Design of Optimal PID Controller with 𝜺-Routh Stability for Different Processes

Table 4

System performances of different tuning methods for plants.1–3.

Methods	𝑘𝑝	𝑘𝑖	𝑘𝑑	Rise time; 𝑡𝑟 (sec)	Delay time; 𝑡𝑑 (sec)	Peak time; 𝑡𝑝 (sec)	Setting time; 𝑡𝑠 (sec)	Peak overshoot; 𝑀𝑝 (%)	Plants
Proposed method	0.13121	0.58138	0.58655	4.060	1.685	5.310	3.54	4.08	Plant.1
Z-N method	0.5971	1.0750	0.2687	1.371	0.877	1.643	6.41	11.08	Plant.1
IA-ISE method	0.4479	0.9994	0.3340	1.678	0.983	4.015	3.13	4.24	Plant.1
IA-ITSE method	0.7377	0.9886	0.3557	1.429	0.845	3.506	4.88	5.27	Plant.1
Proposed method	1.15698	0.52966	0.86781	4.778	1.841	6.622	4.00	3.29	Plant.2
Z-N method	2.8130	1.7194	1.1505	1.620	1.195	2.458	3.81	43.09	Plant.2
Gain and phase method	2.3870	0.8747	0.9476	1.938	1.302	2.478	3.34	15.02	Plant.2
A-H method	2.5778	1.4518	1.2941	1.763	1.286	2.537	4.43	33.65	Plant.2
Proposed method	0.32447	0.01537	1.45256	19.486	14.306	20.87	60.56	6.67	Plant.3
Z-N method
Z-N method (C-C)	0.3060	0.0205	1.1384	19.238	14.367	24.98	51.60	18.18	Plant.3
Z-N method (PRC)	0.3000	0.0150	0.0600	20.286	14.635	26.43	56.06	21.17	Plant.3
Cohen-Coon method	0.3958	0.0219	1.2178	17.252	13.400	21.43	67.05	38.06	Plant.3

A-H method (real PID controller form) with derivative filter constant 𝑇_𝑓=0.04947.