OPTIMAL CONTROL SYSTEM

PREPARED BY : UPADHYAY RAKSHITA R.

Er No : 140370707018 Roll No : 24

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Contents..

Introduction Performance index Optimal control design Optimal control problem Conclusion References

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Introduction

Limitations of conventional control system : Not reliable and rely heavily on trial and error. For MIMO system doesn’t provide satisfactory design. Optimal control system: Best possible control with respect to a performance

index. State variable formation is often used for representation

of dynamic process.

Performance index

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Optimal control design

In design J is replaced by peak overshoot, damping ratio, gain margin and phase margin.

Proper choice of J result in satisfactory design. Optimal control system depends upon output of the

system therefore it is a close loop system. Various possible formation of J gives solutions of

different problems,

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Optimal control problem

Minimum-time problems: Transfer the system from initial state to final state in the

shortest possible time. J = Tf - T0 = ∫ dt Linear regulator problem : Keep the state at equilibrium state. J = Tf - T0 = ∫ X’QX dt

To

Tf

To

Tf

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Tracking problem : follow a track or target trajectory Xd of state X. J = Tf - T0 = ∫ (X-Xd)’Q (X-Xd) dt

Tf

To

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Conclusion

Optimal control system gives best possible result with considering different value of performance index J and gives accurate result.

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References

Automatic Control Systems, High Education Press, 2003- B. C. Kuo

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THANK YOU