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

In this paper, the feedforward controller design problem for high-precision electromechanical servo systems that execute finite time tasks is addressed. The presented procedure combines the selection of the fixed structure of the feedforward controller and the optimization of the controller parameters on the basis of measurement data from iterative trials. A linear parameterization of the feedforward controller in a two-degree- of-freedom control architecture is chosen, which for a linear time-invariant (LTI) plant results in a feedforward controller that is applicable to a class of motion profiles as well as in a convex optimization problem with the objective function being a quadratic function of the tracking error. Optimization by iterative trials results in the controller parameter values that are optimal with respect to the actual plant, which leads to a high tracking performance. The use of iterative trials in general outperforms techniques that are based on a detailed a priori plant model only, whereas the fixed structure of the feedforward controller, i.e., the approximative inverse plant model, guarantees a high tracking performance for a class of motion profiles, unlike for example iterative learning control (ILC). Experimental results on a high-precision wafer stage illustrate the procedure.

http://www.mate.tue.nl/mate/pdfs/7506.pdf

Fixed Structure Feedforward Controller Tuning Exploiting Iterative Trials, Applied to a High-Precision Electromechanical Servo System

Non-periodically repeating (NPR) disturbances are fixed-shape disturbances that occur randomly in time. We can provide a control system with the capability to suppress this type of disturbance by adding in parallel to the input of the nominal feedback controller a learning look-up-table based feedforward controller that is activated using an NPR-disturbance detector.

Suppressing non-periodically repeating disturbances in mechanical servo systems

Robust-Control-Relevant Coprime Factor Identification with Application to Model Validation of a Wafer Stage

Iterative Learning Control (ILC) is a control strategy to improve the performance of digital batch repetitive processes. Due to its digital implementation, discrete time ILC approaches do not guarantee good intersample behavior. In fact, common discrete time ILC approaches may deteriorate the intersample behavior, thereby reducing the performance of the sampled-data system. In this paper, a generally applicable multirate ILC approach is presented that enables to balance the at-sample performance and the intersample behavior. Furthermore, key theoretical issues regarding multirate systems are addressed, including the time-varying nature of the multirate ILC setup. The proposed multirate ILC approach is shown to outperform discrete time ILC in a realistic simulation example.

/pdf/suppressing-intersample-behavior-in-iterative-learning-47i54c29yr.pdf

Suppressing intersample behavior in Iterative Learning Control

High measured performance does not imply that the true system performance is satisfactory. Indeed, in many systems, these performance variables cannot be measured directly and have to be inferred from the measured variables by using model knowledge. The aim of the present paper is to develop an identification and control design approach that can deal with this situation. Hereto, identification techniques for inferential control, uncertainty structures for robust inferential control, and appropriate control design structures are presented. As a result, a novel coordinate frame is obtained that transparently connects nominal model identification, quantification of model uncertainty, and robust inferential control, thereby enabling high performance robust inferential control.

http://www.dct.tue.nl/toomen/files/OomenBosWal2009.pdf

OH Okko Bosgra

Papers

Fixed Structure Feedforward Controller Tuning Exploiting Iterative Trials, Applied to a High-Precision Electromechanical Servo System

Suppressing non-periodically repeating disturbances in mechanical servo systems

Robust-Control-Relevant Coprime Factor Identification with Application to Model Validation of a Wafer Stage

Suppressing intersample behavior in Iterative Learning Control

Identification for robust inferential control