Control of an unstable, nonminimum phase hypersonic vehicle model

In this work, a control law for an unstable, non-minimum phase model of a hypersonic vehicle is developed. The control problem is difficult due to the locations of the plant poles and zeros. For an unstable system, feedback is required to stabilize the plant. However, one cannot make the loop gains arbitrarily large without driving one or more of the closed-loop poles into the right-half of the s-plane, since the system is nonminimum phase. Thus, there is a limited range of feedback gain that results in a stable system. The nonminimum phase behavior also places restrictions on the closed-loop bandwidth. For the hypersonic vehicle control problem, low frequency control is desired and a rule of thumb is that the closed-loop bandwidth must be less than one-half the right-half plane zero location. A right-half plane zero located in the region of the desired gain-crossover frequency makes it impossible to achieve the desired level of tracking performance. The achievable closed-loop bandwidth might be so small that adequate control of the system is not achieved. Direct cancellation of the right-half plane zero with an unstable pole in the controller is not an option. In this work, a modified dynamic inversion controller is developed for a linear, time-invariant model of a hypersonic vehicle. This modified dynamic inversion controller differs from the standard dynamic inversion approach in that it does not attempt to cancel the right-half plane zero with a pole, instead, it retains right-half plane zeros in the closed-loop transfer functions and uses an additional feedback loop to stabilize the zero dynamics