Modelling and analysis of digital control systems

Control systems are mostly modelled in continuous time. Implementation however happens in general by digital computers (mostly microprocessors), which influences the behavior of the control system. This makes a well-defined method for modelling of digital control systems desirable. In the past Mecal Applied Mechanics BV simulated digital control systems as an analog system with a time delay in its feedback loop. This report investigates whether this method sufficiently reflects digital control properties or another method should be used. For &is the Mecal-method is compared with several other methods in time and frequency domain. The sampled-data method, that uses a model with a controller in discrete time and system in continuous time, gives the best representation of the properties of digital control systems in time domain. Fourier analysis shows that both the sampled-data method and the adjusted Mecalmethod, that is the Mecal-method with time delay in the control loop instead of the feedback loop, can be used to give a good representation of the properties of digital control. Time simulations of a sampled-data model show that AID-conversion of the feedback output signal has little effect on the digital response. It shows that the extra delay in the controller's hardware may destabilize a control system. And it also shows that the response at the Nyquist frequency is equivalent to the step response. Frequency domain analysis show that the analog method can be used up to 5% of the sampling frequency and that sampling induces a frequency dependent phase lag with respect to the analog phase response. Furthermore it is shown that digital control systems are stable at a sampling frequency above about five times the bandwidth depending on the phase margin and that the damping factor decreases as the sampling frequency decreases.