An LPV Fractional Model for Canal Control

Table 3

Model parameters obtained by identification in each operating point 𝑂𝑃_𝑘𝑃1: pool 𝑃₁

Parameters	𝑂𝑃1𝑃1	𝑂𝑃2𝑃1	𝑂𝑃3𝑃1	𝑂𝑃4𝑃1	𝑂𝑃5𝑃1
𝜏	17	10	8	6	5
𝑎1	−1.9527	−1.9287	−1.9008	−1.8960	−1.8659
𝑎2	0.9537	0.9309	0.9051	0.9011	0.8747
𝑎3	0.0010	0.0022	0.0043	0.0051	0.0088
𝑎4	0.0203	−0.0261	−0.0409	0.0063	−0.0028
𝑏1	−0.1313	−0.1144	−0.0757	−0.0667	−0.0080
𝑏2	0.0370	0.0333	0.0261	0.0226	0.0212
𝑏3	0.0019	0.0052	0.0104	0.0139	0.0198
𝑏4(×10^−3)	0.0995	0.1224	0.1793	0.1969	0.3952
𝑏5	633.48	606.00	553.53	544.37	229.55
𝑏6	−345.72	−352.92	−335.57	−363.27	−179.48
𝑏7	55.0820	74.408	82.686	95.255	62.955
𝑐1	−2.1318	−1.7484	−2.1485	−2.2626	−2.0778
𝑐2	2.0729	1.8516	2.1183	2.3379	2.0016
𝑐3	−1.1719	−1.3840	−1.2185	−1.4044	−1.1296
𝑐4	0.4176	0.7331	0.4440	0.5309	0.4104
𝑐5	−0.0948	−0.2552	−0.1036	−0.1270	−0.0985
𝑐6	0.0133	0.0560	0.0151	0.0185	0.0162
𝑐7	−0.0010	−0.0071	−0.0013	−0.0015	−0.0021
𝑐8(×10^−3)	0.0464	0.6397	0.0990	0.1061	0.2949
𝑐9	−1.9148	−1.5150	0.9473	0.9293	1.8894
𝑐10	−2.0112	−1.5179	0.8899	0.8545	1.1611
𝑐11	−1.3216	−0.8523	0.9887	0.9411	0.6570
𝑐12	0.3424	0.5942	1.4846	1.4310	0.9577
𝑐13	2.2736	2.1238	2.0835	2.0224	1.8793
𝑐14	2.1646	1.7134	1.2674	1.1950	1.5309
𝑐15	−3.1753	−2.8745	−2.6283	−2.6231	−2.6879