An LPV Fractional Model for Canal Control

Table 4

Model parameters obtained by identification in each operating point 𝑂𝑃_𝑘𝑃2: pool 𝑃₂

Parameters	𝑂𝑃1𝑃2	𝑂𝑃2𝑃2	𝑂𝑃3𝑃2	𝑂𝑃4𝑃2	𝑂𝑃5𝑃2
𝜏	11	10	9	8	7
𝑎1	−1.9419	−1.9244	−1.9115	−1.8951	−1.8830
𝑎2	0.9434	0.9270	0.9153	0.9005	0.8904
𝑎3	0.0015	0.0026	0.0038	0.0055	0.0074
𝑎4	−0.0188	−0.0190	0.0075	0.0147	0.0205
𝑏1	−0.1515	−0.1931	−0.1361	−0.0535	−0.0244
𝑏2	0.0377	0.0484	0.0356	0.0178	0.0100
𝑏3	0.0032	0.0017	0.0069	0.0154	0.0199
𝑏4(×10^−3)	0.1347	0.3226	0.2270	0.1694	0.1214
𝑏5	603.9000	117.29	307.20	726.79	989.96
𝑏6	−299.6300	−72.221	−204.48	−496.96	−734.07
𝑏7	51.8040	15.713	48.386	122.65	207.87
𝑐1	−2.0539	−1.8107	−2.1661	−2.3208	−2.3517
𝑐2	1.9327	1.6503	2.1372	2.4464	2.5364
𝑐3	−1.0584	−0.9557	−1.2253	−1.4919	−1.5938
𝑐4	0.3661	0.4019	0.4440	0.5688	0.6308
𝑐5	−0.0808	−0.1250	−0.1032	−0.1363	−0.1579
𝑐6	0.0111	0.0283	0.0151	0.0197	0.0241
𝑐7	−0.0008	−0.0042	−0.0014	−0.0016	−0.0021
𝑐8(×10^−3)	0.0434	0.4807	0.1050	0.1112	0.1667
𝑐9	2.1585	−1.5600	−0.6518	−0.1523	1.1259
𝑐10	1.4147	−1.7388	−0.9192	−0.5187	0.0930
𝑐11	0.8165	−1.0839	−0.4348	−0.2286	−0.4165
𝑐12	1.0115	0.6744	1.1870	1.1744	0.5429
𝑐13	1.7673	2.4956	2.8789	2.7318	2.4285
𝑐14	0.9012	1.3293	1.2377	1.1205	1.6084
𝑐15	−2.2559	−2.7775	−2.8406	−2.7515	−2.8369