| Inverted pendulum is a typical nonlinear,under-actuated,multi-variable,strong-coupled,multi-rigid hinge mechanical structure.The number of driver is less than the degree of freedom,the states of non-drive rods can only be influenced though the coupled effect of joints,it's hard to achieve specific goal with single control.The typical problems of control,stabilization and robustness can be directly reflected in inverted pendulum system,which is the preferred platform for inspection control theory and control method,and known as the "Pearl of control" and "the touchstone of control theory".In real life,many control problems can be abstracted as inverted pendulum to study,such as biped walking robot,underactuated manipulator,two wheeled balancing vehicle,rocket verticality,etc.Inverted pendulum related control methods are widely used in military,aerospace,robotics and other fields.Each rod of pendulum has two equilibriums: downward equilibrium and upward equilibrium,so Nth inverted pendulum have 2N equilibriums.Only the point with all rods downward is the natural balance point,all others are critical equilibrium which needs proper control to keep dynamic balance.Currently,most researches foucs on the balance control in the neighbourhood of equilibriums,and swing up control from hanging equilibrium to inverted equilibrium,while there are almost no research about arbitrary transfor control between equilibriums.In order to achive the large scale nonlinear motion control,needs precise control of rods' angle and rapid adjustment for relative attitude and energy of rods,and all this can only be realized through a single control input,which is very difficult.To solve arbitrary transfor control problem of double inverted pendulum,we have done some research works on quasi-equivalent modeling and nonlinear dynamic analysis,control method and controller design,and unmodeled dynamic inhibition.The main works of this paper are as follow:(1)Because of the complex dynamic characteristics of the inverted pendulum,the linearization analysis method can not meet the control requirements.To solve this problem,a nonlinear dynamic analysis method is proposed.Firstly,the quasi-equivalent dynamic model of inverted pendulum is established,and then the angular acceleration expression of passive joints is derived by dynamic decoupling of mathamtic model.The strength functions of control,gravitational force,rotational friction,and rotating centrifugal force are separated.The quantitative relationship between the posture of rods and the control strength of rods is analyzed,as well as physical parameters and control strength.It can be used as reference for the controller design and the mechanical design.(2)There are some limitations of SMIS-HSIC: Formal description of high level intelligent shcema is not detailed enough,and lack specific application algorithm.To solve this problem,an improvement is proposed to SMIS-HSIC.By analysis two basic process of SMIS-HSIC,sensor-motor intelligent schema is proposed to be the basic unit of SMIS-HSIC system,the unified formal description for low order sensor-motor intelligent schema,high order associated schema,balance schema,assimilation schema,and the acclimation is realized.Applying improved SMIS-HSIC,and combine nonlinear dynamic analysis and prior knowledge,and first achived the arbitrary transform control of double inverted pendulum.(3)A kind of unmodeled dynamics inhibition methods,which contains online part and offline part,is proposed to solve the problem of low stability and reliability caused by unmodeled dynamics in real-time situation.The online part is aimed to deal with random unmodeled dynamic,which include key parameters adjustment based on stability characteristic,and gain scheduling compensation control based on reference trajectory.The offline part is aimed to deal with the problem of characteristic drift of controlled object,which include physical parameters identification and control parameter optimization with improved genetic algorithm. |
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