Design And Performance Research On Several Typical Discrete Sliding Mode Control Systems

Due to the urgent requirements of modern engineering systems for high precision and strong robustness,the suppression of external disturbances,parameter variations and unmodeled dynamics has become an important subject.Sliding mode control can drive the controlled system onto the predesigned sliding mode manifold,and then adopt switching control to maintain sliding motion so as to exhibit strong robustness to matched uncertainties.As the price of microprocessor hardware gets cheaper and cheaper,the control algorithm is usually implemented in digital electronic devices.Therefore,it is an urgency to design discrete-time sliding mode control algorithms that can be directly realized digitally.Because the sampling frequency of system and switching frequency of sliding mode are limited,discrete sliding mode control systems show complex dynamic behaviors,such as the domain of attraction in reaching motion phase,the quasi sliding mode domain in sliding motion phase,the self-sustained oscillations in steady state and so on.For second-order switched linear systems,second-order nonlinear systems,high-order nonlinear systems,single-input uncertain systems and multi-input unmatched systems,these complex dynamics of discrete sliding mode control have their own different characteristics,which have not been sufficiently studied.Given all that,in combination with sliding mode control theory,implicit Euler integration method,disturbance observer design,adaptive control technique and other technical methods,this dissertation will design the corresponding discrete sliding mode control algorithm for several typical discrete-time systems,and then analyze the dynamic and steady-state performances of the closed-loop system.The main research works are as follows:Firstly,the design and analysis of discrete linear sliding mode control for secondorder switched linear systems discretized by zero-order holder are studied.Taking Buck converter as the research object,the performance analysis of the second-order switched linear system controlled by discrete linear sliding mode is conducted,focusing on the stability and periodicity of the closed-loop system.Based on the reaching condition of discrete sliding mode,the stability region of Buck converter is derived.The periodic dynamics of the closed-loop system is transformed into the problem of solving a class of binary nonlinear equations.It is proved that the system trajectory tends to period-2orbits with the decrease of sampling period.Upper bounds for the system steady states are innovatively established from the perspective of periodic dynamics,and the effects of parameter variation and external disturbance on the steady-state performance of Buck converter are systematically analyzed.Secondly,the design and analysis of discrete terminal sliding mode control for second-order nonlinear systems discretized by Euler integration method are studied.The explicit and implicit discrete-time models of second-order nonlinear systems are obtained by using explicit and implicit Euler integration methods,respectively.For the explicit discrete-time system,it is deduced that the quasi sliding mode domain of discrete nonsingular terminal sliding mode manifold belongs to a decrement-width type(V-shape),which significantly improves the steady-state accuracy of the sliding mode variable compared with the constant-width-type(H-shape)quasi sliding mode domain of discrete linear sliding mode surface.Based on the movement features of steady-state points,the influence relationship of control parameters including the switching gain and sampling period on the steady-state error of the system is established.For the implicit discrete-time system,the convergence characteristics and implementation issues of discrete nonsingular terminal sliding mode are investigated by utilizing the set-valued signum function.The theoretical analysis shows that the closed-loop system has the advantages of global convergence,chattering attenuation and high-precision control.Thirdly,the design and analysis of discrete higher-order sliding mode control for high-order nonlinear systems discretized by Euler integration method are studied.The explicit and implicit discrete-time models of high-order nonlinear systems are established by using explicit and implicit Euler integration methods,respectively.For the implicit discrete-time high-order nonlinear system,an implicit discrete nested fast terminal sliding mode control based on the high-order disturbance compensation is proposed.The upper bound of steady-state sliding variable is derived,and the finite-time convergence of sliding variable is proved.For the explicit discrete-time high-order nonlinear system,a novel homogeneous higher-order sliding mode manifold is constructed to obtain the standard asymptotic accuracy of homogeneity;a new parameter tuning method is proposed to overcome the limitation that Hurwitz criterion can only be applied to weakly nonlinear sliding mode manifolds;an adaptive discrete control law is designed to drive the system trajectory to converge to the homogeneous higher-order sliding mode manifold.Then,the design and analysis of discrete reaching law for single-input uncertain systems discretized by zero-order holder are studied.The implicit Euler integration method is introduced into the design of discrete reaching law for the first time,and two new types of implicit discrete reaching law are designed for single-input uncertain systems:adaptive implicit discrete reaching law and generalized implicit discrete reaching law.At the different phases of sliding motion,the adaptive implicit discrete reaching law can automatically regulate its power parameter to acquire any high-precision sliding motion.By releasing freedom degrees for parameter design of implicit discrete power reaching law,a generalized implicit discrete reaching law with explicit recursive structure is proposed.The two new reaching laws are simple in form and have good control effect,which effectively expand the design scope of discrete reaching law and provide new thoughts for the design of discrete reaching law based on implicit Euler method.Finally,the design and analysis of discrete adaptive sliding mode control for multiinput unmatched systems discretized by zero-order holder are studied.With the help of coordinate transformation method,the state space of unmatched discrete-time system is decomposed into matched subsystem and unmatched subsystem according to matched and unmatched uncertainties.Using the output information of disturbance observer,the sliding mode manifold with disturbance compensation is constructed,and then adaptive discrete sliding mode control algorithms based on full-order disturbance observer and reduced-order disturbance observer are proposed.The former fully compensates the disturbance to realize the high-precision control of the closed-loop system,but at the same time,the disturbance is required to meet the bounded condition.The latter only compensates the unmatched uncertainty,and thus has low computational complexity,and improves disturbance rejection performance of the controlled system to the unmatched uncertainty.