Research On Distributed Model Predictive Control Based On Gap Metric Decoupling

Large-scale industrial processes have problems such as high structural complexity,strong system coupling,and large computational burden on controllers.Because Distributed Model Predictive Control(DMPC)is not only deal with control problems of large-scale systems effectively,but also reduce the computational burden of controllers,improve system security,and obtain the control performance which is similar to Centralized Model Predictive Control(CMPC).Therefore,DMPC has most research attention in control area.However,the limitation of computing resource and network bandwidth in practical applications that make non-cooperative DMPC calculates the Nash optimal solution while the system is still running.It's the reason of generating the calculation delay.When the sub-MPC controller calculates the optimal control strategy that satisfies the Nash balance,the state of the system has changed.It is no longer to be the initial state which is used by the sub-MPC controller to solve the problem.The calculation delay makes control performance poor,and even makes the system unstable.In order to improve the control strategy quickly,reduce the DMPC computation delay,and ensure the system control performance,this paper proposes the decomposition of DMPC subsystem,the design of DMPC controller and the optimization compensation of DMPC control performance,and achieves the following results:(1)About the decomposition problem of DMPC subsystems,a DMPC decomposition method based on Gap Metric weak decoupling is proposed.The method uses the idea of feedback decoupling to decompose the system.By designing the optimization problem based on Gap Metric weak decoupling,the dynamic characteristic of the subsystem is similar to no decoupling.The coupling effect between subsystems has been reduced.(2)Based on the content of the first part,a design method of DMPC controller based on Gap Metric weak decoupling is proposed.This method is that the objective function of sub-MPC includes the feedback decoupling effect,reduces the coupling effect between subsystems by weak decoupling decomposition,thus reducing the communication between subsystems.On the basis of weak decoupling,sub-MPC needn't performs the iterative calculation to obtain the Nash optimal solution process,because of the optimal control strategy of the previous moment as the input of the coupling subsystem to solve the optimal input of the current subsystem.The design method of DMPC controller reduces the communication between subsystems and avoids the Nash optimal solution process,thereby reducing the DMPC calculation delay and improving the real-time control strategy.(3)The above methods are all designed for linear models.When the controlled object is a nonlinear system,it needs to be linearized at a stable point.This will lead to model mismatch inevitably,which results the weak decoupling decomposition method for linear model can not achieve the expected decoupling effect on the nonlinear system.It leads to the weak decoupled DMPC can not obtain satisfactory control performance.Therefore,the DMPC input compensation strategy based on Gap Metric weak decoupling is proposed.The strategy is to give weights and sum of the optimal input calculated by the weakly decoupled DMPC and the feedback input of the weak decoupling decomposition into the system to improve the robustness of the weakly decoupled DMPC and ensure the control performance of the system.To verify the effectiveness of the above proposed methods,the process model and numerical model have been simulated respectively.