Applying standard characteristic polynomials to designing eigenvalue assignment

Our aim is to resolve to a considerable degree the uncertainty of the choice of ideal eigenvalue assignment and the difficulty of engineering implementation. Section 1 of the full paper briefs the algebraic properties of standard characteristic polynomials. Section 2 derives eqs. (4) through (9) needed for applying standard characteristic polynomials to designing eigenvalue assignment. Section 3 takes as example the longitudinal stability of the control system of a certain aircraft; it gives simulation results comparing the method proposed in this paper with the well-known linear quadratic regulator method. The simulation results in Fig. 3 show preliminarily that the better eigenvalue assignment method can achieve about the same performance as that of linear quadratic regulator method. As is well known, linear quadratic regulator method requires that the designer must have not only sound theoretical grounding but also a great deal of engineering experience, thus making it very difficult for ordinary designers to implement. But our better eigenvalue assignment method is simple and therefore easy to implement. Simulation results, given in Figs. 4 through 6, show preliminarily that the robustness of the control system achievable with our better eigenvalue assignment method is higher than that achievable with linear quadratic regulator method.