Based on the modern control method and an LQR method in which the vibration energy of the structure and the control signal energy are chosen as the object function is adopted to control the vibration of cantilever beam through using piezoelectric material.

Based on the modern control method, a LQR method, in which the vibration energy of the structure and the control signal energy were chosen as the object function, was adopted to control the vibration of plate with various boundary conditions through using piezoelectric material.

To the question of the active vibration control for piezoelectric laminated structure, in order to optimize the effect of the vibration control, based on the modern control method, a LQR method, in which the vibration energy of the structure and the control singal energy were chosen as the object function, was proposed.

By adopting the energy-based and LQR method,a swing up controller and a balancing controller are designed.

In view of the characteristics of the nonlinear of the pendulum system,the LQR algorithm was applied to control the cart position and the pendulum pole angle simultaneously.

By using quadric LQR algorithm, optimal control rule was educed.

This paper presents the basic principles for designing LQR controller and PID controller.

The mathematic model of rotational inverted pendulum is analysed, with the aids of LQR control and fuzzy control, a double structure control scheme compared with conventional LQR control is advanced.

Based on actual vehicle suspension system, three typical LQR controllers based on various control objects are designed and analyzed.

Optimization design for weighting matrix of LQR controller based on chaos variable;

LQR controller design with pole's moving-range

Using the de- sign process of LQR controller as an example,the weighting matrixes Q and R of th.