Fig. 1 Characteristic roots of the ( a ) open-loop system given by Eq. (1) with u ( t )   =   0, i.e., open-loop poles (OLP), ( b ) augmented system given by Eq. (9) , i.e., augmented system poles (ASP), and ( c ) closed-loop poles with LQR control, i.e., ECLP More about this image found in Characteristic roots of the ( a ) open-loop system given by Eq. (1) with ...

Fig. 2 Results from Eq. (20) for ( a ) N  =   21 and ( b ) N  =   201. Magnified views are shown in ( c ) and ( d ). Integral of Eq. (21) shown in ( e ) N  =   21 and ( f ) N  =   201. All six plots are for a 1   =   1 ,   a 2   =   1 ,   a 3   =  ... More about this image found in Results from Eq. (20) for ( a ) N  =   21 and ( b ) N  =   201. Magnifi...

Fig. 3 ( a ) Function e ( s ) obtained from Eq. (21) for N  =   2001 along with its piecewise cubic polynomial approximation e ¯ ( s ) . ( b ) Kernel w ( s ) obtained by differentiating e ¯ ( s ) with respect to s . ( c ) ECLP of the LQR controller and the characte... More about this image found in ( a ) Function e ( s ) obtained from Eq. (21) for N  =   2001 along wit...

Fig. 4 Kernel function fitted with ( a ) piecewise linear and ( b ) piecewise quadratic polynomials. ECLP of the LQR controller and the characteristic roots (OCLP) of ( c ) Eq. (30) and ( d ) Eq. (31) . Time response and the LQR control input of ( e ) Eq. (30) and ( f ) Eq. (31) . All these ... More about this image found in Kernel function fitted with ( a ) piecewise linear and ( b ) piecewise quad...

Fig. 5 Antiderivative of the kernel function as obtained from eigenfunction expansion and direct fitting More about this image found in Antiderivative of the kernel function as obtained from eigenfunction expans...

Fig. 6 Compare with Fig. 1 . Characteristic roots of the ( a ) open-loop system given by Eq. (32) with u ( t )   =   0 (OLP), ( b ) augmented system given by Eq. (34) (ASP), and ( c ) closed-loop poles with LQR (ECLP). More about this image found in Compare with Fig. 1 . Characteristic roots of the ( a ) open-loop system g...

Fig. 7 ( a ) Function e ( s ) obtained for N  =   2001 along with its piecewise cubic polynomial approximation e ¯ ( s ) . ( b ) Kernel w ( s ) obtained by differentiating e ¯ ( s ) with respect to s . ( c ) ECLP of the LQR controller and the characteristic roots (OC... More about this image found in ( a ) Function e ( s ) obtained for N  =   2001 along with its piecewise ...

Fig. 8 Kernel function fitted with ( a ) piecewise linear and ( b ) piecewise cubic polynomials. ECLP of the LQR controller compared with roots (OCLP) of Eq. (39) in subplot ( c ) and Eq. (40) in subplot ( d ). Time response and the LQR control input of Eqs. (39) and (40) in subplots ( e )... More about this image found in Kernel function fitted with ( a ) piecewise linear and ( b ) piecewise cubi...

Fig. 9 Antiderivative of kernel function for the three delay problem, as obtained from eigenfunction expansion and direct fitting of a few rightmost closed-loop poles More about this image found in Antiderivative of kernel function for the three delay problem, as obtained ...

Fig. 10 Comparison of kernel functions obtained using our approach and Gibson's approach. The discontinuity at s  =   0, represents Dirac's delta function. More about this image found in Comparison of kernel functions obtained using our approach and Gibson's app...

Fig. 1 Schematic diagram of the EHS controlled by 4/3 PDC valve More about this image found in Schematic diagram of the EHS controlled by 4/3 PDC valve