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

Conventional PID-like SISO controllers are still common in industrial servo systems, but the ever increasing performance requirements call for advanced MIMO control. This paper presents /spl mu/ feedback controller design for high-precision wafer stage motion. Weighting filters-are proposed to straightforwardly and effectively impose performance and uncertainty specifications. The performance has been experimentally verified and compared with conventional multiloop SISO control.

http://ieeexplore.ieee.org/iel5/7709/21128/00981125.pdf

Experimentally validated multivariable /spl mu/ feedback controller design for a high-precision wafer stage

In this paper, we present a new finite-time robust Iterative Learning Control (ILC) strategy which can guarantee robust stability of the ILC controlled system in presence of model uncertainty as quantified by an additive or multiplicative uncertainty model. The presented finite-time robust ILC controller distinguishes itself from other robust ILC controllers by 1) exploiting non-causality in its control structure and 2) taking into account the finite time span of a single trial. The different steps in the control design and analysis are extensively discussed and illustrated by means of an example.

http://www.mate.tue.nl/mate/pdfs/8269.pdf

Noncausal finite-time robust iterative learning control

High-performance robust control hinges on explicit compensation of performance-limiting system phenomena. Hereto, such phenomena need to be described with high fidelity by the model set. Clearly, this demands for a delicate mutual selection of the nominal model and the uncertainty bound. Both should have a limited complexity to enable successful controller synthesis and implementation. The aim of this paper is to investigate model order selection for robust-control-relevant identification. Therefore, it is investigated how the worst-case performance that is associated with a model set is influenced by the complexity of the nominal model and the uncertainty bound. It turns out that, using a judiciously selected uncertainty coordinate frame, worst-case performance can be made invariant for the order of the uncertainty bound. Nevertheless, dynamic uncertainty modeling may still be worthwhile when accounting for approximations that are commonly made in robust-control-relevant identification, as is analyzed in this paper as well.

/pdf/a-robust-control-relevant-perspective-on-model-order-3enuh8edjs.pdf

A robust-control-relevant perspective on model order selection

High performance continuously variable transmission (CVT) operation requires a reliable control design for its actuation system. The aim of the present paper is to design a high performance robust controller for a range of operating conditions. High performance robust control is achieved by identifying a robust-control-relevant model set that represents the relevant dynamics of the actuation system for a range of operating conditions. Specifically, a new coordinate frame for representing model uncertainty is adopted that transparently connects the size of the model uncertainty and the control criterion, consequently a nonconservative control design can be obtained. Subsequent robust control synthesis reveals that robust performance has been significantly improved over the entire operating range, with respect to both the criterion value and relevant simulated and measured closed-loop step responses.

http://www.dct.tue.nl/toomen/files/OomenMeuBosSteElf2010.pdf

A robust-control-relevant model validation approach for continuously variable transmission control

The quality of model-based controllers hinges on a careful specification of performance and robustness requirements. In typical norm-based control designs, these performance and robustness requirements are specified in a scalar optimization criterion, even for complex multivariable systems. This paper aims to develop a novel and systematic approach for the formulation of this optimization criterion for complex multivariable systems. Hereto, characteristics of the underlying system are exploited. In contrast to pre-existing approaches that typically lead to multiloop SISO weighting functions, the proposed approach enables the design of multivariable weighting functions. Experimental results confirm that the proposed procedure significantly improves the performance of an industrial motion system compared to earlier approaches.

OH Okko Bosgra

Papers

Experimentally validated multivariable /spl mu/ feedback controller design for a high-precision wafer stage

Noncausal finite-time robust iterative learning control

A robust-control-relevant perspective on model order selection

A robust-control-relevant model validation approach for continuously variable transmission control

Enhancing performance through multivariable weighting function design in ℋ − loop-shaping: with application to a motion system