Input-Shaped Model Reference Control for Flexible Systems
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Heavy-lifting machines, such as cranes and aerial lifts, are widely used to perform material handling in various applications. However, their operational efficiency and throughput are degraded by the inherent flexible dynamics of the systems. For example, cranes carrying a payload can experience large payload swings, and aerial lifts extending or rotating their arms can vibrate due to the flexibility in the arms and the joints. The oscillation problems are further complicated by complex nonlinear dynamics, time-varying parameters, and lack of full state information. This thesis investigates a simple and robust control method that improves the operation of flexible systems, even in the absence of an accurate system model and sensing. The goal is achieved via the combination of input shaping and model reference control (MRC). The input-shaped model reference control (IS-MRC) design compensates for the weakness of input shaping with the MRC scheme, while input shaping improves the performance of MRC by modifying the reference command. The benefits of the proposed controller design include increased robustness against plant uncertainties and parameter estimation errors, while also achieving good vibration suppression and control effort reduction. The IS-MRC design is first developed for controlling a crane with a single-pendulum payload. The state space representation and parameter values of the reference model and plant are developed. A Lyapunov control law with asymptotic stability and the corresponding input shaper design are derived. Numerical simulations reveal that IS-MRC contributes to reducing the control effort magnitude for large ranges of system parameter values. The robustness of IS-MRC to parameter estimation errors is analyzed. The performance of IS-MRC in state tracking, oscillation suppression, and control effort reduction is verified via experiments. The IS-MRC design is further tested on a nonlinear double-pendulum payload. The double-pendulum dynamics are derived and the state space representation of the the plant is obtained. The possible ranges of oscillation modes are calculated, and multi-mode input shapers are designed to suppress the range oscillations. To address practical implementation issues, a linear single-pendulum is used as the reference model. A Lyapunov control law using only the first mode states of the plant is derived. The robustness of various IS-MRC designs are tested via numerical simulations and experiments. The robustness to the plant modeling error is analyzed by inducing error in the estimated plant natural frequency. The robust IS-MRC effectively suppresses the hook and payload oscillations. The trade-off to effective suppression, however, is a slower motion. The thesis then extends the study to improve the performance of IS-MRC. An optimized input-shaped model reference control (OIS-MRC) scheme is developed to obtain the optimal combination of input shaping and model reference control. An optimization technique is used to concurrently design the controller parameters that realize the shortest time duration, while satisfying a set of design constraints. The controller performance is tested on a more complex plant; an uncertain, time-varying double-pendulum crane. The OIS-MRC demonstrates superior performances in all evaluated criteria, while maintaining the same level of large robustness as the initial IS-MRC design. The effectiveness of OIS-MRC is also validated by conducting human operator testing. In the testing, the subjects drive a small-scale bridge crane and navigate a payload through an obstacle course. The course is designed to examine the proposed controller's handling of the parameter variations and rejection of external disturbances. In each trial, the course completion time and number of collisions with obstacles were recorded. Furthermore, the test subjects rated the controller's ease of use. The outcomes were analyzed and they validated the predicted improvements of OIS-MRC performance compared to the non-optimized IS-MRC design. The findings in this thesis provide a significant tool for controlling complex machine systems with uncertain flexible dynamics. The proposed IS-MRC scheme is practical and compatible with physical machine applications as the theory can be easily extended to different mechanical systems. The experimental results and operator testing data provide confidence for the study's accuracy and practicality.