Auto-tuning PID using loop-shaping ideas

In this paper we present a direct approach for auto-tuning PID controllers. The approach is based on loop-shaping principles. Auto-tuning is accomplished under closed-loop system excitation without fitting a model of the system. The tuning procedure recursively adapts PID parameters to achieve a target loop-shape. In simulation testing the procedure works very well for systems with integrators, dead-time, lead dynamics, inverse response, sensor noise and colored noise disturbances. Here we present an example of a first order plant with delay operating under a colored noise disturbance