$\mathrm{H}_2$-optimal tuning algorithms for fixed structure controllers

An $\mathrm{H}_2$-method of optimal tuning is proposed for a fixed order controller. The SISO plant model is considered in state space. The $\mathrm{H}_2$-method of tuning parameter design is based on the minimization of a transient process closeness criterion for appropriate open-loop and closed-loop control systems and their reference models. The controller tuning algorithms use the plant parameter estimations obtained during the plant parameter identification. The analytical expressions are obtained for the square of $\mathrm{H}_2$-norm of a stable dynamic system. The following theorem is proven: the minimum necessary conditions for the functionals of transfer function $\mathrm{H}_2$-norm of open-loop and closed-loop systems are the same as the minimum necessary conditions for the Frobenius norm of the controller parameter tuning polynomial.