System Identification I

This dissertation focuses on efficiently forming reduced-order models for large, linear dynamic systems. Projections onto unions of Krylov subspaces lead to a class of reduced-order models known as rational interpolants. The cornerstone of this dissertation is a collection of theory relating Krylov projection to rational interpolation. Based on this theoretical framework, three algorithms for model reduction are proposed. The first
algorithm, dual rational Arnoldi, is a numerically reliable approach involving orthogonal projection matrices. The second, rational Lanczos, is an efficient generalization of existing Lanczos-based methods. The third, rational power Krylov, avoids orthogonalization and is suited for parallel or approximate computations. The performance of the three algorithms is compared via a combination of theory and examples. Independent of the precise algorithm, a host of supporting tools are also develop ed to form a complete model-reduction package. Techniques for choosing the matching frequencies, estimating the modeling error, insuring the model's stability, treating multiple-input multiple-output systems, implementing parallelism, and avoiding a need for exact factors of large matrix
pencils are all examined to various degrees

https://tel.archives-ouvertes.fr/tel-01711328/document

Krylov Projection Methods for Model Reduction

We consider the problem of security constrained optimal control for discrete-time, linear dynamical systems in which control and measurement packets are transmitted over a communication network. The packets may be jammed or compromised by a malicious adversary. For a class of denial-of-service (DoS) attack models, the goal is to find an (optimal) causal feedback controller that minimizes a given objective function subject to safety and power constraints. We present a semi-definite programming based solution for solving this problem. Our analysis also presents insights on the effect of attack models on solution of the optimal control problem.

Safe and Secure Networked Control Systems under Denial-of-Service Attacks

In this paper, we present two novel algorithms to realize a finite dimensional, linear time-invariant state-space model from input-output data. The algorithms have a number of common features. They are classified as one of the subspace model identification schemes, in that a major part of the identification problem consists of calculating specially structured subspaces of spaces defined by the input-output data. This structure is then exploited in the calculation of a realization. Another common feature is their algorithmic organization: an RQ factorization followed by a singular value decomposition and the solution of an overdetermined set (or sets) of equations. The schemes assume that the underlying system has an output-error structure and that a measurable input sequence is available. The latter characteristic indicates that both schemes are versions of the MIMO Output-Error State Space model identification (MOESP) approach. The first algorithm is denoted in particular as the (elementary MOESP scheme)...

Subspace model identification-Part 1. The output-error state-space model identification class of algorithms

Model predictive control (MPC) has demonstrated exceptional success for the high-performance control of complex systems [1], [2]. The conceptual simplicity of MPC as well as its ability to effectively cope with the complex dynamics of systems with multiple inputs and outputs, input and state/output constraints, and conflicting control objectives have made it an attractive multivariable constrained control approach [1]. MPC (a.k.a. receding-horizon control) solves an open-loop constrained optimal control problem (OCP) repeatedly in a receding-horizon manner [3]. The OCP is solved over a finite sequence of control actions {u0,u1,f,uN- 1} at every sampling time instant that the current state of the system is measured. The first element of the sequence of optimal control actions is applied to the system, and the computations are then repeated at the next sampling time. Thus, MPC replaces a feedback control law p(m), which can have formidable offline computation, with the repeated solution of an open-loop OCP [2]. In fact, repeated solution of the OCP confers an "implicit" feedback action to MPC to cope with system uncertainties and disturbances. Alternatively, explicit MPC approaches circumvent the need to solve an OCP online by deriving relationships for the optimal control actions in terms of an "explicit" function of the state and reference vectors. However, explicit MPC is not typically intended to replace standard MPC but, rather, to extend its area of application [4]-[6].

/pdf/stochastic-model-predictive-control-an-overview-and-1kyy9166uh.pdf

Stochastic Model Predictive Control: An Overview and Perspectives for Future Research

Iterative Learning Control (ILC) enables high tracking performance of batch repetitive processes. Common ILC approaches resort to discrete time system representations and hence are not able to guarantee good intersample behavior in case the underlying system evolves in continuous time. The aim of this paper is to explicitly deal with the intersample behavior in ILC. A multirate, parametric, and low-order approach to both identification for ILC and subsequent optimal ILC is presented that results in a low computational burden. The approach appropriately deals with the time-varying nature of multirate systems. The proposed multirate identification and ILC algorithms are shown to outperform common ILC approaches in a simulation example.

