Observer Design And Improvement For A Class Of Fractional Order Systems

With the continuous improvement and development of calculus theory,fractional order calculus and fractional order systems theory have been fully developed.At present,fractional order calculus have been widely used in mechanical manufacturing,polymer materials,machine learning and other cutting-edge science and technology fields.The order of fractional systems is no longer limited to integers,so it extends the expressive power of integer order systems.It may cause the controller produces incorrect measurement command and result in poor performance,when the systems exist sensor fault.In real life,all components may have more or less errors or faults.Measurement noise can’t be avoided in measurement,which makes it difficult to obtain the real state of the system.So it is important to design a appropriate state observer to estimate the state variables which are difficult to measure.In this paper,the observer design and improvement for uncertain fractional order systems with sensor fault and measurement noises are studied.Based on the study of relevant research and literature,take advantage of existing conclusions,the observer design method of uncertain fractional order systems with sensor fault and measurement noise are investigated.The stability of the error dynamic system are analyzed,and an improved observer method of uncertain fractional order systems is presented at last.The main contents are as follows:First of all,the observer design method for uncertain fractional order systems with sensor fault and measurement noises are studied with the fractional order satisfying 0<q<1.Because of the sensor fault and measurement noise,it increase the uncontrollability of the system.The system state variables can’t be obtained directly.Use the method of augmented matrix,we can estimate the original state and fault at the same time.Make use of the property of matrix rank to design state observer.A necessary and sufficient condition for asymptotic stability of the error dynamic system are obtained by LMI method,and solved numerical simulation by using LMI toolbox.At the end of the chapter,Simulink toolbox is used to simulate the system,the accuracy of the obtained criterion and the rationality of the observer design are verified.Secondly,the problem of the error dynamic system is solved with the fractional order satisfying 1<q<2.Based on the LMI method,a necessary and sufficient condition and a sufficient asymptotic stability criterion of the error dynamic system are proved.At the end of the chapter,base on the numerical examples and Simulink simulation,the accuracy of the obtained criterion are verified.Finally,according to the conclusion of the third chapter,the accurate estimation of sensor fault and measurement noise are solved.The observer is improved so that it is easier to implement in the control system synthesis.At the end of the chapter,through numerical examples and Simulink simulation,the validity of the sensor fault reconstruction and compensation method are proved.The rationality of the improvement of the observer is verified.