CAD enabled trajectory optimization and accurate motion control for repetitive tasks

As machine users generally only define the start and end point of the movement, a large trajectory optimization potential rises for single axis mechanisms performing repetitive tasks. However, a descriptive mathematical model of the mecha- nism needs to be defined in order to apply existing optimization techniques. This is usually done with complex methods like virtual work or Lagrange equations. In this paper, a generic technique is presented to optimize the design of point-to-point trajectories by extracting position dependent properties with CAD motion simulations. The optimization problem is solved by a genetic algorithm. Nevertheless, the potential savings will only be achieved if the machine is capable of accurately following the optimized trajectory. Therefore, a feedforward motion controller is derived from the generic model allowing to use the controller for various settings and position profiles. Moreover, the theoretical savings are compared with experimental data from a physical set-up. The results quantitatively show that the savings potential is effectively achieved thanks to advanced torque feedforward with a reduction of the maximum torque by 12.6% compared with a standard 1/3-profil

Identification of dynamic systems with position dependent load parameters

Cascaded control is still the most common and convenient structure in standard commercial drives. The most convenient tuning method is to apply calculation rules on an offline identified frequency response of the open-loop system. Obviously, this standard approach is only valid for linear time-invariant systems. However, the mechanical dynamics of modern machines very often depend on the angular position of the driven axis. Consequently, the system is time-variant and linearisation is needed to obtain an open-loop frequency response. In this paper, a system identification approach based on this linearisation is presented for dynamic systems with variable load torque and variable load inertia. The feasibility of this approach is validated with measurements on an industrial case

On-line estimation of the mechanical stiffness of rod mechanisms

The stiffness of a mechanism is an important parameter for control design and position accuracy. A value of this parameter is usually obtained from a data-sheet of the coupling between the motor and the load, or from a measured frequency response. These methods are however not applicable to rod mechanisms, which are widely used in industry due to their rotary-linear conversion. Firstly, the load is typically directly connected to the rotor without a physical coupling. Secondly, the mechanical parameters and especially the inertia of these mechanisms are position and time dependent. Rod mechanisms are thus non-linear time-varying systems, which excludes off-line methods such as measuring a frequency response for estimation. This paper therefore presents a novel approach, based on the Sliding Discrete Fourier Transform (SDFT), for on-line estimation of the mechanical stiffness. The feasibility is verified with simulations on an equivalent two-mass system of an industrial pick and place unit, existing of a combined four-bar/slider-crank mechanism. Simulations show that accurate estimates are obtained and changing stiffness can be detected, which can serve as a new diagnostic tool

Stiffness estimation of a lumped mass-spring system using sliding DFT

Obtaining an accurate parametric model of a mechanism enables optimised control. System identification through noise injection is a common method for obtaining frequency responses which are suited for control design, but not for feedforward control and motion profile optimisation as the response is non-parametric. Especially when the mechanism consists of multiple sources of flexibility, extracting parameters from frequency responses is challenging and often requires model order reduction. Moreover, if the parameters are either time or position-dependent, an on-line estimator is required for enabling adaptive control and optimisation. This paper therefore presents a computationally efficient approach, based on the sliding Discrete Fourier Transform, for tracking stiffness during operation. A lumped mass-spring system with 4 degrees of freedom is used as a proof of concept. Through simulations, the expected accuracy of the developed estimator is analysed and its ability to deal with noise is demonstrated

Trajectory optimization of a high speed pick and place unit using soft switching multiple model predictive control

In this work, an online optimal trajectory design strategy based on Soft Switching Multiple Model Predictive Control (SSM-MPC) for an industrial pick-and-place machine is proposed. By using the SSM-MPC, the generated trajectory will be adaptive to system parameters variations such as load inertia, etc