Sir
I am having state space model of a power system (8X8 matrix). I am having a feedback controller with 3 more state variables. total order of system with controller - 11X11.

For optimal control of gain (K) and Time constant(T1) in the feedback loop, can i use LQR design or any other design methods

kindly help me,
shivakumar

 

Hello,
LQR is an optimal state-space control design method. You will tune the controller response based on weighting functions applied to error and control action, which determine if you optimal design is fast or gentle.

If you want to have your closed loop response designed with a specific time constant, you might want to consider using a pole-placement method (look for Akermann's method). This might be better to start, as it is simpler than LQR.

I should add that if this is to end up as a practical solution, you should bear in mind:

- are all of the states in your model available as measurements. You will need to estimate any that are not (e.g. kalman filter)
- the size and nature of any nonlinearities as LQR is a linear design method
- have you a set-point to track - LQR is a regulator with zero setpoint
- the high order of the controller might make it very difficult to realise in practice. Test by making any simulations realistic by including sampled data, time delays, quantisation, numerical rounding, plant-model mismatch etc. You could try to implement a reduced-order version of the controller, but you will need to analyse for that situation.

Good luck,

Andy Clegg
http://www.isc-ltd.com