| Most industrial preparation processes of materials often require a long reaction at high temperatures.For example,the ternary cathode material which is the most promising cathode material in the field of power batteries is usually sintered in the high temperature environment of the electric roller kiln.The sintering environment,as the carrier of energy supply,provides sufficient energy for the complex process reactions.The temperature field optimal control of sintering process is very important for the materials quality and consistency.Due to the lack of effective optimal control methods on the temperature field,the problem of low quality of materials widely exists,which seriously restricts the improvement of the material preparation.Therefore,the optimal control methods of the sintering temperature field in industrial preparation are studied and applied to the sintering process of roller kiln in this paper.The research contents and innovations of this paper mainly include:(1)A parameter estimation error based optimal control method of temperature field is proposed.Parameter estimation is generally required during the controller design.Most of existing methods rely on the states error information of the observer/predictor,which cannot directly reflect the variation of the parameters to be estimated.The accuracy of these methods depends on the observer/predictor performance.The temperature field is a highly dissipative partial differential equation(PDE)system.Under the control framework of the PDE system “reduce-and-design”,this paper proposes a parameter estimation error based temperature field adaptive dynamic programming(ADP)optimal control method according to KarhunenLoève decomposition.The policy iteration(PI)method of the ADP is used to design the optimal controller in this method.A neural network(NN)is used in a critic network to approximate the value function.Then,by defining the parameter estimation errors based on the differences between the estimated and true values of NN weights,a new weight updating method based on the estimation errors of critic NN is proposed to realize the rapid convergence of weights.Simulation verification demonstrates the effectiveness of the proposed method.(2)An event-triggered optimal control method of temperature field based on ADP is proposed.In view of the difficulties such as a large amount of data transmission and calculation of ADP,the high complexity of temperature field control process,and the instability of temperature distribution due to the frequent updating of control inputs,the research of the event-triggered optimal control method for the temperature field PDE system is carried out based on ADP.Firstly,the event-triggered optimal control problem of the temperature field is described.In order to determine the controller updating instants,an event-triggered condition for the PDE system is designed based on the system state information,control information,and system stability.The existence of the upper bound of the real system performance index and the positive lower bound of the interexecution times are proved.It can effectively avoid zeno behavior.Then,the event-triggered optimal control method of the temperature field PDE system is designed by a critic network and an actor network of ADP,and the system stability is provided.The effectiveness of the proposed event-triggered optimal control method is verified in the simulation.In order to further reduce the controller update frequency and the variation degree of system performance,an improved event-triggered condition is designed based on Hamilton-Jacobi-Bellman(HJB)equation.ADP is also used to design the event-triggered optimal control method.Finally,the effectiveness of the proposed control method under this condition is verified by the simulation.(3)A constrained event-triggered optimal control method of temperature field in roller kiln is proposed.In view of the limited adjustment range of the temperature field control inputs in sintering process,based on the in-depth analysis and discussion of the event-triggered optimal control method of the PDE system,a constrained event-triggered optimal control method of the temperature field PDE system is proposed.Firstly,the temperature field event-triggered optimal control problem with input constraints is described.Based on the improved event-triggered condition mentioned above,the event-triggered condition with constrained inputs is designed by ensuring the PDE system stability.Simultaneously,the boundedness of the performance index and interexecution times are both proved.On this basis,an event-triggered optimal control method under the input constraints is designed based on the ADP technology.A nonperiodic impulsive dynamic system is constructed,and the stabilities under the designed triggered control method of the impulsive dynamic system and the PDE system are proved.Finally,the simulation is used to verify the convergence and effectiveness of the proposed method.(4)The application research of temperature field optimal control methods in roller kiln.The above-mentioned optimal control methods of temperature field are applied to the roller kiln.First,a roller kiln temperature field modeling method is studied on the basis of sintering process analysis,which is based on the energy conservation equation of the porous medium.A transformation method is proposed that the related items of the width direction in the model are equivalently transformed with the boundary conditions,so a temperature field model of the saggers region is established.Then,the above control methods are applied to a roller kiln to solve the problems in the sintering,such as the hardness of the temperature field control and the instability caused by the frequent changes of control inputs.The application results show that the proposed methods can not only stable the temperature distribution,but also make the real system performance close to that of the periodic control,so the corresponding effectiveness is verified in the practical process. |
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