Studied the control problem concerning the swinging-up and handstand-control of the cart-triple-pendulum system (CTPS, a typical under-actuated, unsteady and nonlinear system) based on the human-simulated intelligent control (HSIC) theory.

The development of control theory and strategies on triple inverted pendulum system (TIPS) could facilitate not only to the development of control theory but also to the real control technology in practice.

The Lagrangian equations are chosen to es-tablish the nonlinear mathematical model of the triple inverted pendulum system,and then the model is linearized in its equilib-rium point and the control law by using LQR(Linear Quadratic Regulator)optimal control theory is acquired.

he method of averaging is applied in this paper to deal with a primary resonance of a three circular plates torsion vibration system having cubic nonlinearities which is excited by a simple_harmonic excitation.