Overcoming the limitations of linear control

Control is a discipline that is very present in most areas of engineering and, in particular, in the generation, transformation and consumption of energy. The control is able, from measured signals, to improve the behavior of most systems. In energy systems, control is used at different levels. At the physical level, it is necessary to regulate physical values; at the interconnection level, it is necessary to stabilize relevant variables in the network while at higher levels it is necessary to plan the evolution of different elements.

By far, linear control techniques and linear systems are the most exploited. Linear control techniques offer a structured and constructive framework to design controllers, which currently is supported by many computational tools. The performance one might achieve with these techniques is limited by the inherent linear structure, between others the well-known waterbed phenomena establishes a relationship between the achievable error and the range of frequencies where it can be obtained, similarly non-minimum-phase systems are limited in the achievable settling times. Although nonlinear techniques, like the popular sliding mode control are being used, its applicability is being limited by the required mathematical knowledge required to understand it. Additionally, these techniques usually contain many ad hoc steps which need to carefully be addressed to achieve good performance.

In recent times, many research has focused in designing control techniques which allow to maintain the constructive linear framework while overcoming some of their limitations. Event based control is one of the most popular ones. In particular, reset control offers a very interesting framework with allows to improve controller performance with simple modifications in the controller implementation.

As an example of the potential of reset control techniques, a concrete example will be given: many practical systems, including most popular power converters, can be modeled as simple first order systems. A Proportional Integral controller is usually selected for this type of systems, it has two design parameters (proportional and integral gain) which are usually selected to fix the closed-loop poles. As it is well-know if a fast response is desired one will get an overshoot. Figure 1 shows a typical response for PI controlled system, it has been tuned to be fast while preserving reasonable robustness margins. As expected, step response has a relevant overshoot.

 

Fig. 1 - Closed-loop system behavior with a linear PI controller

Fig. 1 - Closed-loop system behavior with a linear PI controller

 

This overshoot comes from the integral part in the controller, although this component is the one guarantee null steady-state error it introduces oscillatory behavior and overshoots. A way to minimize this is resetting the value of the integral part (as the controller is nothing but a computer program this can be easily done). Figure 2 shows what can be achieved by doing that. As it can be observed settling time is preserved while the overshoot has almost been extinguished. This improve has been achieved just by resetting the integral part at the appropriate manner.
Currently, an important effort is being developed to determine when it is the best moment to reset the integral part.

 

Fig. 2 - Closed-loop system behavior with a PI+CI controller (PI with reset)

Fig. 2 - Closed-loop system behavior with a PI+CI controller (PI with reset)

 

As a conclusion, it is time to begin to overcome inherent linear controller limitations to improve energy systems performance, but this must be done without increasing complexity and preserving constructive frameworks.

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