The internal model principle for linear multivariable regulators

Abstract

Necessary structural criteria are obtained for linear multivariable regulators which retain loop stability and output regulation in the presence of small perturbations, of specified types, in system parameters. It is shown that structural stability thus defined requires feedback of the regulated variable, together with a suitably reduplicated model, internal to the feedback loop, of the dynamic structure of the exogenous reference and disturbance signals which the regulator is required to process. Necessity of these structural features constitutes the 'internal model principle'.

Tracking Learning Feedforward Control for High-Speed CD-ROM

“…Since the LFF control signal operates as feedforward after learning, the performance of the existing servo controller in the feedback loop is maintained. A multiple LFF controller can be parallel added to the system to remove a few large harmonics (Francis et al, 1975) present in the error signal. However the learning rate, which will influence the convergence time of the system, is practically difficult to decide beforehand because of the noise of the radial error signal.…”

Asymptotic rejection of sinusoidal disturbances based voltage balance control in back-to-back power converters

“…The second goal is the asymptotic cancellation of the sinusoidal disturbances, that is, the asymptotic cancellation of the disturbances φ r and φ i defined in the previous section. In this way, to achieve a proper output regulation, suitable models of both disturbances should be included in the controller, as stated in [25,26]. The balancing methods here presented are based on an asymptotic disturbance rejection approach.…”

“…The proposed controllers estimate asymptotically the sinusoidal disturbances, having in common the idea of applying a control law to cancel them while regulating the capacitor voltage balance as well. The methods use some control concepts widely discussed in [25,26,[47][48][49], and also proposed for the neutral-point-clamped rectifier in [41,42], extending them to the multiple frequency approach of the back-to-back topology of the current paper.…”

Remarks on feedforward circuits, adaptation, and pulse memory

“…Section 6 revisits the motivating examples and also briefly discusses the systems in [11,29]. Finally, it is known that, under appropriate technical assumptions, perfect adaptation implies that the system may be written, after a suitable nonlinear change of coordinates, as a system in which the integral of the regulated quantify is fed-back, see for instance [6,7,31,24]. This fact is not incompatible with the system being a feedforward system, as remarked in Section 7.…”