控制重構

控制重構（Control reconfiguration）是控制理論中的領域，目的是為了动力系统的容錯控制。其用途是在發生嚴重故障（例如致動器或是感測器損壞），影響控制迴路時，系統可以重新調整其控制組態，以避免系統層的失效。控制重構'不但包括架構的重新調整，也包括控制器參數為了配合新的架構而作的參數調整。控制重構是回控控制系統增加可信任性的重要機能之一。

标题

Reconfiguration problem

Fault modelling

The figure to the right shows a plant controlled by a controller in a standard control loop.

The nominal linear model of the plant is

${\begin{cases}{\dot {\mathbf {x} }}&=\mathbf {A} \mathbf {x} +\mathbf {B} \mathbf {u} \\\mathbf {y} &=\mathbf {C} \mathbf {x} \end{cases}}$

The plant subject to a fault (indicated by a red arrow in the figure) is modelled in general by

${\begin{cases}{\dot {\mathbf {x} }}_{f}&=\mathbf {A} _{f}\mathbf {x} _{f}+\mathbf {B} _{f}\mathbf {u} \\\mathbf {y} _{f}&=\mathbf {C} _{f}\mathbf {x} _{f}\end{cases}}$

where the subscript $f$ indicates that the system is faulty. This approach models multiplicative faults by modified system matrices. Specifically, actuator faults are represented by the new input matrix $\mathbf {B} _{f}$, sensor faults are represented by the output map $\mathbf {C} _{f}$, and internal plant faults are represented by the system matrix $\mathbf {A} _{f}$.

The upper part of the figure shows a supervisory loop consisting of fault detection and isolation (FDI) and reconfiguration which changes the loop by

1. choosing new input and output signals from {$\mathbf {u} ,\mathbf {y}$} to reach the control goal,
2. changing the controller internals (including dynamic structure and parameters),
3. adjusting the reference input $\mathbf {w}$.

To this end, the vectors of inputs and outputs contain all available signals, not just those used by the controller in fault-free operation.

Alternative scenarios can model faults as an additive external signal $\mathbf {f}$ influencing the state derivatives and outputs as follows:

${\begin{cases}{\dot {\mathbf {x} }}_{f}&=\mathbf {A} \mathbf {x} _{f}+\mathbf {B} \mathbf {u} +\mathbf {E} \mathbf {f} \\\mathbf {y} _{f}&=\mathbf {C} _{f}\mathbf {x} _{f}+\mathbf {F} \mathbf {f} \end{cases}}$

Reconfiguration goals

The goal of reconfiguration is to keep the reconfigured control-loop performance sufficient for preventing plant shutdown. The following goals are distinguished:

1. Stabilization
2. Equilibrium recovery
3. Output trajectory recovery
4. State trajectory recovery
5. Transient time response recovery

Internal stability of the reconfigured closed loop is usually the minimum requirement. The equilibrium recovery goal (also referred to as weak goal) refers to the steady-state output equilibrium which the reconfigured loop reaches after a given constant input. This equilibrium must equal the nominal equilibrium under the same input (as time tends to infinity). This goal ensures steady-state reference tracking after reconfiguration. The output trajectory recovery goal (also referred to as strong goal) is even stricter. It requires that the dynamic response to an input must equal the nominal response at all times. Further restrictions are imposed by the state trajectory recovery goal, which requires that the state trajectory be restored to the nominal case by the reconfiguration under any input.

Usually a combination of goals is pursued in practice, such as the equilibrium-recovery goal with stability.

The question whether or not these or similar goals can be reached for specific faults is addressed by reconfigurability analysis.

Reconfiguration approaches

Fault hiding

This paradigm aims at keeping the nominal controller in the loop. To this end, a reconfiguration block can be placed between the faulty plant and the nominal controller. Together with the faulty plant, it forms the reconfigured plant. The reconfiguration block has to fulfill the requirement that the behaviour of the reconfigured plant matches the behaviour of the nominal, that is fault-free plant.

Linear model following

In linear model following, a formal feature of the nominal closed loop is attempted to be recovered. In the classical pseudo-inverse method, the closed loop system matrix ${\bar {\mathbf {A} }}=\mathbf {A} -\mathbf {B} \mathbf {K}$ of a state-feedback control structure is used. The new controller $\mathbf {K} _{f}$ is found to approximate ${\bar {\mathbf {A} }}$ in the sense of an induced matrix norm.

