On Chattering Characteristics And Chattering Suppression In The Sliding-Mode Variable Structure Control

Study of chattering characteristics is an essential part of the variable structurecontrol (VSC), which is closely related to VSC switching surface parameters selection,switching control law design and stability analysis. A generalized describing function(DF) stability criterion and a VSC switching gain adaptive method are proposed to solvethe resonance introduced by VSC chattering and the immeasurability of some statevariables. Methods of calculating and adjusting VSC chattering characteristics areintensively studied, based on which the backlash compensating controller and two kindsof second order sampling VSC are designed and analyzed. Stability problems associatedwith the system initial value of VSC are discussed as well. Simulations and circuitexperiments are used to certify the theoretical method of calculating chatteringcharacteristics which is proposed in this thesis. The main contributions are as follows.1. In order to improve the stability analysis of frequency-dependent describingfunction N(A, ω), a generalized describing function (DF) stability criterion based onnumerical calculation and plotting is derived. By using the generalized DF stabilitycriterion to plot θ-ω curve and survey the slope change of the curve, the number ofchattering point can be judged quickly, the influence of initial value on the VSCstability and chattering characteristics is revealed. By applying the generalized DFstability criterion in the reaching law and the relay VSC system, the relationshipbetween sampling period, zeros and poles distribution and chattering stability is studied,which provides the basic for part of the state switching surface design.2. A dual-loop switching controller and a torque feedback controller are designed forthe output and the internal backlash compensation algorithms by applying the presentedmethod of the chattering characteristics research. By serially connecting ideal relay andbacklash hysteretic model, the DF calculation of output backlash model is simplified inthe dual-loop switching controller. The torque feedback controller estimates thebacklash contact surface transfer torque with the position signal of the system output.Frequency domain relationship between backlash input and feedback torque isestablished with the generalized DF stability criterion, which is also used to calculatestability range of the torque feedback gain. To obtain expected control precision andresponse speed, the chattering characteristics should be flexibly adjusted byappropriately changing gains of the two controllers.3. The stability proofs of the output differential and the output feedback second ordersampling controller are developed, and the relation between controller parameters and chattering characteristics is derived. By analyzing the moving range of the phasetrajectory in the planar coordinate, transfer time between key points in the phase planeis calculated, and the analytical expression of chattering characteristics is obtained.Employing the generalized DF stability criterion in frequency domain, stability of theoutput feedback second order sampling VSC is proved, and the relation between systeminitial values and system stability is also researched, which provides theoretical basis fordesign optimization of the controller. The VSC circuit experiment platform based onDSP and FPGA are designed, and the chattering characteristics analysis methods areverified by drawing and comparison the sliding-mode chattering and limit cycletrajectory.4. A kind of Adaptive Unscented Kalman Filter (AUKF) is proposed, which judgesthe abrupt change of the state variable by computing the differentiation accumulationvalue. The algorithm resets the covariance matrix at the sudden changing of state toimprove speed and reduce overshoot of the state estimation. Besides, the covariancematrix can finally match system noise model again after iterations. Based on the AUKF,a kind of nonlinear system VSC chattering suppression scheme is designed. Byestimating external disturbance, the VSC switching gain can be adaptively adjusted.Hence, the switching gain could change with the external disturbance, and the chatteringcan be suppressed. The chattering suppression effect of the scheme is verified by astraightforward pendulum control simulation.5. For a class of discrete systems with uncertainties, a switching gain scheduledsliding-mode controller is proposed. The controller suppresses chattering amplitude,guarantees the H_∞performance and improves transient response performancesimultaneously. According to the system output error, the switching gain schedulingrules are designed. Furthermore, the relation between quadratic stability and robust H_∞performance are derived based on switching system theory. By solving the LinearMatrix Inequality (LMI), the parameters of the controller meeting the performancerequirements are obtained.