![Figure 7: Bode plot of FO-PD and FO-[PD] controllers](/figures/figure-7-bode-plot-of-fo-pd-and-fo-pd-controllers-n2gti3l1.webp)
Q2. What are the contributions mentioned in the paper "Linear fractional order controllers; a survey in the frequency domain" ?
FO-controllers have been studied in both time an frequency domain. The scope of this paper is to review research which has been carried out on FO-controllers in the frequency domain. In this review paper, the concept of fractional calculus and their applications in the control problems are introduced. Finally, advantages and disadvantages of using FO calculus in the control area are discussed. To wrap up, this paper helps beginners to get started rapidly and learn how to select, tune, approximate, discretize, and implement FO-controllers in the frequency domain. Furthermore, some useful continuous and discrete approximation methods of FO-controllers and their digital and analogue implementation methods are elaborated.
Q3. What is the solution for modelling dynamic systems?
when the dynamic of a system has a distributed parameter nature, the best solution for modelling is using FO-calculus [5, 6].
Q4. What is the main reason why researchers are interested in tuning FO controllers?
Among several constraints, iso-damping behaviour (constraint (32)) has attracted a lot of attention from researchers in tuning FO controllers.
Q5. What is the reason why IO-PID controllers are not proper for some cases?
It is concluded that IO-PID controllers are not proper for some cases because they cause systems to become unstable and also FO[PD] controllers are more robust and have better performances than FO-PD ones.
Q6. What is the way to solve the dilemmas of the operator?
To overcome these dilemmas, the δ operator can be a proper solution because it allows a gradual transformation from the discrete to continues time domain.
Q7. What are the main barriers to the development of FO-controllers?
Apart from the water-bed effect from which all linear controllers are suffered [28], there are other significant barriers which confine development of FO-controllers.
Q8. What is the sensitivity constraint for the CRONE controller?
This constraint limits the control effort in respect of noises and disturbances, so this increases the energy efficiency of the controller.
Q9. What are the tuning methods for a PID controller?
Similar to Section 3, tuning methods are fallen down into four categories including tuning methods for TID controllers, tuning methods for CRONE generations, tuning methods for FO lead/lag compensators, and tuning methods for PIλDµ controllers.
Q10. What is the method for tuning a FO-PID controller?
They reported that the FO-PID which is tuned by this method is more robust than IO-PID (controller (23)) which is tuned by the Ziegler-Nichols method.
Q11. What is the prediction for the future of FO controllers?
All in all, it is predicted that overcoming mentioned barriers leads to substitution of IO-PID controllers with FO ones in the near future.
Q12. What is the equivalent impedance of the circuit in figure 14a and 14b?
Memristor is an electrical element which exhibits a fractional order behaviour with the impedance of [92]:ZMS = Ks ν (ν,K) ∈ R (81)Two configurations which are shown in figure 14a and 14b are considered for the analogue implementation of fractional order controllers.
Q13. What is the optimum gain function for the tamed series IO-PID?
Three types of controllers including the tamed series FO-PID (similar to the controller (26)), the tamed series IO-PID controller (controller (26) with λ = µ = 1 and ωh = 10ωl) and the ideal or parallel tamed FO-PID (controller (25) with a low-pass filter) are tuned for this purpose.