behaviour, and coloured noise disturbances with sensor noise in the frequency range of the significant plant dynamics. The design shows that, to satisfy performance criteria, a high order controller is needed. The paper also demonstrates a trade-off between the reduction of controller order and the loss of controller performance.