Design of Optimal Regulators

Current research suggests the use of a liner quadratic performance index for optimal control of regulators in various applications. Some examples include correcting the trajectory of rocket and air vehicles, vibration suppression of flexible structures, and airplane stability. In all these cases, the focus is in suppressing/decreasing system deviations rapidly. However, if one compares the Linear Quadratic Regulator (LQR) solution with optimal solutions (minimum time), it is seen that the LQR solution is less than optimal in some cases indeed (3 -6) times that obtained using a minimum time solution. Moreover, the LQR solution is sometimes unacceptable in pra ctice due to the fact that values of control extend beyond admissible limits and thus the designer must choose coefficients in the linear quadratic form, which are unknown. The authors suggest methods which allow finding a quasi -optimal LQR solution wi th bounded control which is closed to the minimum time solution. They also remand the process of the minimum time decision.