Design of virtual controllers for systems with hard constraints

Many actual control problems are subjected to the constraints on the system states since the physical motion is always limited. Therefore, designing a linear controller with physical constraints is a challenge. This paper introduces a novel virtual control approach to deal with the saturation control problems for linear time invariant systems by first utilizing the novel virtual mechanisms and then incorporating them into the control design for real-time implementation. The principle of operation is to increase the control cost virtually when the system states are nearing the constrained region, and activate the virtual control strategy to prevent these states from reaching their hard constraints or saturation limits. A finite receding horizon LQR-based model predictive controller is then designed based on the model that is augmented with virtual constraint mechanisms. To demonstrate its feasibility and effectiveness, the proposed method is applied to a ball and beam system, in which the virtual mechanisms are in the form of mechanical springs and dampers. In addition, to show the flexibility and variability of the proposed virtual control, various virtual mechanical profiles are also investigated.