Analysis And Research On Control For Periodic Piecewise Vibration Systems

Many phenomena in nature show obvious periodic characteristics.As a special type of periodic system,the periodic piecewise system can describe the periodic system with piecewise characteristics better.With the characteristic of piecewise,the periodic piecewise system has also attracted a large number of scholars and experts to conduct more in-depth research and analysis.The periodic piecewise vibration system can be regarded as the application of the periodic piecewise system in practical engineering.It can be regarded as a kind of periodic piecewise system with stable subsystems.For the periodic piecewise vibration system,some scholars have designed a periodic piecewise constant controller to attenuate the vibration of the system.However,this type of controller relies too much on the initial value and is highly conservative.Therefore,this paper proposes a more flexible and less conservative controller design method.For the periodic piecewise vibration system,this paper proposes a time-varying H_? controller design method.Firstly,the concept and characteristics of periodic system and periodic piecewise system are introduced,and the exponential stability criterion,performance index criterion and design method of a periodic piecewise constant controller are discussed.Then the exponential stability criterion of periodic piecewise vibration system with partial time-varying term is introduced.The H_? performance index theorem of periodic piecewise vibration systems with partial time-varying terms is proposed.Finally,the design method of time-varying H_? controller for periodic piecewise vibration systems is given.The main points of this article are as follows:The H_? performance index theorem for periodic piecewise vibration systems with partial time-varying terms is proposed.The periodic piecewise vibration system of the lumped parameters is modeled,and the Dini-differentiable and Lyapunov functions are used to obtain the exponential stability criterion of the periodic piecewise vibration system with partial time-varying terms.Based on this, H_? performance index theorem for periodic piecewise vibration systems with partial time-varying terms is given.A time-varying H_? controller design method is proposed for the periodic piecewise vibration system.Based on the H_? performance index theorem,the theorem of time-varying H_? controller design with discontinuous controller gain is proposed.And for practical consideration,the corollary of time-varying H_? control design with continuous controller gain for periodic piecewise vibration system is given.Finally,the simulation results are used to verify the feasibility of the proposed controller.