A Novel PID Controller Design Methodology for Specified Performance Using Ultimate Plant Parameters

Advanced Methods of PID Controller Tuning for Specified Performance

“…A setup for the proposed harmonic excitation based method [7] is in Figure 11, where G(s) is a transfer function of the controlled plant with unknown mathematical model, G R (s) is a PID controller transfer function, and SW is a switch.…”

“…It is recommended to choose U n = (3÷7)%u max [7]. Identified plant parameters are described by the triple {ω n ,Y n /U n ,φ}.…”

“…In case of the proposed sinusoid excitation based method γ varies over a considerably broader interval (0.5;16) found empirically and depends strongly on ϕ M , that is γ =f(ϕ M ) at the given excitation frequency ω n . To examine closed-loop settling times for plants with different dynamics, it is advantageous to define the relative settling time [7]…”

“…The dependency (41) obtained empirically for different excitation frequencies ω nk is depicted in Figure 16b; it is evident that at every excitation level σ k with increasing phase margin ϕ M the relative settling time τ s first decreases and after achieving its minimum τ s_min it increases again. The empirical dependences in Figure 16 have been approximated by quadratic regression curves, thus they are called Bparabolas [7].…”

“…Consider the benchmark plants G 2 According to the ratio α/T unknown plants with an unstable zero can be classified in following two groups [7]:…”