Robust data-driven fixed-order H∞ controller synthesis using convex optimization

Abstract

The main objective of this thesis study is to develop fixed-order (low-order) structured controller design methods for frequency domain non-parametric uncertain systems using convex optimization. The majority of the available controller synthesis methods are based on the mathematical model of the system dynamics. The performance of these model based control methods entirely relies on the accuracy of the model. Model uncertainty, due to unmodeled system dynamics, nonlinearities and operating point changes, are almost inevitable and may cause controller performance degradation due to the fact that there is always a trade-off between performance of the closed loop system and robustness. Therefore, model based methods may impede desired high performance requirements of today's industrial complex dynamical systems. In this thesis, a novel robust data-driven fixed-order H∞ controller design method based on convex optimization is proposed for linear single input single output systems. Linear time-invariant systems represented by non-parametric frequency domain data and linearly parameterized controllers are considered. The proposed approach renders the need for a mathematical model of the controlled plant unnecessary. First, a semi-definite convex optimization algorithm, which is based on the concept of the Chebyshev center of a set of points, is proposed to simultaneoiusly compute a minimal uncertainty bound and corresponding nominal model from the experimental data. Thanks to this algorithm, multiple measurements can be considered in the robust control design method instead of one set of measurement with minimal uncertainty bound. Then, a new sufficient robust performance condition is derived using Nyquist stability theorem and synthesis methods on the Nyquist plot. Low-order controllers such as lead-lag compensators and proportional integral derivative (PID) controller are much desired in today's industrial process due to their engineering advantages. Therefore, a convex optimization method is developed which optimizes the coefficients of the fixed-order controllers while guaranteeing internal stability and robustness. Furthermore, the proposed method allows formulating closed-loop model matching objective and control input constraints by convex functions. An extension of the one degree of freedom controller design algorithm is proposed to synthesise two degree of freedom controllers for reference tracking of the non-parametric systems. The presented theoretical design approaches are experimentally verified on position control of an electromechanical actuation systems of an air vehicle.