Experimental Study of Adaptive Sliding Mode Control for Vibration of a Flexible Rectangular Plate

Abstract

This paper aims to address the intelligent active vibration control problem of a flexible rectangular plate vibration involving parameter variation and external disturbance. An adaptive sliding mode (ASM) MIMO control strategy and smart piezoelectric materials are proposed as a solution, where the controller design can deal with problems of an external disturbance and parametric uncertainty in system. Compared with the current 'classical' control design, the proposed ASM MIMO control strategy design has two advantages. First, unlike existing classical control algorithms, where only low intelligence of the vibration control system is achieved, this paper shows that high intelligent of the vibration control system can be realized by the ASM MIMO control strategy and smart piezoelectric materials. Second, the system performance is improved due to two additional terms obtained in the active vibration control system. Detailed design principle and rigorous stability analysis are provided. Finally, experiments and simulations were used to verify the effectiveness of the proposed strategy using a hardware prototype based on NI instruments, a MATLAB/SIMULINK platform, and smart piezoelectric materials.

Generalized Predictive Control of an overhead crane

“…The objective of the control was positioning a crane to x r = 1 m and reducing the payload deflection within tolerance ± 0.02 m. Figure 2 presents the examples of control performances of GPC system with RLS method tested for different constraints limiting the transient payload deflection: +/-0.09 m, +/-0.07 m and +/-0.05 m. The results of experiments proved that the model-based predictive algorithm proposed in this study ensures the safety requirements. The maximum acceptable value of payload deflection during experiments was not exceed over the specified in cost function (13) limit, and residual deviation was reduced to the desired range ± 0.02 m. The settle time increases due to the constraint of payload deflection is decreased from +/-0.09 m to +/-0.05 m. …”

“…The GPC strategy was tested for experimentally selected weighting coefficients λ 1 = 2.4 and λ 2 = 0.3 specified in the cost function (13), sample time T s = 0.1 s, and control signal range 10 )…”

“…Taking into consideration the constraints limiting the control signal and transient payload oscillations, and assuming that the reference signal x r is a constant value, the cost function is formulated as (13) where v 1 and v 2 are the Lagrangian multipliers. Considering the Kuhn-Tucker conditions: (14) the function (13) …”

“…The off-line motion planning methods for overhead cranes are developed with respect to the control constraints such as maximum payload swing [7,8]. The feedback-based approaches are proposed based on a proportional-derivative (PD) controller coupled with nonlinear controllers [9], hybrid PID control and input shaping technique [10], gain-scheduling [11], sliding mode control [12][13][14], and delayed reference noncolocated control [15]. Feedback control methods are also adapted to ensure the robustness to external disturbances and model uncertainty in feedforward or optimal control strategies [16][17][18].…”

Adaptive vibration control of piezoelectric cantilever beams with uncertainties

“…We can be seen from the existing research that the larger amplitude vibration of the cantilever beam can be rapidly attenuated to a small amplitude value, but the small amplitude vibration will last for a long time. In order to ensure the rapid attenuation of large and small amplitude vibration of the flexible beam with uncertainties, some sliding mode control algorithms [22][23][24] are proposed. Among the many nonlinear control strategies, sliding mode control is an efficient control strategy, which can improve anti-disturbance ability and robustness of nonlinear system with uncertainties [23][24].…”