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

Table 2

Plant.1’s system performances of proposed method under various control weight matrices.

Control weight matrix	Plant.1			Rise time	Delay time	Peak time	Setting time	Peak overshoot
Q = diag (𝑞1𝑞2𝑞3𝑞4)	𝑘^∗𝑝	𝑘^∗𝑖	𝑘^∗𝑑	𝑡𝑟 (sec)	𝑡𝑑 (sec)	𝑡𝑝 (sec)	𝑡𝑠 (sec)	𝑀𝑝 (%)
diag (5 5 1 1)	0.13121	0.58138	0.58655	4.060	1.685	5.31	3.54	4.08
diag (5 2 1 1)	0.01633	0.58138	0.51933	3.681	1.801	5.00	6.07	6.69
diag (10 2 1 1)	0.23263	0.82219	0.64449	2.850	1.318	4.02	5.35	8.47
diag (10 10 1 1)	0.47606	0.82219	0.77901	3.161	1.140	4.38	2.756	4.58
diag (10 10 4 2)	0.15570	0.58138	0.64101	4.120	1.691	5.37	3.60	4.23