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

Table 3

System performances of proposed method under different ε values (for plant.2).

Control matrix Q and ε value	𝑘𝑝	𝑘𝑖	𝑘𝑑	Rise time; 𝑡𝑟 (sec)	Delay time; 𝑡𝑑 (sec)	Peak time; 𝑡𝑝 (sec)	Setting time; 𝑡𝑠 (sec)	Peak overshoot; 𝑀𝑝 (%)	Plants
Q = diag (0.2 1 1 1) and ε = 0.5	1.15698	0.52966	0.86781	4.778	1.841	6.622	4.00	3.29	Plant.2
Q = diag (0.2 1 1 1) and ε = 2.5	1.45019	0.62500	1.30523	4.201	1.655	6.451	7.20	5.41	Plant.2
Q = diag (0.2 1 1 1) and ε = 3.0	1.79987	0.75000	1.78883	3.727	1.488	5.961	8.08	7.61	Plant.2
Q = diag (0.2 1 1 1) and ε = 4.0	2.31710	1.00000	2.00000	3.151	1.316	4.201	7.35	11.00	Plant.2
Q = diag (0.2 1 1 1) and ε = 5.0	2.46310	1.25000	1.00000	1.795	1.266	2.587	3.97	28.46	Plant.2