Stable Inversion Based Precise Tracking Control For Linear Systems

The linear system theory is very mature,but the output tracking of linear periodically time-varying systems and linear non-minimum phase systems has always been a challenging con-trol problem.In addition,the tracking problems of periodically time-varying systems and non-minimum phase systems have been widely encountered in practical engineering applications.Al-though,there are many algorithms to achieve approximate tracking,with the increasingly high requirements of tracking accuracy for the industrial application,the research on precise tracking control has great demand and application value.The inversion techniques are effective precise tracking algorithms,the classical inversion technique can only deal with the precise tracking of minimum phase systems,it leads to divergent solutions when the classical inversion technique is applied in non-minimum phase systems.Precise tracking performance is achieved by the stable inversion algorithm for non-minimum phase systems,but with additional restrictions.The initial time for the stable inversion algorithm needs to be negative infinity,thus the length of the extended time interval is infinite,when it is applied in the actual situation with finite initial time,precise tracking can not be guaranteed,so the extended time interval should be large enough to ensure the tracking accuracy.In addition to the above defects,the stable inversion algorithm focus on the research of square systems,there is a lack of systematic research results on the non-square systems.There is also a lack of research on the periodically time-varying systems for the stable inversion algorithm,though,there is research on time-varying systems,the explicit solutions can not be obtained.However,the tracking problems of these two kinds of systems have been wide-ly encountered in the engineering application domain like the under-driven flexible manipulator control,the magnetic based attitude control for the polar-point satellites,etc.Therefore,it is ur-gent to propose new design methods to solve the defects of stable inversion and improve the stable inversion theory,which leads to the research results of this dissertation.The main contents and the innovations of this dissertation are:1.In order to solve the problem that infinite extension time is required for the stable inversion algorithm,the optimal state transition(OST)based stable inversion algorithm is proposed for the single input and single output linear continuous-time non-minimum phase(NMP)system.By this algorithm,precise tracking control is achieved by the NMP systems with finite initial time,and the constraint that the initial time should be zero is relaxed.In order to shorten the length of the extended time interval and improve the tracking performance in the extended time interval further,the pre-actuation based stable inversion algorithm,the stable inversion algorithm based on the combination of pre-actuation and OST and the sta-ble inversion using the optimal combination of pre-actuation and OST are proposed in this dissertation.In comparison with the classical stable inversion algorithm,precise tracking for the specified trajectory is achieved,under this premise,not only the extended time is short-er,but also the better tracking performance is obtained in the extended time interval by the proposed method in this dissertation.2.The precise tracking control algorithms for the linear continuous-time non-minimum phase systems with finite initial time are extended from the single input and single output system to the multi-input and multi-output system,thus,the improved stable inversion(ISI)algo-rithm is proposed and the precise tracking control for the linear continuous-time multi-input and multi-output non-minimum phase system is achieved.The ISI algorithm is the stable inversion based on the optimal integration of pre-actuation and OST,which is fit for the multi-input and multi-output non-minimum phase system.Precise tracking for the specified reference trajectory is achieved,on this basis,the extended time is short and the tracking performance in the extended time interval is nice.Only the optimal inverse to achieve opti-mal output tracking of the linear continuous-time non-square system in the form of transfer function is analyzed by the existing inverse techniques,while the precise tracking for the non-square linear continuous-time NMP system is comprehensively studied in the form of s-tate space by the ISI algorithm;The relative degree is required and only approximate tracking is obtained in the actual situation for the existing inverse techniques,but for the ISI algorith-m,the relative degree is not needed,and precise tracking performance in the actual situation of finite initial time is achieved.3.For the square or non-square discrete-time linear periodically time-varying systems,the sta-ble inversion algorithms to achieve precise tracking with infinite initial time for the discrete-time periodically time-varying systems are proposed.In addition,the stable inversion algo-rithms for the non-square linear time-invariant extended system are proposed and analyzed,explicit formulas of the stable inversions are realized.Under the condition of infinite initial time,a special kind of stable inversion named periodic inversion is proposed to achieve pre-cise tracking for periodic reference trajectories,in comparison with the above methods,the method is a simpler control method with less computational complexity.4.In order to achieve precise tracking for the discrete-time linear periodically time-varying systems with finite initial time,the optimal discrete time transition(ODT)algorithm and the OST algorithm to state transition for the discrete-time linear time-varying systems are proposed,the necessary and sufficient condition for ODT algorithm to get a globally unique solution is obtained in this dissertation.