Data Driven Fault Tolerant Control: A Subspace Approach

Data Driven Fault Tolerant Control: A Subspace Approach

Dong, J.

Verhaegen, M. (promotor)

Mechanical, Maritime and Materials Engineering

Delft Center for Systems and Control

2009-11-11

The main stream research on fault detection and fault tolerant control has been focused on model based methods. As far as a model is concerned, changes therein due to faults have to be extracted from measured data. Generally speaking, existing approaches process measured inputs and outputs either by a filter designed based on a known model (e.g. for additive faults), or by an identification scheme to estimate the changed model parameters (e.g. due to multiplicative faults). Since the classical system identification methods are usually more involved than solving a linear least-squares problem, they can hardly be implemented online. The contribution of this thesis is hence the development of reliable numerical methods that try to extract fault information from data, in a manner as easy as solving a linear least-squares problem. These methods include “data driven” controller reconfiguration (CR) and fault detection and identification (FDI), and online experiment design to ensure that the “data” are informative enough to discover the changed system properties due to faults. The focus of Chapter 2 is on the development of the “data driven” controller reconfiguration approach, i.e. the closed-loop subspace predictive control (SPC). The key step in this approach is identifying a future output predictor (in terms of Markov parameters), which maps the past I/Os and future inputs to the future outputs of a system. A predictive controller is then parameterized by the identified predictor. The closed-loop SPC skips the realization of the system model and relies only on its Markov parameters; and can therefore be easily implemented online to adaptively accommodate multiplicative faults. It has been proven that with infinitely long measurement and prediction horizons, the closed-loop SPC is equivalent to the classical LQG design for LTI systems. In the case of a limited number of noisy data samples, the identified Markov parameters are biased and noisy, which then lead to a stochastic uncertainty in the output predictor of the SPC. This chapter develops a probabilistic robust solution in an explicit form, which is “cautious” to this uncertainty. The closed-loop SPC for LTI systems is extended to linear parameter varying systems. Chapter 3 focuses on developing Fault detection and Identification approaches Connected to Subspace Identification (FICSI) for both LTI and LPV systems. FICSI avoids projecting a residual vector onto the left null space of the extended observability matrix, as the classical parity space approach (PSA) requires. The advantage of avoiding this projection is the preservation of the degree of freedom in the residual vector, and consequently, the fault information contained therein. The thesis proves that FICSI produces residualsmore sensitive to faults than PSA does. It then proves the asymptotic unbiasedness of the FICSI fault estimation schemes. The novelty of the FICSI algorithms compared to the existing fault detection and estimation approaches based on PSA or unknown input observer (UIO), can also be attributed to the fact that FICSI requires only a sequence of Markov parameters mapping the I/O measurements to the residual. As a consequence, the FICSI detector and estimation filters can be directly identified from I/O measurements in a closed-loop plant, without modeling its dynamics in a state-space form. Both the SPC and FICSI algorithms rely on a sequence of Markov parameters identified from data. To identify these parameters, the inputs to the plant have to be “informative” enough; i.e. they must persistently excite the system to a sufficient order. Classical experiment design and the recent literatures on identification for control parameterize the spectrum of input signals in frequency domain. The persistency of excitation condition is ensured, if the input autocorrelation coefficients are nonzero up to a sufficient order. In recently developed identification for control approaches, optimal input signals (in terms of robust closed-loop performance achievable by the identified model) need to be searched on a grid of frequency points. This is unfortunately not suitable for online implementations. This thesis hence develops in Chapter 4 an online input design approach in time domain, which avoids parameterizing the input spectrum. This approach requires constraining input signals by a set of LMIs, and can be incorporated into a convex optimization problem. The combination of these input constraints with the SPC approach leads to an adaptive predictive control scheme with guaranteed parametric convergence. Due to its convexity and the recursive nature, this online design approach is more suitable than the classical approaches to capture the abruptly changed system conditions due to faults in a timely manner.

Subspace predictive control
Fault detection and identification
System identification
Experiment design
Linear parameter varying systems
Stochastic uncertainty
Data driven methods
Numerical algorithms

http://resolver.tudelft.nl/uuid:6bc9a353-adaa-40ef-af76-ad79ea983ee7

2011-11-11

9789090247724

Institutional Repository

doctoral thesis

(c) 2009 Dong, J.