Scalar sign function-based digital controller design for constrained continuous-time nonlinear systems

This dissertation work focuses on digital controller design for constrained nonlinear systems using the scalar sign function approach. It is motivated by the fact that nonlinear systems with absolute value function constraints are typically difficult to control due to their non-smooth and nonlinear nature. This work novelly adopts the scalar sign function (SSF) approach to transform the originally non-smooth model to a smooth one. This key step greatly facilitates the subsequent modeling and controller design tasks.;Based on the resulting smooth models, systematic digital controller design methods are proposed. First, an optimal linear model (OLM) is established; the derived OLM has the exact dynamics of the original nonlinear system at the operating points of interest and minimum modeling errors in the vicinity of those operating points on the trajectory. Then, analog controllers (e.g., LQR and optimal PI-based controllers) are developed for the linearized models. After the analog controllers are in place, digital redesign methods such as the prediction-based digital redesign method and the Chebyshev quadrature method are employed to achieve the same effective performance as that of the original analog controllers. A digital observer using the prediction-based digital redesign technique is constructed to estimate the practically inaccessible or unavailable system states. For clarity, Chua's circuits and the piezoelectric actuator systems are used to illustrate the proposed digital control schemes. Multiple successful simulation results also validate the utilization of the SSF approach and the digital redesign techniques.;A new control method, also centered on the SSF, is proposed to deal with the sampled-data system control of continuous-time nonlinear systems that are subject to input saturation constraints. This method uses the SSF to reformulate the optimal linear model of the nonlinear system as input saturation occurs. The smooth nature of the SSF can be effectively used to approximate a non-smooth limiter function. Starting from the new SSF-based formulation, a practical digital design procedure is designed in which the desired digital control inputs are obtained by systematically updating the weighting matrices of an LQR scheme to achieve control inputs with smaller magnitudes. The proposed digital control law has been applied to two nonlinear systems under actuator saturation limits. The simulation results demonstrate the effectiveness of the proposed method.