Clas A. Jacobson

Control oriented system identification: a worst-case/deterministic approach in H/sub infinity /

The authors formulate and solve two related control-oriented system identification problems for stable linear shift-invariant distributed parameter plants. In each of these problems the assumed a priori information is minimal, consisting only of a lower bound on the relative stability of the plant, an upper bound on a certain gain associated with the plant, and an upper bound on the noise level. The first of these problems involves identification of a point sample of the plant frequency response from a noisy, finite, output time series obtained in response to an applied sinusoidal input with frequency corresponding to the frequency point of interest. This problem leads naturally to the second problem, which involves identification of the plant transfer function in H/sub infinity / from a finite number of noisy point samples of the plant frequency response. Concrete plans for identification algorithms are provided for each of these two problems. >

An adaptive algorithm for control of combustion instability

We propose an adaptive algorithm for control of combustion instability suitable for reduction of acoustic pressure oscillations in gas turbine engines, and main burners and augmentors of jet engines over a large range of operating conditions, and supply an experimental demonstration of oscillation attenuation, the first for a large industrial-scale gas turbine combustor. The algorithm consists of an Extended Kalman Filter based frequency tracking observer to determine the in-phase component, the quadrature component, and the magnitude of the acoustic mode of interest, and a phase shifting controller actuating fuel-flow, with the controller phase tuned using extremum-seeking. The paper also identifies a closed-loop model with phase-shifting control of combustion instability from experimental data; supplies stability analysis of the adaptive scheme based upon the identified model, and stable extremum-seeking designs used in experiments.

Linear state-space systems in infinite-dimensional space: the role and characterization of joint stabilizability/detectability

Several fundamental results from the theory of linear state-space systems in finite-dimensional space are extended to encompass a class of linear state-space systems in infinite-dimensional space. The results treated are those pertaining to the relationship between input-output and internal stability, the problem of dynamic output feedback stabilization, and the concept of joint stabilizability/detectability. A complete structural characterization of jointly stabilizable/detectable systems is obtained. The generalized theory applies to a large class of linear state-space systems, assuming only that: (i) the evolution of the state is governed by a strongly continuous semigroup of bounded linear operators; (ii) the state space is Hilbert space; (iii) the input and output spaces are finite-dimensional; and (iv) the sensing and control operators are bounded. General conclusions regarding the fundamental structure of control-theoretic problems in infinite-dimensional space can be drawn from these results. >

Adaptive control of combustion instability using extremum-seeking

We present results of experiment with two distinct extremum-seeking adaptive algorithms for control of combustion instability suitable for reduction of acoustic pressure oscillations in gas turbine over large range of operating conditions. The algorithms consists of a frequency tracking extended Kalman filter to determine the in-phase component, the quadrature component, and the magnitude of the acoustic mode of interest, and a phase shifting controller with the controller phase tuned using an extremum-seeking algorithms. Even though the algorithms were designed specifically for control of combustion instability in gas turbine engines, they are applicable for control of oscillations of systems whose oscillation frequency and optimal control phase shift depends on operating conditions, and which are driven by strong broad-band disturbance. The algorithms have been tested in combustion experiments involving full-scale engine hardware and during simulated fast engine transients.

Linear and nonlinear analysis of controlled combustion processes. II. Nonlinear analysis

The results of analysis using a reduced-order model of combustion instability derived at UTRC and experiments with active control using fuel modulation motivated a study of what performance is achievable using active control. Limitations due to lightly damped or unstable eigenvalues, delay, disturbances, and limited actuator authority and bandwidth are studied. In this part of the paper we focus on linear analysis of a combustion model and study effect of delay in the model and limited actuator bandwidth.

Worst-case/deterministic identification in H/sub infinity /: the continuous-time case

Results obtained by the authors (1991) worst-case/deterministic H/sub infinity / identification of discrete-time plants are extended to continuous-time plants. The problem involves identification of the transfer function of a stable strictly proper continuous-time plant from a finite number of noisy point samples of the plant frequency response. The assumed information consists of a lower bound on the relative stability of the plant, an upper bound on a certain gain associated with the plant, an upper bound on the roll-off rate of the plant, and an upper bound on the noise level. Concrete plans of identification algorithms are provided for this problem. Explicit worst-case/deterministic error bounds for each algorithm establish that they are robustly convergent and (essentially) asymptotically optimal. Additionally, these bounds provide an a priori computable H/sub infinity / uncertainty specification, corresponding to the resulting identified plant transfer function, as an explicit function of the plant and noise prior information and the data cardinality. >

Least squares methods for H/sub infinity / control-oriented system identification

A series of system identification algorithms that yield identified models which are compatible with current robust controller design methodologies is presented. These algorithms are applicable to a broad class of stable, distributed, linear, shift-invariant plants. The a priori information necessary for their application consists of a lower bound on the relative stability of the unknown plant, an upper bound on a certain gain associated with the unknown plant, and an upper bound on the noise level. The a posteriori data information consists of a finite number of corrugated point frequency response estimates of the unknown plant. The extent to which certain standard Hilbert-space or least-squares method are applicable to the H/sub infinity / system identification problem considered is examined. Results are established that connect the H/sub 2/ error of the least-squares methods to the H/sub infinity / error needed for control-oriented system identification. >

Design of robust controllers for resonant DC/DC converters

This paper pursues a quantitative feedback theory (QFT) approach to robust controller design for series resonant DC/DC converters. The model is derived using the generalized averaging procedure and the design approach explicitly reveals the tradeoffs involved in the controller synthesis. A nonlinear model is used to verify the performance of the compensator under several load transients.

Limits of achievable performance of controlled combustion processes

This paper presents a fundamental limitations-based analysis to quantify limits on obtainable performance for active control of combustion (thermoacoustic) instability. Experimental data from combustor rigs and physics-based models are used to motivate the relevance of both the linear and nonlinear thermoacoustic models. For linear models, Bode integral-based analysis is used to explain peak-splitting observed in experiments. It is shown that large delay in the feedback loop and limited actuator bandwidth are the primary factors that limits the effectiveness of the active control. Explicit bounds on obtainable performance in the presence of delay, unstable dynamics, and limited controller bandwidth are obtained. A multi-input describing function framework is proposed to extend this analysis to the study of nonlinear models that also incorporate the effects of noise. The fundamental limitations are interpreted for a modified sensitivity function defined with respect to noise balance. The framework is applied to the analysis of linear thermoacoustic models with nonlinear on-off actuators and Gaussian noise. The results of the analysis are well-supported by experiments and model simulations. In particular, we reproduce in model simulations and explain analytically the peak-splitting phenomenon observed in experiments

Ill-posed distributed parameter systems: a control viewpoint

The use of linear time-invariant distributed parameter systems (LTIDPSs) as models of physical processes is considered from a control viewpoint. Specifically, classes of LTIDPSs exhibiting properties which potentially limit their usefulness in feedback design are defined and termed ill-posed. The structure of these classes is investigated within a general mathematical framework which encompasses many distributed parameter systems of engineering interest. Within this framework necessary and sufficient conditions are derived which completely characterize these classes and establish their equivalence. >