Data Driven Fault Tolerant Control: A Subspace Approach
Data Driven Fault Tolerant Control: A Subspace Approach
复制标题
DOI：
--
复制
发表时间：
2009-11
期刊：
影响因子：
--
通讯作者：
Jianfei Dong
中科院分区：
文献类型：
--
作者：
Jianfei Dong
故障检测和容错控制的主流研究一直集中在基于模型的方法上。就模型而言，由于故障导致的模型变化必须从测量数据中提取出来。一般来说，现有的方法处理测量的输入和输出，要么是通过基于已知模型设计的滤波器（例如，对于加性故障），要么是通过识别方案来估计模型参数的变化（例如，由于乘法故障）。由于传统的系统辨识方法通常比求解线性最小二乘问题更复杂，因此很难在线实现。因此，本文的贡献在于开发了可靠的数值方法，试图从数据中提取故障信息，其方式与求解线性最小二乘问题一样简单。这些方法包括“数据驱动”控制器重构（CR）和故障检测与识别（FDI），以及在线实验设计，以确保“数据”具有足够的信息来发现由于故障导致的系统属性变化。第2章的重点是“数据驱动”控制器重构方法的发展，即闭环子空间预测控制（SPC）。这种方法的关键步骤是确定未来输出预测器（根据马尔可夫参数），它将过去的I/ o和未来的输入映射到系统的未来输出。然后，通过识别的预测器对预测控制器进行参数化。闭环SPC跳过系统模型的实现，只依赖于系统的马尔可夫参数；因此，可以很容易地在线实现，以适应乘法故障。结果表明，在无限长的测量和预测范围内，闭环SPC与经典LQG设计相当。在有限数量的噪声数据样本的情况下，识别的马尔可夫参数是有偏差的和有噪声的，这将导致SPC输出预测器的随机不确定性。本章开发了一个显式形式的概率鲁棒解，它对这种不确定性是“谨慎的”。将LTI系统的闭环SPC扩展到线性变参数系统。第3章重点讨论了LTI和LPV系统的故障检测和识别方法与子空间识别（FICSI）的关联。FICSI避免了像经典的宇称空间方法（PSA）那样将残差向量投影到扩展可观测矩阵的左零空间上。避免这种投影的优点是保留了残差向量的自由度，从而保留了残差向量中包含的故障信息。本文证明，与PSA相比，FICSI产生的残差对故障更敏感。然后证明了FICSI故障估计方案的渐近无偏性。与基于PSA或未知输入观测器（UIO）的现有故障检测和估计方法相比，FICSI算法的新颖性也可归因于FICSI只需要将I/O测量值映射到残差的马尔可夫参数序列。因此，FICSI检测器和估计滤波器可以直接从闭环工厂的I/O测量中识别出来，而无需以状态空间形式建模其动态。SPC和FICSI算法都依赖于从数据中识别的马尔可夫参数序列。为了识别这些参数，工厂的输入必须具有足够的“信息性”；也就是说，它们必须持续地激发系统达到足够的秩序。经典的实验设计和最近的控制辨识文献都是在频域参数化输入信号的频谱。如果输入自相关系数在足够的阶数内不为零，则保证了激励条件的持续性。在最近发展的控制方法识别中，需要在频率点网格上搜索最优输入信号（就识别模型可实现的鲁棒闭环性能而言）。不幸的是，这并不适合在线实现。因此，本文在第四章中提出了一种时域的在线输入设计方法，避免了输入频谱的参数化。这种方法需要通过一组lmi来约束输入信号，并且可以合并到凸优化问题中。将这些输入约束与SPC方法相结合，得到了一种保证参数收敛的自适应预测控制方案。由于其凸性和递归性，这种在线设计方法比经典方法更适合于及时捕捉由于故障而突然变化的系统状态。
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.