Input Saturation Treatments: A Performance Comparison of Direct Adaptive Control and θ - D Control Methodologies

Input saturation is an operating condition that is well known to the control community for its "side effects" which cause both conventional and adaptive controllers to lose their control performance (i.e., agility/bandwidth and command tracking) as well as stabilization capability. Characterizing the effects of input saturation via the angle of domain attraction and/or Eigen-values shifting as a function of input amplitude variation (in addition to frequency dependency of linear system) can be useful in providing directions for developing conventional treatments to the fixed-gain controller design paradigm. However, on-line treatment or adaptive control treatment to input saturation has shown limited proven success. This paper presents an effective adaptive control treatment to input saturation using two types of controllers: direct adaptive control and θ-D control. Detailed descriptions of both controllers formulated for spacecraft (SC) attitude control are provided, and design guidelines for both direct adaptive control and θ-D controllers are also included as generalized rules for selecting the initial sets of respective adaptation parameters (i.e., initial weighting matrices for both control laws). Their effective treatments are characterized, analyzed, and interpreted via a quadratic Lyapunov based function and Hamilton-Jacobi-Bellman (HJB) optimization based technique, respectively. Dynamic stability behavior in the context of adaptive control via simulation based approach is also captured for both θ-D and direct adaptive control approaches. Their asymptotic stability behaviors via simulation based approach reflect the theoretical Lyapunov framework. The effectiveness of these two solutions is then demonstrated via a nonlinear SC environment subject to two classes of input saturations: (1) actuator authority limit and (2) attitude and rate error limits which a traditional fixed-gain proportional-integral-derivative (PID) controller fails to stabilize using similar operating conditions,. It is worth pointing out here that both θ-D and direct adaptive controllers are robust enough to handle nominal operating conditions and input saturation situations without relying on other control augmentation schemes (e.g., pseudo control hedging (PCH), direct adaptive control+PID, PCH+neural network based) as presently offered by mainstream controllers. Both proposed control laws are attractive and directly applicable to future missions like aerocapture vehicle technology demonstration which requires not only adaptive robust performance and high precision orbit entry and exit (based on a single pass constraint) but also the ability to solve the guidance and control in a truly integrated guidance and control (IGC) sense. As a result, they offer a low risk and low cost design feature for aerocapture technology and practically help achieving the design within its constraint and accelerated schedule timeline.