Tuning Rules for PID Controllers for Unstable Systems

This chapter proposes the tuning formula for the parameters of the PID controller for a first-order plus time delay unstable system. The correlations between controller settings (K c, τ I and τ D) and the system parameters (gain, time delay and time constant) are proposed so that there is no need to perform the second test to calculate the update controller gain as done in the previous chapter. In addition, to improve the ZN continuous cycling method, correlations between the controller parameter and the ultimate values of the control system gains (K c,max, P u) are proposed. These can be applied by the using the results of the single relay feedback test or the stability criteria.