Eigenstructure assignment of constrained second-order linear systems: an optimised positively-invariant set control approach

Abstract

Second-order systems constitute a mathematical model class used to represent a variety of physical processes to be controlled, such as vehicle damping systems, hydraulic pump flow, and robot manipulators. Due to the practical limitation inherent to physical systems (or their mathematical representation) and constraints on the input variables, the constrained control theory became an important research field. In this work, based on set-invariance theory, we propose an eigenstructure assignment optimisation using a state-feedback control law that guarantees the respect of state and control constraints for second-order systems. Positive invariance is the property of keeping the trajectory of the system states inside the set. This characteristic is incorporated into the analysis and design of the control law to ensure local stability and constraint fulfilment.