Balance Control For A Class Of Underactuated Mechanical Systems Driven By Virtual Un-modeled Dynamics

Pendubot which is a typical nonlinear underactuated mechanical system is an underactuated planar robot with two degrees of freedom. It has a special structure of single input and two outputs. Underactuated mechanical systems play a leading role in industries and are used in the fields of aerospace and robot because they have the advantages of reducing the number of actuators, lightening the weight of the equipments and lowering the cost. The conventional linear controllers are difficult to obtain ideal control performance because of their high order nonlinear property. Besides, the multivariable decoupling methods are no longer applicable to those systems because of their underactuation. It is well known that it is impossible to use smooth feedback nonlinear strategies to stabilize those underactuated mechanical systems. Consequently, the class of underactuated mechanical system has very high theoretical and practical value. Pendubot is different from conventional linear inverted pendulum and rotational inverted pendulum. Its linear models are different in every point. The control of Pendubot can be divided into swing-up control and balance control. This paper mainly researched the balance control strategy. The existed balance control algorithms have the following problems. Firstly, most of the existed balance control algorithms have steady state error because of ignoring of the friction influence. Secondly, most of balance control algorithms depend on accurate dynamic model of Pendubot. Thirdly, some of existed algorithms are more complicated, hard to assure the stability of Pendubot system and only stay in simulation.Aimed at the questions mentioned above, supported by the "985" project of the National Key Laboratory of Synthetical Automation for Process Industries (Northeastern University), this paper proposes the balance control strategy for a class of underactuated mechanical systems driven by virtual un-modeled dynamics, and the obtained main results are as follows:(1) Combined with the advantages of conventional PD controller in industry and in order to eliminate the influences of nonlinear characteristic, friction, gravity and uncertainty, this paper uses the last-step and the estimated value of the increment to substitute the un-modeled dynamics to design the PD controller driven by virtual un-modeled dynamics and analyses the stability of the closed-loop system.(2) When the control target of Pendubot is the uppermost unstable equilibrium position, Pendubot is mainly affected by friction. We can obtain better performance of Pendubot using the last-step to instead of the un-modeled dynamics. But when the last-step and the estimated value of the increment are applied in uppermost unstable equilibrium position, we can further improve steady accuracy.(3) When the control target of Pendubot is the non-equilibrium position, the friction becomes more complicated because of the affect of gravity. Using of the last-step to estimate of the un-modeled dynamics does not meet demand. This paper applies the last-step and the estimated value of the increment to estimate of the virtual un-modeled dynamics. The results of simulation show that the proposed strategy expands the attraction domain and reduces the steady state error of Pendubot.(4) By using Pendubot system, the proposed control algorithm experiment study is launched. When the control target of Pendubot is the uppermost unstable equilibrium position, the experimental results show that the controller proposed by this thesis expands the attraction domain and reduces the steady state error of Pendubot compared with LQR and SDRE methods. And when the control target of Pendubot is the non-equilibrium position, the virtual un-modeled dynamics compensator designed by the last-step and the estimated value of the increment improves the performance of Pendubot.