In computer-controlled systems, the calculated actuator forces are not continuous functions in time any more. This is because of the time needed by the computer to perform the required calculations. In this case, we can study the system using digital control theory which takes the calculation time into account when analyzing the system. To be able to use the continuous model, we must use high update rates (i.e., reduce the computation time). This can be achieved by using a faster computer, and/or using parallel architectures and using some parallel algorithm to calculate the complicated parts in the computations (usually the dynamics of the system). The effect of choosing the update rate on the system performance and stability is discussed in Section 2.4.
Another method is to use a mixture of continuous and discrete control for the system. This can be done by using the computer to generate the required trajectory and the torques for the actuators in discrete time, and an analog PID controller in the interval between the computer samples. This will enable us to assume a continuous control law and will minimize the error during the computation time.