Minimal-norm state-feedback globally non-overshooting/ undershooting tracking control of multivariable systems

Abstract

The non-overshooting/undershooting (NOUS) tracking control objective in the output response of the closed-loop system has several practical applications in “positioning” control problems. Recently, a state-feedback gain matrix based on Moore’s eigenstructure assignment technique to achieve the above control objective with a desired convergence rate in the output error from any initial condition is designed, referred to as globally monotonic tracking control, which is a convex optimization problem. From a practical viewpoint, a feedback gain matrix of a minimal norm is often required to install low-cost actuators in the overall closed-loop system. However, there is always a trade-off between the control objectives of achieving a NOUS tracking response with the desired convergence rate and a minimal norm of the feedback gain matrix. Besides, the latter control requirement renders the globally NOUS control optimization problem nonconvex. In this paper, a convex optimization-based iterative algorithm is developed to synthesize a minimal-norm state-feedback globally NOUS tracking controller. An upper bound on the achievable settling time in all output responses for the closed-loop eigenvalues lying in a prespecified region of the complex plane is also provided. The effectiveness of the proposed algorithm is demonstrated through a numerical example, followed by experimental validation on a multitank system.