Iterative Learning Control For Singular Distributed Parameter Systems

Singular distributed parameter systems is widely used in the fields of aerospace engineering,bioengineering,material chemistry and so on.Iterative learning control is an intelligent control algorithm with memory and correction mechanism,which adopts the learning strategy of"learning in repetition and correcting in learning",and it has been applied in engineering control field because of its accurate tracking,simple structure and engineering realize easily.However,to date,most of the research results on iterative learning control about conventional systems,and the iterative learning control algorithm is relatively less used in the singular distributed parameter systems.Therefore,it is of great significance to study iterative learning control for singular distributed parameter systems.The main research work of this dissertation is as follows:(1)For a class of parabolic singular distributed parameter systems with two singular matrix coefficients,the distributed P-type learning law is utilize to consider the learning tracking control problem of expected trajectory.On the one hand,in view of the nonsingular matrix transformation,singular distributed parameter systems with parabolic type are transformed into the coupled partial differential equations which can describe the dynamic characteristics,and the algebraic equations which can describe the static characteristics.On the other hand,by estimating the relationship between the two sub states of the dynamic equivalence system and the system output tracking error,the convergence condition of the system tracking error under the ~2L norm mean is presented by means of the differential inequality and Green formula.Then,discussing the problem of learning tracking in the case of direct transfer matrix is zero,the sufficient convergent condition of tracking error is given.Finally,the convergence of the error is verified by the simulation results.(2)The iterative learning control problem of parabolic and second-order hyperbolic time-varying singular distributed parameter systems are consider in the light of a restricted equivalence form about linear time-varying singular distributed parameter systems.According to the theory of matrix singular value decomposition,two kinds of singular distributed parameter systems are converted into restricted equivalent forms.An open-loop P-type learning control law is designed for two classes of constrained equivalence learning systems.Based on the contract mapping principle and the(L~2,?)norm,and the actual system output is proved to completely tracking the given desired surface.Finally,the effectiveness of open-loop P-type learning control law is validated by numerical simulations.(3)According to the idea of design learning control law based on the model of distributed parameter system,the singular distributed parameter system is simplified to infinite singular systems for a class of constant coefficient parabolic singular distributed parameter systems in the light of intrinsic function method.Secondly,In view of matrix singular value decomposition theory,infinite singular systems are transformed into fast subsystems and slow subsystems.Then,a finite-dimensional hybrid PD-type learning control law is designed based on the characteristics of fast and slow subsystems.For the low dimensional modal part,the sufficient condition of learning convergence of the algorithm is presented,and it is proved that the actual output of the learning system can completely track the desired output.The high dimensional mode part can be selected by the low dimensional mode dimension,which makes the tracking error of the whole output of the system reach the corresponding precision.The results show that for any small tracking precision,it can be achieved by increasing the number of low-dimensional modes with learning control law.