The proposed problem of reconstructing fault-tolerant control considers the mass spring system shown <1>. A mass m of object is suspended from a fixed spring at the upper end. The spring has a spring constant of k and an original length of l0. Below the fixed point h is a fluid having a viscosity coefficient of c. In the absence of any external force, the mass m stays at a fixed point l, ie l=mg/k+l0. A control force Fc is now applied to the mass m to cause it to move according to certain rules and requirements. The control objectives are: 1) to move the mass m according to the trajectory, that is, the mass m reciprocates from p1 → p2 → p3 → p4 → p1; 2) the spring break fault in the fault-tolerant object (k = 0).
The quality spring system under normal operating conditions (no fault), the linear dynamics of the mass m are described by two differential equations: undamped (outside the fluid) myb+ky=Fc, y≤ys(1) with damping (in the fluid) Myb+cya+ky=Fc, y≥ys(2) where ys is the critical value of the fluid surface position, ie the point at which the mass m enters or leaves the surface of the fluid. This threshold divides the system dynamic space into two distinct regions. In each region, the model is linear time-invariant (LTI), but when one region (model) transients to another region, there are mutations or discontinuities in the dynamic characteristics of the object.
Let the object spring breakage occurs during the work. At this time, the system dynamics are described by the following two differential equations: faulty undamped model myb=Fc, y≤ys(3) faulty damping model myb+cya=Fc, y≥ Ys(4) The mass spring system described above is a nonlinear complex system that needs to be described by four different models (structures), and the system dynamically mutates when the system changes from one structure to another. The traditional control system design method is based on a deterministic model or a gradual adaptation model, which does not satisfy the multimodal and abrupt conditions of the system. Therefore, reconstruction and fault-tolerant control design methods are needed. This example can be used as a test platform for reconfiguring fault-tolerant control.
Reconstruction Fault Tolerant Control Scheme The design of an active reconstruction fault tolerant control system for predictive dynamics and faults is shown. The scheme uses a method of parsing the margin. To effectively accommodate faults in objects and controllers, the entire system should be of mixed margin type (parallel margin and analytical margin) <6>. In the case of the known object model, the controller can be designed in advance according to the corresponding model, and as long as the dynamic change or failure of the system can be detected in time, the reconstruction fault-tolerant control can be realized according to the switching control. Document <8> has proved that the system after switching control is stable and has satisfactory performance as long as the controller under each mode ensures stable and satisfactory performance.
CMFD-based active reconstruction fault-tolerant control method The system also has a state feedback control method. Feedback control is a basic fault-tolerant control method that can stabilize and asymptotically improve (improve) system performance to a certain extent. Therefore, any fault-tolerant control system should have feedback control. For the control object of this paper, state feedback control is especially important, because in the four modes of the object, except for mode 2, the other three modes (1, 3, 4) are open-loop unstable, so it is necessary. State feedback control is used to achieve closed loop stability. This is the primary task of reconfiguration and fault-tolerant control.
Conclusion Theoretical analysis and simulation experiments show that the active reconstruction and fault-tolerant control methods proposed in this paper can effectively realize the reconstruction control of the inherent dynamic changes of the mass spring system and the fault-tolerant control of spring fracture faults. In the case of reconstruction and fault tolerance, the stability of the system and the tracking performance requirements of speed and displacement are guaranteed, and the reconstruction and fault-tolerant control are fast. This paper does not consider the robustness of chattering and detection in handover, which will be discussed in a future article.
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