Dalin control algorithm principle

As early as 1968, Dalin of IBM Corporation in the United States proposed a new algorithm that is different from the conventional PID control law, namely the Dalin algorithm. The biggest feature of this algorithm is that the desired closed-loop response is designed as first-order inertia plus pure delay, and then the controller that can meet this closed-loop response is obtained in turn.

For the single-loop control system shown in the figure below, Gc(z) is the digital controller and Gp(z) is the controlled object, then the closed-loop system transfer function is