| Cyber Physical Systems (CPS), the unity of computing and physical process, is the next generation intelligent system which is the integration of computation, communication and control. The system manipulates the physical entity remotely, reliably, real-time, safely, and collaboratively via networked space. CPS is the argument in telligence of Internet of Things, and also is the key technology of next generation networked mechatronics control systems. Cyber Physical Control System (CPCS) is one of important parts of CPS; multiple closed loop control systems of Single Input-Single Output (SISO) systems can be modeled as a closed loop CPCS of Multiple Inputs-Multiple Outputs (MIMO) system with network induced delays since they are inter-connected into CPS.Network induced delay is one of the vital factors influencing the real-time performance of CPCS; and even worse, the controller designed in delay-free environment doesn’t work in network anymore. So, research on real-time control and delay compensation technology for networked MIMO system, especially for nonlinear MIMO system, is of great scientific value and very important for the applications of CPS in control field, and now it has been the advanced hot research area in the field of CPCS.This dissertation is to find a networked real-time control method for a class of networked nonlinear MIMO systems by taking2DOF helicopter model as the representative, and the goal is to assure that the local controller designed in delay-free environment still can be used in the CPCS with network induced I/O delays, thus, the networked controller of a class of nonlinear MIMO system in CPCS can be designed by the method of controller design in delay-free environment.This dissertation begins with delay compensation technology of linear MIMO system based on a novel virtual observer by taking famous Wood-Berry model as an example. And then, a class of nonlinear MIMO sytem addressed in this dissertation was transformed to a linear MIMO system approximately by the method of local linearization; furthermore, a virtual MIMO system with combined delays was constructed; based on the virtual MIMO system, an observer was designed for the actual delayed nonlinear MIMO systems. With the aid of such a virtual observer, the networked nonlinear system can still be controlled well by the controller designed in delay free environment. The simulation and actual test results of2DOF helicopter networked control system proved the correctness and effectiveness of this method.The main content is as bellow.1) A method of construction of an equivalent virtual linear system was proposed in this dissertation. Network induced Input/Output (I/O) delays are firstly combined, and then the combined delay is allocated to output channels or system states, which results in the mathematical construction of a virtual linear MIMO system. It is proved that the virtual system with combined delay is equivalent to the original system with I/O delays in terms of system input-output relationship. Furthermore, the observability of the virtual system in the form of state space model was also proved, which is required to design the virtual observer.2) A modified Luenberger observer was designed, and delay compensation of linear MIMO system is realized based on the modified observer. Firstly, the modified Luenberger observer was designed based on the equivalent virtual system with combinded delay; and the estimated states of the original I/O delayed system were obtained by the modified observer. Secondly, the estimated states were fed back to the state-feedback-controller (for example, LQR) which was designed for the corresponding delay-free system. Because that the observer states were output in ahead of the combined delay, the stability of the closed loop control system with the observer is almost the same as delay free. So the delay compensation for the state-feedback control system was realized. Finally, taking the famous delay-sensitive Wood-Berry model as an example, the simulation shows that the local state-feedback controller designed in delay-free environment cannot work yet in the network due to the network induced delays, but it can resume working well when the virtual observer-based delay compensation method is applied.3) In order to compensate the delay of variable time constant, this dessertation proposed a proportional factor namely ε to modify observer gain Jo. And the optimal solution of ε was presented as well. Firstly, approximate the delay in characteristic equation of observer with Pade method. Then, solve the equation with different value of ε to obtain the characteristic poles of observer. Finally, the value of ε with which the principal pole of observer is farthest from imaginary axis can be considered as the optimal value corresponding to the current delay.4) The problem of delay compensation for a class of nonlinear MIMO system is drew forth from the issue of networked control of two Degree of Freedom (2DOF) helicopter model. Firstly, the nonlinear dynamic equations of a2DOF helicopter model were obtained by means of Lagrange method. Then, the dynamic equations were un-completely linearized, which results in delay-free simi-linearized state space model of a class of nonlinear MIMO systems. The next, local delay free controller, that is LQR+FF+I controller (Linear Quadratic Regulator+Forward Feed controller+Integrator) was designed based on the simi-linearized state space model. The next, network induced I/O delays were introduced into the state feedback control system, and then by mathematical transformation the nonlinear item in the delayed semi-linearized state space model was converted and combined into the linear part, which leads to an equivalent I/O delayed linear MIMO system. Finally, following the delay compensation method for linear MIMO system, the delay compensation for the delayed nonlinear MIMO system was implemented. Simulation and hardware control of the2DOF helicopter model proves the effectiveness of the method, that is, the unstable networked closed loop control system of helicopter due to the network induced I/O delays resumes being stable with the aid of the virtual observer.5) Several issues relative to the application of networked control technology into actual CPCS were also discussed. For example, limited random delay can be converted into fixed delay by means of delay stack to realize the delay compensation simply; the state number of virtual system with combined delay may increase and as a result the observer state cannot be fed back to the original state-feedback controller directly, so this dissertatin proposed to use matrix Ω to decrease the observer order; at last, it is pointed out that it would be better if ε is a proper matrix when the difference of time constant of input or output delays is considerable large, and it will improve the effectiveness of corresponding delay compensation. |
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