Terminal Sliding Mode Control For Descriptor Systems

Descriptor systems are the representations of dynamic systems and they can also be called singular systems,they are such powerful that we use them in our daily life widely.More and more scholars have devoted themselves to researching the theoretical value of singular systems recently.Over the past few decades,sliding mode control(SMC)method was applied to descriptor systems considerably because of its strong robustness to the uncertain systems.What is more,in the field of SMC,terminal sliding mode control(TSMC)has brought a lot of attention to its advantages that system states can converge to sliding modes and system equilibrium points in finite time.A large number of scholars have carried out extensive research on normal systems and achieved significant results,but the research on descriptor systems is still lacking.Therefore,this paper put forward terminal sliding mode control method for descriptor systems and the theoretical analysis and simulation verification are given,the results of the paper are as follows.1.A nonsingular terminal sliding mode control method for single input single output(SISO)descriptor systems is presented in chapter three.Firstly,we transform descriptor systems into normal systems by using nonsingular transformations.Secondly,we design terminal sliding surfaces and controllers which guarantee that the system states can converge to system equilibrium points in finite time.In addition,we give the ranges of parameters which enables the controllers to be bounded.As for the singularity problems of controller,we analyze the reasons and give the corresponding solutions.Finally,simulation results are given to exhibit the validity of the theoretical results.2.A fast nonsingular terminal sliding mode control method for SISO descriptor systems is presented in chapter four.Firstly,we transform descriptor systems into normal systems by using nonsingular transformations.Secondly,we construct a series of fast terminal sliding mode surfaces and controllers,they can guarantee the convergence to be faster,the number of sliding modes to be fewer,the chattering phenomenon to be weaker.Besides,we give the ranges of parameters and the conditions for initial states which enable the controllers to be bounded and nonsingular.Finally,simulation results are given to testify the effectiveness of the theory.3.An exponential fast terminal sliding mode control method for multiple input multiple output(MIMO)uncertain descriptor systems is presented in chapter five.Firstly,we transform descriptor systems into normal systems by using nonsingular transformations.Secondly,we design switching manifolds and corresponding controllers with exponential terms which ensure that the system states can converge to zero in finite time.In contrast to fast terminal sliding mode control design approach,exponential fast terminal sliding mode control method enables the convergence of system to be faster.Finally,we make two sets of corresponding simulation examples which illustrate the effectiveness of the theoretical results.