Virtual control with hard constraints

Ali M.H. Al-Hajjar, Sean Shan Min Swei, Guoming Zhu

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Practical control problems are always subject to plant state and/or input constraints, which make designing an effective controller a challenging task. This paper introduces a novel virtual control approach to handling the presence of hard constraints in control systems by utilizing virtual mechanisms in the form of nonlinear springs and dampers. The augmented virtual mechanisms are to assist in better shaping the closed-loop responses, especially when operating near the constrained boundary. A linear quadratic regulator based model predictive control method is utilized to develop stabilizing controllers that not only achieve desired system performance, but also meet the imposed hard constraints. The basic idea is to dramatically increase control penalty by way of tuning the spring and damper effect when the constrained state/input response is close to its hard constraint. The proposed method is applied to a balancing ball problem to demonstrate its applicability and effectiveness, and the simulation results validate the proposed concept.

Original languageBritish English
Pages (from-to)155-165
Number of pages11
JournalAsian Journal of Control
Issue number1
StatePublished - Jan 2021


  • ball and beam system
  • discrete control
  • hard constraints
  • LQR control
  • model predictive control
  • Virtual control


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