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Q1.1. First part: digital PI controller (50 marks)

Please attend the following steps in order to design a digital PI controller for the HB inverter:

a) Obtain an analytic expression for the open-loop pulse transfer function, Go(z), (see page 4.13 in

Lecture Notes) and input disturbance ?i

. Then, evaluate Go(z) with the system parameters.

b) Design a digital PI controller, CP I (z), considering a damping factor ? = 0.707 and a natural

frequency less or equal than 1200 (rad/sec). See Section 4.4.3 (page 4.29) in Lecture Notes.

c) Determine whether the resulting closed-loop system is able to track sinusoidal current references

and reject sinusoidal input disturbances of 50 Hz.

d) Derive a control algorithm for the digital PI controller and implement it in the provided simulation,

inside the “Control Algorithm” block (Do not use transfer functions). Provide plots of the

closed loop response to track the given references (comparison of the actual grid current with its

reference, duty-cycle applied by the controller, grid voltage and inverter voltage, and any other

graph that you consider important).

e) From a electrical power engineering point of view, please explain what are the implications of

using a PI controller to govern a grid-connected power converter system.

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Introductory Control 48560Spring 2019Coordinator: Dr Ricardo P. AguileraAssignment 4Discrete-time Control System DesignDeadline: Sunday 9th June 2019.Q1. Digital Control of a Grid-Connected Inverter (100 marks)Grid-connected inverters play an important role in many residential and industrial applications, e.g.,renewable energy integration and energy storage systems. In essences, power electronic inverterstransfer power from a DC-source to an AC-load (or vice-verse). This is achieved by manipulatingthe internal power switches (on or o) to synthesize an AC-voltage in order to generate a desiredAC-current. A key feature of these power converters is that they are autonomous systems. Hence, acontroller is needed to properly operate them. See [1] for further details on control of power converters.For this assignment, consider the case where a controller for a H-Bridge is needed; see Fig. 1. Here,it is required that the digital controller provides a suitable duty-cycle, d, in order to track a desiredsinusoidal grid current reference, i . The PWM stage is working with a frequency of f = 2 kHzg PWMoperating in a unipolar mode. Therefore, the inverter voltage, v , can generate only three distinctiveivoltage levels, i.e, v 2f