With High-end Integrator Chain Saturated Control

Saturation is one of the most commonly encountered nonlinearity in control engineering, and most actuators inevitablely exhibit saturation. To this end, a so-called saturation approach is developed in which the affect of saturation is taken into account in the design process, and stabilization controls including saturation functions are set. Using the saturation approach, Teel and Sussmann had ever presented stabilization designs for the chain of integrators that might be the simplest linear system. Expanding the method, this paper investigates the stabilization of the chain of integrators that is subject to higher order terms, with the purpose of obtaining simple control laws and formulating a kind of systematical design method. The main results of this paper can be stated as follows:1. A saturation control is presented for the chain of integrators that is an additive form. Meanwhile, a significant inspiration is achieved that will be helpful for the stabilization of the chain of integrators with nonlinearities. Namely, system states can be guaranteed to enter the prescribed small domains, if the saturation levels can be appropriately set.2. The design idea of the chain of integrators is rudimentarily expanded to the chain of integrators with higher order terms. Due to the feedforward structure and the bottom-up recursive analysis technique, the higher order terms can be found to have a minor effect on the convergence. As a result, some nonlinear system in the literature can be dealt with in a different way. As illustrations, the algorithm is applied to the van del Pol equation and an interlaced system.3. The robust decentralized stabilization of large-scale uncertain feedforward systems is investigated and simple controls are presented. By using the approach of attenuating the higher order terms as well as the criteria for the stability and boundedness of cascade systems, there is no need to depend on the usual linear matrix inequality technique and nor need to heaviliy rely on Lyapunov functions.4. The approach of attenuating the higher order terms is applied to two classical practical models: the industrial active magnetic bearings system and the inertia wheel inverted pendulum, and stabilization designs are presented that are different from the existing ones.