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.
The challenge: To control the re-entry path of a space shuttle by calculating and examining the stability boundaries of constant gain and phase margins.
The engineer uses Maple to:
- Create a closed loop model of the system with the addition of a gain-phase margin tester
- Symbolically manipulate the closed-loop transfer function equations, which include a gain-phase margin tester, into the desired form and create a procedure to automatically generate values of the unknown parameters
- Create stability boundary plots for constant gain and margins
Adding the gain-phase margin tester allows the engineer to immediately calculate the control parameters necessary to stabilize the space shuttle within the specified design constraints. By utilizing Maple, the engineer can easily perform the required algebraic manipulations that would otherwise be too complex to do by hand or with purely numeric software. This saves the engineer time by providing the solutions immediately, avoiding the countless iterations required by traditional brute-force methods that could take days to perform.