Stability and robustness are fundamental design requirements of any control system. Consequently, stability analysis is a vital stage in the design and development process of a control system; it not only provides information about the stability of the system, it also gives insight into the operating conditions that affect the stability of the system. In the case of identifying the control parameters required to stabilize the re-entry path of a space shuttle into the earth’s atmosphere, most control engineers typically apply a brute-force trial-and-error approach despite the existence of advanced methods, such as one developed by Chang and Han in 1989 that follows a more systematic approach. Although it is extremely precise, this method has not gained much popularity due to the difficult nature of the equations and the inability of traditional software to solve the equations symbolically. Using Maple, Maplesoft’s advanced computation tool, the re-entry path of a space shuttle can be controlled by calculating and examining the stability boundaries of constant gain and phase margins.
Maple can be used to create a closed-loop model of the system with the addition of a gain-phase margin tester. The closed-loop transfer function equations are symbolically manipulated into the desired form. A procedure to automatically generate values of the unknown parameters is created, as well as the stability boundary plots for constant gain and margins.
Adding the gain-phase margin tester allows the immediate calculation of the control parameters necessary to stabilize the space shuttle within the specified design constraints. By utilizing Maple, the required algebraic manipulations that would otherwise be too complex to do by hand or with purely numeric software can easily be performed. This saves valuable time by providing the solutions immediately, avoiding the countless iterations required by traditional brute-force methods that could take days to perform.
Contact Maplesoft to learn how Maple can be used in your projects.