If we have a 5th order system and we have transformed it into a LTI state space representation in Brunovsky form where we have a chain of four integrators, then what will be the advantages for controller design for such a model?
What control techniques can be applied to it (i) for full state feedback, and (ii) output feedback?
The realization in state space enables us to deal with first order differential equations in place of 5th order equations. Added state space realization makes a unified representation of data enabling the flexibility to modify the parameters. For full state feedback, pole placement and LQR are classical techniques that can be used for control. However, you can use advanced conrollers defined using meta heuristic algorithms such as particle swarm, BAT, firefly etc.
You can find some work related to classical control bed of inverted pendulum analysis in my papers which might be of help
http://journal.uad.ac.id/index.php/TELKOMNIKA/article/view/3403
Article Rotary inverted pendulum control and the impact of time dela...
Article Rotary Inverted Pendulum stabilization with time delays usin...
Article Naturally Inspired Firefly Controller For Stabilization Of D...
Dear Anirudh
In a Brunovsky canonical model, all the states are derivatives of the first state (called position). In this contrition, stabilization problem usually will be simplified to designing Hurwitz stable polynomials of the states. Just for instance, in sliding-mode control, this polynomial can be considered as a surface to be regulated by a first-order nonlinear robust controller (see J. J. Slotine, “Sliding controller design for non-linear systems,” Int. J. Control, vol. 40, no. 2, pp. 421–434, 1984).
Note that when the states are NOT derivatives of the first state, their stable relationship cannot be described as a Hurwitz stable polynomial. Indeed, when the system is not in a Brunovsky Canonical form, you should employ methods such as back-stepping whose design is more complex.
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