Research Article

Nonlinear Tracking Control Algorithm for Dynamical Output Systems Manipulated by the Hardly Constrained Oscillatory Actuator

Table 1

Geometric and inertia parameters of the three-modulus vibrational system and ANSYS® APDL simulation parameters of the MMI control algorithm.

MMI tracking control algorithm operational parameters
ParametersDescriptionQuantity valuesDimensions

Dynamic output trajectory filter parameters[3.5] [1.3] [0.13] [1.85]Not applicable
Support desired trajectory filter parameters[2.5] [1.1] [0.05] [1.25]Not applicable
Actuator output desired trajectory filter parameters[10.0] [1.5] [0.01] [1.7]Not applicable
Sliding function parameters[0.2] [0.2]Not applicable
Saturation level of the command control input[3000.00](N)
Damping ratio and the natural frequency of the actuator[0.7] [157.079][Dimensionless] (rad/sec)
Discretization time-step[0.001](sec)
Numerical time differentiation lowpass filter parameters[0.001] [0.001]Not applicable
Beam tip harmonic desired trajectoryW 0 = 0.7,  = 4.398(m) (rad/sec)
Beam tip piecewise rectangular desired trajectoryW 0 = 0.7,  = 4.398(m) (rad/sec)

Moving support and beam geometrical and inertial parameters
ParametersDescriptionQuantity valuesDimensions

Cart mass[1.0](kg)
Beam mass[1.979](kg)
Load mass[1.50](kg)
Beam length1.00(m)
Beam effective mass0.2235MB(kg)
Cantilever beam equivalent stiffness3EI/L3(N/m)
Nonlinear stiffness of foundation[3.0] [4.0](N/m) (N/m3)
Nonlinear damping of foundation[4.0] [3.0] [3.0] [2.0](Ns/m) (Ns2/m2)
(Ns/m3) (m)
Disturbance force parameters(N) (Ns3/m3)

ANSYS mechanical APDL environment setting parameters

Point masses typeMASS21
Beam typeBEAM188
Node number101
Beam cross-sectionCircular [d = 6 cm]
Beam bulk density
Beam young modulus
Beam Poisson’s ratio0.10
three degrees of the freedom element type for all nodes except node1 = 1 DoF
cross-section is scaled as a function of the axial stretch
cubic shape function along the length
shear stress output is a combination of torsion-related and flexure-relatedtransverse-shear stress