Stabilization Control Of Underactuated TORA Systems Subject To Input Constraints And External Disturbances

The Translational Oscillator with Rotating Actuator(TORA)has fewer control inputs than the number of degrees of freedom,and is a typical underactuated system.At the same time,because of its strong coupling and highly nonlinear characteristics,it is often used as an underactuated benchmark system for nonlinear controller design and performance testing of nonlinear control algorithms.In addition,in engineering,TORA system is often used as Active Mass Damper(AMD)for active vibration suppression of large practical engineering systems.Therefore,the research on control problems of TORA system has important theoretical and practical significance.At present,extensive research has been carried out on the underactuated TORA system at home and abroad,and rich research results have been obtained.However,in practical applications,the input of the system can only provide limited control torque due to the limitation of physical characteristics,and due to cost and Considering the system structure,the angular velocity information of the system is often difficult to measure.In addition,the system will inevitably be affected by various uncertain external disturbances,so it is necessary to study the output feedback control problem of the underactuated TORA system when the input is limited and the influence of external disturbances.In this paper,to address these problems,the underactuated horizontal TORA system is taken as the study object,a nonlinear bounded input output feedback stabilization control method is proposed by combining with a biologically inspired model,a novel energy storage function and Linear Extended State Observer(LESO)technology.The main contributions of this thesis are as follows:(1)To address the problem of limited input,a bounded input stability control method for underactuated TORA system based on a biologically inspired model is proposed,which solves the problem of actuator saturation constraints in practical applications.Firstly,a novel Lyapunov function is constructed according to the passive characteristics of the system.Then considering the saturation constraints of the actuator,a biologically inspired neural dynamics model is introduced,and its bounded and smooth output characteristics are used to design a realization of input restricted controller.Finally,according to the Lyapunov stability theory and the LaSalle invariance principle,the stability of the system is analyzed and proved strictly mathematically,and the simulation test is carried out on MATLAB.The test results show that the proposed method ensures that the control input torque required by the system does not exceed the maximum input torque that the actuator can provide,and has better performance in terms of settling time,oscillation amplitude and robustness.(2)To address the problem of unmeasurable angular velocity of small ball,an output feedback control method is proposed for underactuated TORA system based on novel energy storage function,solving the problem of unmeasurable angular velocity.First,a novel energy storage function is constructed with the addition of auxiliary signals.Then,using the Lyapunov stability theory,the limiting control law realized by the saturation function and the auxiliary signal for dynamically generating the virtual angular velocity signal are directly deduced,and the output feedback control of the system is finally realized.Finally,according to Lyapunov stability theory and LaSalle invariance principle,the stability of the system is analyzed and proved strictly mathematically,and verified by simulation test.The simulation test shows that the proposed control method can realize the stable control of the system without the feedback of angular velocity information,and the input torque never exceeds the set maximum input torque.In addition,the proposed control method has the advantages of short stabilization time,low overshoot,and strong robustness.(3)To address the problem of external disturbance,a continuous state feedback control method based on LESO is proposed.First,the whole system is transformed into a cascade model consisting of two subsystems through coordinate transformation.Then,using the idea of Backstepping control,a virtual control input is designed for the first inner-loop subsystem to realize the stabilization control of the inner-loop subsystem.For the second subsystem,a LESO is constructed to observe the external uncertain disturbance,based on which a continuous state feedback controller is designed.Finally,the closed-loop stability of TORA system and the convergence of LESO are strictly analyzed and proved by Lyapunov stability theory and LaSalle invariant principle.The simulation test shows that the proposed method can effectively estimate and compensate for the unknown external disturbance,which not only reduces the dependence of the control system on the system model,but also makes the controller have better robustness,and the design process is clear and the control process is continuous,achieving a smoother control performance.