LQR Q and R matrices for a DC boost converter

A question on the theory behind the LQR controller with a boost converter.

In "conventional" PI control for a boost converter, we usually tune the inner current loop first (the "fast" loop), and then we tune the outter voltage loop second (the "slow" loop).

Now, when using LQR control for a boost converter, I have a desired output voltage of 400V. Normally, an LQR controller calculates the K gains based on a zero setpoint (that is, it calculates the K gains to drive the states to zero). In this case, we have nonzero setpoints. I DO know that my desired output voltage is 400VDC, but I don't know what my desired input current should be.

--> Is there a way to use the lqr() command for this system [two states :input current and output voltage], while setting the "desired output voltage" state, and not knowing what the "desired input current" state should be? I'm not quite sure how to model this.

--> If I set the "desired input current" to 0, I think this would mean that the controller would try to drive the input current to 0, which is NOT what I would want. [There must be some input current flow, to drive the output voltage to the desired value]

Answer 1

[Darshan Pandit]

Hi richard,

I am not familiar with LQR controller, but I guess the following may be helpful.

What you're looking for is:

i.e. Minimum inductor current needed to provide .

You may get started from the following two parameters:

1. : output power rating of the boost converter
2. : steady state operating voltages at input and output

Using these, within the boundaries of certain assumptions, it's possible to get to the right answer.

In one switching cycle , the charge is transferred from input to output only when the switch is Open. i.e. , where d is the duty cycle of the PWM switching.

Using the above two, it is possible to establish a relationship between input and out voltages at steady state,

Using (1), you may also find rated / steadystate value of .

But maybe that's something you're probably not interested at the moment. What you need is .

This needs somewhat familiarity with converter design. It also depends on topology.

For simplicity, I'm assuming non-isolated boost converter operating in Continuous Conduction Mode (CCM).

The values for inductor & capacitor for such a coverter maybe computed by [1],

Where, is the Inductor current ripple & is the switching frequency.

The boost converter will be in CCM (and hence start working) at .

There lies your answer. Depending upon converter topology and control system, you'd have to derive new equations for arriving at above value.

Hope this helps. Have a good day.

[1] Singh B, Singh S. Single-phase power factor controller topologies for permanent magnet brushless DC motor drives. IET power electronics. 2010 Mar 1;3(2):147-75.