Conventional Linear Quadratic Regulator Research Articles

Vibration Reduction by Semiactive Spring Stiffness Control.

This paper presents a semiactive spring stiffness control approach for vibration reduction of one-degree of freedom mass spring system. The spring stiffness can be determined from the displacement and velocity feedback. However, because of the limitation that negative spring stiffness cannot be realized, it is impossible to obtain optimal feedback gain by means of the conventional linear-quadratic regulator. Therefore, this paper proposes a new on-off control law, in which the spring stiffness varies between the positive minimum value and the maximum value determined from the feedback, where the feedback gain is set with consideration of the vibration characteristics and performance of the device. The switching criterion is found by applying Pontryagin's maximum principle. Experimental results show good agreement with the numerical results, and it is found that the method presented in this paper is effective for vibration reduction.

Use of negative weights in linear quadratic regulator synthesis

An inverse problem of optimal linear quadratic regulators (LQR) is examined for single-input systems, and the selection of the weighting matrices that achieve a specified pole location is also discussed. In particular, the Kessler polynomial is used as a desirable pole location, and the weighting matrices are derived in an analytical form. Although this pole specification results in the use of some negative diagonal weights in the performance index, the existence and uniqueness of the Riccati solution are guaranteed by Molinari's theorem. Through the sacrifice of the circle condition, it is shown that some of the deficiencies of the LQR controllers are avoided, and that several characteristics (which classical controllers provide, but which modern methods cannot) are retained. An application to roll autopilot systems for missiles is given to illustrate and substantiate the proposed method, as well as to compare it with the conventional LQR.

The ‘unreachable poles’ defect in LQR theory: analysis and remedy

In virtually every application of optimum linear-quadratic regulator (LQR) theory there exists a hidden region of ‘unreachable poles’ (in the left half-plane) which cannot be realized as optimum closed-loop poles. These regions of unreachable closed-loop poles are not visible using the solution procedures ordinarily employed in LQR applications and their lurking presence has (apparently) been overlooked by many professors, textbook writers and industrial users of LQR control theory for the past 25 years. The existence of these regions of unreachable poles represents a serious defect in the LQR method because those regions may (and often do!) contain closed-loop pole patterns which are considered highly desirable by classical control engineering standards, i.e. by ITAE and other classical standards of ‘ideal’ transient response. We first show how one can identify the regions of unreachable poles in an LQR problem. Then, it is shown how one can modify conventional LQR theory to overcome this defect and make...

負の重みを使った最適レギュレータとオートパイロットへの応用

An inverse problem of optimal linear quadratic regulators (LQR) is examined for single-input systems, and the selection of the weighting matrices which achieves a specified pole location is discussed in this paper. In particular, the Kessler polynomial is used as a desirable pole location, and the weighting matrices are derived in an analytical form. Although this pole specification results in the use of some negative weights in the performance index, the existence and uniqueness of the solution are guaranteed by Molinari's theorem. At the sacrifice of the circle condition, it is shown that some of deficiencies of the LQR controllers are avoided and several characteristics which classical controllers provide, but which modern methods cannot so far, are retained. An application to roll autopilot systems for missiles is given to illustrate and substantiate the proposed method as well as to make a comparison with the conventional LQR.