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How to Get From Here to There

How to Get From Here to There

Companies must always look for innovative ways to get to the next competitive level. Innovate or perish is the order of the day. They know very well that what got them here won't get them there.

Engineers are often engaged in flexible, dynamic system motion control, ranging from nano-positioning devices to large industrial cranes. Once they decide on a specific motion task, e.g. move a mass from one point to another, they need to give careful thought about how they will execute the task. Techniques include trajectory planning, command shaping, and feedforward control, but they all intend to mitigate undesirable motion effects: oscillation, vibration, noise, and stress.

Knowledge from the past combines with new technology, resulting in innovation. More than 50 years ago, Professor O.J.M. Smith invented a command-shaping method to dampen oscillations in systems having otherwise acceptable transient performance. He called it posicast control, from the term "positive cast," referring to the technique fishermen use to cast a fly. It is illustrated in the gantry positioning problem shown and is based on the idea that a step input is divided into two separate excitations.

The first part is a scaled step that causes the first peak of the oscillatory response to precisely meet the desired final value (1 → 2). The second part is full scale and time delayed to precisely cancel the remaining oscillatory response (2 → 3). Posicast control has spawned new feedback-based approaches from what was originally a feedforward control technique, and digital computers have enabled new applications.

A motion trajectory profile should have a smooth acceleration profile, or more generally, a limited bandwidth, to limit vibrations. Trajectories with discontinuous acceleration profiles (e.g. constant acceleration, harmonic, elliptic, 3rd-order polynomial) generate larger oscillations compared to trajectories with continuous acceleration profiles (e.g. cycloidal, 5th-order polynomial, modified trapezoidal).

From a frequency response point of view, keep the harmonic content of the acceleration small at high frequencies; this implies a smoother motion profile in the time domain. Pick a trajectory by comparing its spectral content with the frequency characteristics of the motion system. In high-speed machines, suppression of residual vibrations is a critical problem. This problem can be solved by different methods -- trajectory smoothing (a trajectory with high-order continuity combined with filters), and control optimization (a combination of feedback and feedforward control).

Command shaping is a very effective method for the reduction of vibrations. It consists in convolving a sequence of impulses, which form the input shaper, with the desired trajectory and applying the signal obtained in this way to the controlled system. The main idea of command shaping, based on the knowledge of a model of the stable system, consists in generating an input able to cancel out the vibrations induced on the plant.

The success of this technique is strictly related to the knowledge of the system's behavior. So, command shaping enables an acceptable dynamic response without the use of added sensors and feedback control (which must wait for an error to arise and be sensed before it starts to suppress it), or the need to redesign the mechanical hardware.

All command shaping methods use a dynamic model to anticipate the occurrence of a vibration so it can effectively start to act as soon as the system starts to move. The required dynamic model is usually quite simple -- just estimates of natural frequencies and damping ratios. However, this information will always have some degree of inaccuracy. So, for command shaping to be successful in real applications, it must have an adequate level of robustness to uncertainties and modeling errors.

Yes, to get from here to there, in both business and motion control, requires careful planning.

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