Non linear system identification : a state-space approach

In this thesis, new system identication methods are presented for three particular types of nonlinear systems: linear parameter-varying state-space systems, bilinear state-space systems, and local linear state-space systems. Although most work on nonlinear system identication deals with nonlinear input-output descriptions, this thesis focuses on state-space descriptions. State-space systems are considered, because they are especially suitable for dealing with multiple inputs and outputs, and they usually require less parameters to describe a system than input-output descriptions do. Equally important, the starting point of many nonlinear control methods is a state-space model of the system to be controlled

A novel indirect control methodology for load-leveling of space heating appliances

Demand Side Management (DSM) programs provide utility companies with amethod to shift consumer electricity usages away from peak electricity hours. DSMprograms use alternative appliance usage schemes that maintain their usefulness whileproviding ancillary services for utilities. This thesis aims to develop a linear controlmethodology that can provide signicant ancillary services for utilities without re-ducing customer comfort.A prototype enclosure was built and equipped with a heater and thermalmeasuring equipment. Data was collected during a 17 hour temperature regulationexperiment using a bang-bang controller similar to those commonly used for residen-tial heating control. An experimental thermal system identication methodology wasdeveloped for online system identication. First and second order mathematical mod-els were developed for thermal system identication. The mathematical models werecalibrated using data collected experimentally and used to estimate the net thermalresistance and capacitance using system identication techniques.The enclosure system model was also used to determine if peak power couldbe reduced by slowly varying loads utilizing a dierent type of controller. Two dier-ent linear control techniques (using K-Factor and PI approaches) and the associatedpower electronics circuitry were implemented and tuned in PSpice platform. Both controller systems successfully leveled the load and reduced the peak power demand.Finally the prototype enclosure was modied to include a linear controller us-ing an available DC power supply and a buck converter power stage. The PI controlscheme was used with a 60 phase margin for smoother and faster settling charac-teristics. The phase margin was acquired using appropriate linear approximation ofsystem transfer functions. The temperature response of the experimental system wascompared to theoretical responses

A system identication approach to baroreflex sensitivity estimation

The body contains a bewildering array of regulatory systems which maintain homeostasis. There is considerable dificulty in isolating a single control loop for analysis, due to the interactions with other systems/loops. One important such regulatory loop is the baroreflex, and baroreflex sensitivity is a characteristic open-loop parameter which can help us to assess the health of the baroreflex. A diverse range of methods have been proposed to determine baroreflex sensitivity from experimental data. Unfortunately, there appears to be little consistency of result among the different methods and some explanation can be found in the nature of the problem: In most cases, an attempt is being made to determine open-loop measures from a system operating in closed-loop, subject to poor excitation. In this paper we propose a strict procedure, based on a rigourous mathematical framework, from which reliable estimates of baroreflex sensitivity can be obtained. A comparison with other methods for baroreflex sensitivity estimation, using the EuroBaVar data set, is performed

A new kernel-based approach for overparameterized Hammerstein system identification

In this paper we propose a new identification scheme for Hammerstein systems, which are dynamic systems consisting of a static nonlinearity and a linear time-invariant dynamic system in cascade. We assume that the nonlinear function can be described as a linear combination of $p$ basis functions. We reconstruct the $p$ coefficients of the nonlinearity together with the first $n$ samples of the impulse response of the linear system by estimating an $np$-dimensional overparameterized vector, which contains all the combinations of the unknown variables. To avoid high variance in these estimates, we adopt a regularized kernel-based approach and, in particular, we introduce a new kernel tailored for Hammerstein system identification. We show that the resulting scheme provides an estimate of the overparameterized vector that can be uniquely decomposed as the combination of an impulse response and $p$ coefficients of the static nonlinearity. We also show, through several numerical experiments, that the proposed method compares very favorably with two standard methods for Hammerstein system identification.Comment: 17 pages, submitted to IEEE Conference on Decision and Control 201

Dynamic mode decomposition with control

We develop a new method which extends Dynamic Mode Decomposition (DMD) to incorporate the effect of control to extract low-order models from high-dimensional, complex systems. DMD finds spatial-temporal coherent modes, connects local-linear analysis to nonlinear operator theory, and provides an equation-free architecture which is compatible with compressive sensing. In actuated systems, DMD is incapable of producing an input-output model; moreover, the dynamics and the modes will be corrupted by external forcing. Our new method, Dynamic Mode Decomposition with control (DMDc), capitalizes on all of the advantages of DMD and provides the additional innovation of being able to disambiguate between the underlying dynamics and the effects of actuation, resulting in accurate input-output models. The method is data-driven in that it does not require knowledge of the underlying governing equations, only snapshots of state and actuation data from historical, experimental, or black-box simulations. We demonstrate the method on high-dimensional dynamical systems, including a model with relevance to the analysis of infectious disease data with mass vaccination (actuation).Comment: 10 pages, 4 figure

An Algorithmic Approach to Loop Shaping With Applications to Self-Tuning Control Systems

An algorithmic approach to feedback control design is introduced. It simplifies the existing iterative design process, which is often tedious, by reducing the design problem to solving a set of linear algebraic equations. The algorithmic nature of such an approach makes it attrative to not only off-line designs but also self-tuning control systems, where the compensators are continuously tuned on-line as the dynamics of the physical process vary with time. This is demonstrated in the example where the proposed algorithm is implemented for an industrial tension regulation system with successful simulation results. Extensions of the algorithm to multi-input and multi-output systems, as well as discrete time systems, are also introduced