In perfect model following, a dynamic compensator is introduced to allow for the exact recovery of the complete loop behaviour under certain conditions.

In eigenstructure assignment, the nominal closed loop eigenvalues and eigenvectors (the eigenstructure) is recovered to the nominal case after a fault.

Optimisation-based control schemes

Optimisation control schemes include: linear-quadratic regulator design (LQR), model predictive control (MPC) and eigenstructure assignment methods.

Probabilistic approaches

Some probabilistic approaches have been developed.

Learning control

There are learning automata, neural networks, etc.

數學工具及框架

有許多種達到控制重新組態的方式。以下是一些常用的作法。

• 自适应控制（AC）
• 擾勳解耦（DD）
• 特徵值指定（EA）
• 增益規劃（GS）/線性參數變化（LPV）
• 廣義內部模型控制（GIMC）
• 智能控制（IC）
• 线性矩阵不等式（LMI）
• LQR控制器（LQR）
• 模型追隨（MF）
• 模型預測控制（MPC）
• 广义逆阵法（PIM）
• 鲁棒控制控術

相關技術

在控制重新組態前，需要先知道是否有出現故障（故障檢測），以及故障影響的元件（故障檢測和隔離）。最好也可以提供故障系統的模型（故障識別）。這些都是工程診斷希望得到的資訊。

Fault accommodation is another common approach to achieve 故障容許度. In contrast to control reconfiguration, accommodation is limited to internal controller changes. The sets of signals manipulated and measured by the controller are fixed, which means that the loop cannot be restructured.

延伸閱讀

• Blanke, M.; Kinnaert, M.; Lunze, J.; Staroswiecki, M., Diagnosis and Fault-Tolerant Control 2nd, Springer, 2006 
• Steffen, T., Control Reconfiguration of Dynamical Systems, Springer, 2005 
• Staroswiecki, M., Fault Tolerant Control: The Pseudo-Inverse Method Revisited, Proceedings of the 16th IFAC World Congress, Prague, Czech Republic: IFAC, 2005 
• Lunze, J.; Rowe-Serrano, D.; Steffen, T., Control Reconfiguration Demonstrated at a Two-Degrees-of-Freedom Helicopter Model, Proceedings of European Control Conference (ECC), Cambridge, UK., 2003 
• Maciejowski, J.; Jones, C., MPC Fault-Tolerant Flight Control Case Study: Flight 1862, Proceedings of the SAFEPROCESS 2003: 5th Symposium on Detection and Safety for Technical Processes, Washington D.C., USA: IFAC: 265–276, 2003 
• Mahmoud, M.; Jiang, J.; Zhang, Y., Active Fault Tolerant Control Systems - Stochastic Analysis and Synthesis, Springer, 2003 
• Zhang, Y.; Jiang, J., Bibliographical review on reconfigurable fault-tolerant control systems, Proceedings of the SAFEPROCESS 2003: 5th Symposium on Detection and Safety for Technical Processes, Washington D.C., USA: IFAC: 265–276, 2003 
• Patton, R. J., Fault-tolerant control: the 1997 situation, Preprints of IFAC Symposium on Fault Detection Supervision and Safety for Technical Processes, Kingston upon Hull, UK: 1033–1055, 1997 
• Rauch, H. E., Autonomous control reconfiguration, IEEE Control Systems Magazine, 1995, 15 (6): 37–48, doi:10.1109/37.476385 
• Rauch, H. E., Intelligent fault diagnosis and control reconfiguration, IEEE Control Systems Magazine, 1994, 14 (3): 6–12, doi:10.1109/37.291462 
• Gao, Z.; Antsaklis, P.J., Stability of the pseudo-inverse method for reconfigurable control systems, International Journal of Control, 1991, 53 (3): 717–729, doi:10.1080/00207179108953643 
• Looze, D.; Weiss, J.L.; Eterno, J.S.; Barrett, N.M., An Automatic Redesign Approach for Restructurable Control Systems, IEEE Control Systems Magazine, 1985, 5 (2): 16–22, doi:10.1109/mcs.1985.1104940 .
• Esna Ashari, A.; Khaki Sedigh, A.; Yazdanpanah, M. J., Reconfigurable control system design using eigenstructure assignment: static, dynamic and robust approaches, International Journal of Control, 2005, 78 (13): 1005–1016, doi:10.1080/00207170500241817 .