Analysis And Synthesis Of Switching Linear Parameter-varying Systems For Automotive Air Conditioning Control

With the rapid development of modern science and technology,along with the im-provement of people’s living standards,people have higher requirements for the comfort,safety and stability of automobile system.In traditional automotive air conditioning con-trol system,because of the complicated external disturbances,unmatched system model parameters,and varying mission objectives,system parameters often change continuous-ly or even jump.The traditional linearization control methods are difficult to meet the requirements of modeling and control of automotive air conditioning system,where the parameters vary greatly in the whole working range.In order to accurately model and con-trol these nonlinear dynamic systems with complex time-varying parameters,an effective solution is to design the corresponding controllers based on linear parameter-varying and switched systems methods to ensure the stability and robustness of the output tracking of automotive air conditioning control system in the whole working range.In view of this,this thesis first conducts an in-depth study on the stability and robustness of the linear parameter-varying systems with several typical dwell time constraints,then extends the theoretical results to the modeling and controller design of automotive air conditioning systems.The obtained results not only verify the effectiveness of the proposed analy-sis methods for the corresponding control systems,but also provide an effective design thought for the control synthesis of automotive air conditioning system.The main inno-vations of the thesis can be summarized as follows.Firstly,for a class of switching linear parameter-varying systems,a bumpless trans-fer control approach is proposed.For continuous-time systems,a Lyapunov function which can be constructed by designing the Lyapunov matrix is introduced,then the sys-tem energy decreases at switching instants and the intervals between two adjacent switch-ing instants.For discrete-time systems,the Lyapunov function is designed to decrease at a given rate in the intervals between two adjacent switching instants,and to decrease at a given amplitude at the switching instants.Based on the Lyapunov function method,a criterion,which ensures that the switching parameter-varying systems are asymptotical-ly stable,is established.Then,the proposed stability criterion and the bumpless transfer constraint are solved simultaneously,such that the designed controller has the bumpless transfer performance.A numerical example is given to verify the effectiveness of the proposed approach.Secondly,the guaranteed cost control problems for a family of linear parameter-varying systems with dwell time constraints are studied,and a class of non-weighted quadratic performance is considered.Specifically,a novel quasi-time-varying Lyapunov function based on parameter-varying positive definite matrix is proposed,in which the system energy at the switching instants and the intervals between two adjacent switch-ing instants are decreasing.Furthermore,a class of stability conditions based on the mode-dependent dwell time constraint is established to ensure that the linear parameter-varying systems are asymptotically stable.Then,a quasi-time-varying mode-dependent state feedback controller is designed such that the corresponding closed-loop system is asymptotically stable,and the upper bound correlated with the initial condition for the non-weighted quadratic performance is obtained.In order to minimize the upper bound,an optimization method to minimize the upper bound of quadratic performance index is proposed.The effectiveness and superiority of the theoretical results are verified by a numerical simulation.Thirdly,the mode-dependent persistent dwell time technique is used to investigate the modeling and controller design for a class of switching linear parameter-varying sys-tems with dwell time constraints.A class of nonlinear systems with parameter-varying are modeled as linear systems without loss of generality,and the mode-dependent per-sistent dwell time switching signal is introduced.In addition to relaxing the dwell time constraints of the switched systems,the slow switching dynamics and fast switching dy-namics that may coexist between two subsystems are also described.Then,with the help of multiple Lyapunov function and projection theorem,mode-dependent state feedback controllers and static output feedback controllers are designed to guarantee that the non-smooth linear parameter-varying systems are globally asymptotically stable and satisfy the H₂performance.Numerical examples verify the desired control performance of the two types of controllers for switching linear parameter-varying systems with dwell time constraints and external disturbances.Furthermore,the modeling and H_∞control problems of a class of automotive air-conditioning systems are studied via the switching linear parameter-varying method.Specif-ically,the methods based on Jacobian matrix and tensor product decomposition are used to linearize the mathematical model of automotive air conditioning systems.By adding pre-filters and post-filters,a linear parameter-varying controller is designed,and a weight-ed function is introduced to improve the control performance of the closed-loop systems.The simulation results show that the automotive air conditioning systems based on linear parameter-varying systems achieve the desired control performance both for nominal sys-tems and disturbed systems,and the tracking performance and robustness of the algorithm are verified.In addition,a control strategy for automotive air conditioning systems based on switching linear parameter-varying method is proposed,which allows the system to switch fast,and makes compensation by slow switching later,enhancing the flexibility of control synthesis while relaxing the established stability conditions.Finally,based on the constructed automotive air conditioning dynamic model,a fault-tolerant control framework based on generalized internal model control and gain-scheduling method is established,and the switched gain-scheduling problems with H_∞control synthesis for automotive air conditioning systems against sensor and actuator fail-ures are studied.Based on the disturbance decoupling method,the fault detection filters and fault isolation filters are designed respectively to identify the potential sensor and actuator failures.The effectiveness of the proposed filters are verified by using the non-linear moving boundary model in the simulation,both for nominal systems and disturbed systems.Then,the fault-tolerant control of automotive air conditioning system is studied in the case of sensor and actuator failures,respectively.Compensators corresponding to sensor and actuator failures are designed based on the optimization of minimizing the ef-fect of the fault on system inputs or outputs.The passive and active fault-tolerant control approaches are compared by examples,and the fault adaptability of the designed com-pensators and the effectiveness of the proposed fault-tolerant control framework are also verified.