/pdf/low-order-system-identification-and-optimal-control-of-18oitigu33.pdf

Low-order system identification and optimal control of intersample behavior in ILC

In fixed-point implementation of digital controllers, the effects of quantisation can be reduced by proper scaling of the controller parameters. Commonly, controllers are scaled using l/sub 1/ norm based calculations, i.e. determining the worst case impulse response of the controller. However, this is only possible if the controller is asymptotically stable. If this is not the case, a solution is to calculate the scaling transformation on the basis of the closed-loop impulse responses. From the experience with actual implementation on a compact disc system, frequency weighting reflecting the disturbance spectrum has to be applied as well in order to obtain good experimental results.

Closed loop l/sub 1/ scaling for fixed-point digital control implementation

This paper introduces a dynamic simulation model for investigation of local and transient effects in catalytic reaction systems. More specifically, the model allows inspection of the effects of supplying thermal energy directly to the catalytic particles in stead of applying energy to the whole reactor volume. With simulation results it is shown that for a certain type of catalytic reaction system the obtainable yield of product and the selectivity of the reaction toward that product can be significantly increased when thermal energy is supplied directly to the catalyst. It is also shown that the results can be improved even further by supplying thermal energy periodically in stead of continuously.

/pdf/modeling-local-periodic-temperature-variation-in-catalytic-4hadnpnk9i.pdf

Modeling local/periodic temperature variation in catalytic reactions

In this paper a novel method is presented for the reduction of bias caused by harmonic excitation in the identification of higher order sinusoidal input describing functions (HOSIDF). HOSIDF are a recently introduced generalization of the theory of the describing function. HOSIDF describe the magnitude and phase relations between the individual harmonic components in the output signal of a non-linear system and the sinusoidal excitation signal. In the presented method, the output signal of a non-linear system subjected to harmonic excitation is numerically split up into a fraction caused by the non-linear response due to the fundamental input signal component and the fraction caused by the quasi-linear response due to the harmonic input signal components. This separation is based on the assumption that the non-linear effects of intermodulation can be neglected, compared to the the effects caused by the generation of harmonics and gain compression/expansion. The method is demonstrated with real measurements on a mechanical system with friction.

http://www.mate.tue.nl/mate/pdfs/9675.pdf

Bias Removal in Higher Order Sinusoidal Input Describing Functions

Vacuum operation and increasing performance requirements lead to the design of lightweight stages. As a result, stages become flexible and exhibit internal deformations while tasks are performed. The aim of this research is to accept and explicitly compensate for the flexible plant behavior in control design. Control techniques that explicitly address flexible plant behavior include methods based on overactuation/oversensing [5] and inferential control [2]. In the latter case, the performance variables are not equal to sensed variables. A typical example involves the internal deformation of a stage, since the position measurement is performed at the edge of the stage, while performance should be achieved in a central position. Hence, the performance of the system has to be predicted by means of a model, since it cannot be measured. In this case, the performance of the system crucially depends on the quality of the underlying model. In this research, an approach to model-based control of multivariable flexible systems is investigated that can roughly be divided into three steps, see Figure 1. Firstly, a novel approach that can deal with the experimental modeling of flexible multivariable systems is being developed, see [4] and [1]. The experimental modeling approach in [4] enables an inexpensive, fast, and accurate identification of flexible systems in view of subsequent compensation of the dominant flexible behavior. Specifically, a low-order multivariable model is obtained that emphasizes the control-relevant flexible dynamics. Secondly, a model validation approach is being investigated, see [3]. Model validation amounts to testing the predictive power of the model using new data sets. Model validation 1) is an essential ingredient if the practical limit of compensating the flexible plant behavior is being determined; 2) is crucial if the performance of the system is predicted, as is the case in inferential control; 3) enables a characterization of the obtained model quality by means of an uncertainty model. Thirdly, optimal control of flexible multivariable systems is considered, extending the rigid-body approach in [6] to enable the control design for flexible systems. The control approach enables a direct multivariable control design, using the model from Step 1, while taking into account the model uncertainty of Step 2. Fig. 1: Research approach. First experimental results of the presented approach on a next-generation wafer stage, see Figure 1, reveal promising results. Concluding, a model-based approach is being investigated that aims at improving the present state-of-the-art tools, thereby enabling beyond-rigid-body control.

http://www.mate.tue.nl/mate/pdfs/9716.pdf

OH Okko Bosgra

Papers

Low-order system identification and optimal control of intersample behavior in ILC

Closed loop l/sub 1/ scaling for fixed-point digital control implementation

Modeling local/periodic temperature variation in catalytic reactions

Bias Removal in Higher Order Sinusoidal Input Describing Functions

High performance beyond-rigid-body control of next-generation Flexible Stages