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Input shaping is an established technique to generate inputs that move flexible mechanical systems with little or no residual vibration. While traditional input shaping design strategies are often analytical, the present paper introduces a design method based on numerical optimization. It is shown that, through a careful selection of the optimization variables, objective function and constraints, it is possible to obtain a linear optimization problem. As a result, it is guaranteed that the globally optimal input shaper be found in a few seconds of computational time. The presented optimization framework is able to handle higher-order, linear time-invariant dynamic systems, as opposed to traditional input shapers, which are mainly based on secondorder systems. Moreover, constraints on input, output and state variables are easily accounted for, as well as robustness against parametric uncertainty. Numerical results illustrate the capability of the proposed design approach to reproduce existing input shaping design approaches, while experimental results illustrate its potential for higher-order systems.

Model predictive control (MPC) is an on-line control technique originally developed for slow processes which makes an assessment between input effort and output error while respecting constraints on inputs and outputs. Due to improved computing power and algorithms, MPC is nowadays also applied to mechatronic systems. For these systems, achieving minimal settling time is the main concern, while the input cost is usually of less importance. Hence, this paper presents a new type of MPC; time optimal MPC (TOMPC) which minimizes the settling time of the system. Theoretical considerations show that TOMPC is stabilizing. Simulations show the merits of this technique and indicate that it is applicable in real-time.

Traditional input shaping filters are linear mappings between reference input and system input. These filters are often unnecessarily conservative with respect to input and output bounds if multiple references with different amplitudes are applied. This conservatism is due to its offline design and linear mapping. This paper presents an online input prefilter design approach to overcome this conservatism. The resulting prefilters are called predictive prefilters because the online design is based on the model predictive control (MPC) framework. By theoretical considerations, simulation results and experimental results, it is shown that this new prefilter is at least as good as traditional prefilters, and can result in substantial gains in settling time. Tests show that a 30% decrease in settling time is possible in a common input shaping application.

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