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Modelling, analyses and control of non-deterministic systems

Challenge

Given a particular input, a deterministic plant will always produce the same output. This is not the case for use cases where non-deterministic elements are present. These non-deterministic elements make the control of these systems more difficult. In order to control in an optimal way these systems, because of these non-deterministic elements, the distribution of the output (uncertainty) must be observed, rather than one particular value or measurement.

In general, non-deterministic behaviour of the plant can be due to influential non-observable inputs, like material properties or environmental conditions. A system can for example also get non-observable inputs because of a broken sensor. Non-deterministic behaviour also occurs also when using model approximations in the controller where not all influential phenomena relevant for the dynamics of the system are modelled or when a model parameter may change over time due to uncertainty on the system behaviour. Another type of influential behaviour is when the control reference is not a fixed value or trajectory, but a stochastic distribution.

Traditionally, the non-deterministic behaviour of the plant can be dealt with in the design of the controller by assuming a bounded uncertainty and making a robust controller for a worst case scenario. This might lead to too conservative controllers with suboptimal performances. By explicitly modelling the uncertainty and by taking the actual uncertainty into account, instead of the maximum bound, a controller with better performance could probably be realized.

For example, if a parameter can be estimated in a model-based way (e.g. with a Kalman filter) and the influence of this parameter on the system output is known (through a model), then this effect together with the uncertainty on the parameter, can be taken into account. The actual uncertainty increases if this parameter varies in function of the time or if the system changes. The controller now can take this increased uncertainty temporary into account.

Project Goals

The project goal is to develop technology and competences in order to build model-based controllers which can handle plant uncertainties in an optimal and robust (for performance) way. Technology will be developed in order to:

  • Select the appropriate control strategy
  • Identify and characterize control relevant uncertainties
  • Test the effect of the uncertainty on the performance and robustness of model-based deterministic controllers
  • Build controller with limited computing resources

Economic Value

Controllers that don’t take uncertainty into account are often tuned too conservatively and as such working suboptimally. This project will help project partners to take uncertainty into account and adapt the controller such that the system/machine performs better and is more robust.

Project partners 

Duration: 
1/04/2013 to 31/03/2015