Design Of Sliding Mode Controller Based On Reaching Law Method

Sliding mode control(SMC)is representative in variable structure control methods,and has attracted wide attentions from academia and industry.Theoretical researches and engineering application explorations based on SMC have developed as an important branch of modern control science.Generally,SMC changes the structure of the controlled system according to the value of the current switching function,so as to force the system trajectory to move alongside the pre-determined sliding surface.The sliding surface of the system can be designed independently and is free from the change of system parameters.Controlled system states in the sliding mode are independent of parameter perturbations and external disturbances that satisfy the matching conditions.Advantages of the sliding mode control method lie in its remarkable robustness and model independency.Despite many good features,SMC still faces various challenges in practical uses.Firstly,the switching characteristics of the sliding mode controller and the physical inertia constraints of the actuator make it difficult to maintain the state of the system in sliding mode,which results in chattering and time-consuming state converge processes.Secondly,controllers in modern days are usually implemented via computer systems.The limited sampling frequency of the system will make it difficult for SMC to remain its advantages.Here are some questions worth considering when it comes to the design of SMC in either continuous-time systems or discrete-time systems:How to reduce the chattering of sliding mode controllers in continuous systems;How to realize fast system state converge;What are the unique properties of discrete sliding mode control(DSMC)systems;How to design the DSMC to ensure its robustness property,and how to analyze the corresponding performance of controlled systems.In this dissertation,sliding mode control methods for continuous-time systems and discrete-time systems are studied.Aiming at chattering suppression,finite-time state convergence and analyzing quasi-sliding mode(QSM)state performance in discrete-time domain,this dissertation considers the SMC designs based on reaching law method.Reaching law for the switching function in SMC directly determines the dynamic per-formance of the switching function in its reaching phase.In practice,it will also affect the performance of the switching function within the sliding phase,thus indirectly af-fects the system state trajectory.Therefore,the requirement of sliding mode controller for control tasks can be satisfied by reasonably designed reaching law.The following topics are studied in this dissertation:controller design for linear continuous system with disturbances,controller design for nonlinear continuous systems to achieve finite-time state convergence,controller design for linear discrete-time system to achieve chattering compression.Contributions of this dissertation are summarized as follows.1.Aiming at the contradiction between system reaching time and chattering am-plitude in traditional reaching law for continuous systems,a non-linear adaptive sliding mode reaching law is proposed.In the design process,a negative exponential term that consists of the system switching function is introduced into the gain of the reaching law.Via calculation and analysis,when the proposed two regulation rules for the reaching law are applied,system trajectory has the following characteristics:when the initial states of the system are far from the sliding surface,their reaching speed are accelerated and the reaching time of the system state is reduced;When the sliding surface is reached,chattering amplitude of the switching function on the sliding surface is compressed.The reaching law is then applied to the design of speed controller for the permanent magnet synchronous motor(PMSM),and the motor speed tracking task can be well accomplished.2.While designing the speed SMC with the proposed reaching law,this dissertation extends the research on PMSM control problem in various cases.A sliding mode observer(SMO)is designed to estimate the disturbance of the system.The estimated disturbances are then feedforward into the controller to eliminate the corresponding term,which helps in decreasing the gain of reaching law and reducing chattering level of the system.When the PMSM is not equipped with an encoder or other position sensors,a sensorless position estimation strategy is needed for the PMSM speed control task.This dissertation then proposes an improved SMO and a new phase locked loop structure to extract the rotor electrical position and speed information.The proposed solution guarantees the estimation accuracy with forward and reverse rotor speed.3.For the finite time convergence requirement of a class of nonlinear systems in continuous-time domain,an SMC scheme is proposed based on an improved sliding mode reaching law and a terminal sliding surface design.First,to solve reaching time/chattering dilemma in the traditional reaching law method,a negative power term including the system switching function is introduced into the gain of the discontinuous function of the reaching law,and the initial value of the switching function is used in the parameter design.Compared with the reaching law proposed in 1,users only need to follow one simple parameter tuning rule in order to reduce system reaching time and chattering level at the same time.According to the special expression form of the system,a terminal sliding surface is proposed,which theoretically guarantees that the system state trajectory can converge to the equilibrium point in finite time after entering the sliding mode.The finite-time convergence control of the nonlinear system is realized by qualitatively designing the trajectories of the switching function in the reaching phase and sliding phases respectively.4.In the discrete-time domain,two discrete sliding mode reaching law are proposed for systems with the prior information of different perturbations.The first discrete reaching law is proposed based on the assumption that the upper and lower bounds of system disturbances are known.In addition,the non-continuous term is replaced by a continuous one in the reaching law,so as to successfully reduces the chattering of the controller.The second reaching law relaxes the prior knowledge requirement for system disturbances.Assuming that the second-order difference of disturbance is bounded,the current disturbance of the system is estimated by using the disturbance values from previous moments,and an adaptive gain associated with the switching function is introduced to effectively alleviate the reaching time/chattering dilemma.With the proposed second reaching law,width of the quasi-sliding mode band(QSMD)is maintained in the order of O(T~3),which is smaller compared with most of the existing research results.