Improving stability and performance of digitally controlled systems: The concept of Modified Holds

Digitally controlled systems are getting more and more popular mainly because of their flexibility and convenience but their stability is strongly affected by the time delay introduced by different factors. For common PID type digital controllers, zero-order holds (ZOHs) are commonly employed and the stability characteristics are investigated based on that concept. Mathematical investigations show that higher-order holds may improve the stability and performance of the system and can reduce the steady state errors significantly. This is because the controller tries to learn from the history of the behavior of the system and then predict the behavior for the time period between sampling instances and generate the best possible control force. Furthermore, a new concept of Modified Holds is introduced, which clearly improves the performance of a digital controller. For most control algorithms this does not prolong the processing time significantly (e.g. less than 1%) which can be neglected in the calculations. The varying control force would need an analogue circuitry to follow the proper curve, which might make the controller's electronic circuits more complex. This can be avoided considering that in almost all digital controllers the main core operates at several orders of magnitude higher frequency than that of the control loop itself. Hence, the control force can also be generated digitally at much higher frequencies. In this paper, after investigating the stability of a 1-DoF system equipped with discrete-time PD controller with first and second order holds, the concept of modified holds is introduced and then the results are validated by simulations. Furthermore, the concept is practically implemented on a self-balancing motor bike robot and the experimental results further support the claims of the paper.