4. Conclusion

In this chapter we have studied the design of the temperature control of a diffusive medium by using an unique robust controller for three different materials, namely: aluminum, copper and iron. For the control-system design, the aluminum has been selected as the material defining the nominal model. Then, the second generation CRONE control has been chosen because the parametric uncertainty (due to the copper and the iron) leads to variations of open-loop gain. Finally, the responses in frequency-domain and in time-domain have illustrated the influence of the position of the sensor versus the actuator on the stability degree robustness.

As a future work, three tracks will be studied during the design of robust control:

the first will be to take into account the uncertainties associated with the sensor position xcapt;

the second will be to estimate the temperature T(0,t) from the measurement of the temperature T(xcapt,t);

the third will be to combine the first two.

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Chapter 7

ADAPTIVE SECOND-ORDER FRACTIONAL

SLIDING MODE CONTROL WITH APPLICATION

TO WATER TANKS LEVEL CONTROL

Danial Senejohnny1, , Mohammadreza Faieghi2,†

and Hadi Delavari 3,‡

1School of Electrical Engineering,

Sharif University of Technology, Tehran, Iran

2School of Electrical Engineering, Iran University of Science

and Technology, Tehran, Iran

3Faculty of Electrical Engineering, Hamedan University

of Technology, Hamedan, Iran

Abstract

Combining the fractional calculus with second-order sliding mode control, a novel type of control strategy called second order fractional sliding mode control is introduced for a class of nonlinear dynamical systems subject to uncertainty. A fractional-order switching manifold is proposed and the corresponding control law is formulated based on the Lyapunov stability theory to guarantee the sliding condition. A novel adaptation algorithm is derived to ensure perfect tracking, diminish chattering effect and steady state error by estimating switching controller parameters. Finally, numerical simulation results utilizing the dynamic model of interconnected twin tank system are presented to illustrate the effectiveness of the proposed method.

E-mail address: d.senejohnny@gmail.com (Corresponding author).

† E-mail address: mfaieghi@gmail.com.

‡ E-mail address: hdelavary@gmail.com.

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