# Exercise on Control engineering with matlab/simulink

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The objective of this exercise is to implement a phase advance corrector digitally from an analog corrector. We consider a process whose transfer function is given by: And the phase advance corrector given by: 1) On Simulink create the control scheme for the continuous system. Display the command and the response. 2) Recall the “before” and “behind” discretization methods of the Laplace variable p. Likewise for Tustin's method. What is the advantage of the latter over the first two? 3) Give the discrete version Cd (z) of Cc (p) for these three methods, as a function of the period of sampling Te. 4) Create the Simulink scheme to test these methods for Te = 0.3s. Display the different commands (u) and responses (y). Compare. What do they become for Te = 0.5s? The p approximation methods have the disadvantage that they can modify the pulsations of the frequency response of discrete correctors. This can be problematic when you want to work in a given frequency band. This problem is called “frequency warping”. To solve this problem, we can add a prewarping term, which corrects the distortion for the pulsation ω0: 5) Calculate the corrector by this method for ω0 = 5rad/s, and simulate its behavior in the case Te=0.5s. We can compare it with the approximation by Tustin without prewarping, in response to an echelon, then to a sine of pulsation at 3rad/s 6) Give the temporal form of implementation of this last regulator

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