*Improving Disturbance-Rejection by Using Disturbance Estimator DOI: http://dx.doi.org/10.5772/intechopen.95615*

### **Table 5.**

The ADRC method [27–31] is based on a simple controller with three gains

*Control Based on PID Framework - The Mutual Promotion of Control and Identification…*

The method does not require the process transfer function. However, few userdefined parameters, like the observer speed, the desired settling time and the main controller gain *KC*, should be defined by the user before calculating the rest of ADRC parameters. As shown in **Figure 13**, the ADRC method is using control structure which consists of an extended state observer (ESO) with three gains (*β*1,

Since ADRC method depends on three user-defined parameters, which, in great extent, determine the closed-loop performance, we were limited to the set of processes tested in [27]. Someone would argue that, by limiting our choice to the mentioned processes, we are favouring the ADRC method. However, it should be noted that in [27], the ADRC method was tested on 8 different processes, so the choice of processes was actually not significantly limited. In this regard, the follow-

ð Þ 1 þ *s* ð Þ 1 þ 0*:*2*s* ð Þ 1 þ 0*:*04*s* ð Þ 1 þ 0*:*008*s*

ð Þ <sup>1</sup> <sup>þ</sup> *<sup>s</sup>* <sup>3</sup> (39)

*GP*<sup>6</sup> <sup>¼</sup> *<sup>e</sup>*�5*<sup>s</sup>*

The PID controller parameters for the MOMI, DRMO, DE-MOMI and AH methods are given in **Tables 5** and **6**. The ADRC controller parameters are given in **Table 7**. The chosen high frequency gains for the PID controller and disturbance estimator are *KPIDn* = *KDEn* = 20 for *GP5* and *KPIDn* = *KDEn* = 4 for *GP6*. The higher gains were chosen for *GP5*, since the closed-loop tracking and control performance was substantially improved when using higher gains. Increasing the gains for *GP6*

The sampling time for *GP5* is chosen as *TS* = 0.001 s and for *GP6* as *TS* = 0.01 s. The closed-loop process responses are given in **Figures 14** and **15**. In both experiments the unity-step process input disturbance signal was applied at the half

*The ADRC control structure with the controller gains (up) and the extended state observer (down).*

associated with extended state-observer (ESO), as shown in **Figure 13**.

*β*<sup>2</sup> and *β*3) and three controller gains (*KC*, *KP* and *KD*) [27].

*GP*<sup>5</sup> <sup>¼</sup> <sup>1</sup>

above 4 did not significantly improve the performance.

ing two processes have been selected:

of experiment time.

**Figure 13.**

**60**

*The calculated controller parameters for the processes (39) for MOMI, DRMO, DE-MOMI and AH method.*


#### **Table 6.**

*The calculated disturbance estimator's parameters for the processes (39) for DE-MOMI method.*


#### **Table 7.**

*The calculated ADRC controller parameters for the processes (39).*

It can be seen that the proposed DE-MOMI method, when compared to some other methods, gives quite good responses. The AH method for process *GP5* gives somehow oscillatory response. For the same process, the ADRC method gives slightly oscillatory response during the reference change (see the process input signal). While DE\_MOMI and MOMI methods clearly give the best tracking responses on process *GP6*, all of the methods have similar disturbance-rejection performance. Only slightly oscillatory response can be observed for ADRC method.

For more objective comparison between the methods, the integral of absolute error (IAE) measure is used. The IAE value has been measured on tracking response (unity step-change of the reference *r*) and on disturbance rejection response (unity step-change of the process input disturbance *d*). The results are given in **Table 8**. It can be seen that the best values (marked with greyed colour) were obtained with DE-MOMI method.

The DE-MOMI method, therefore, compares favourably with few other methods, based on the non-parametric description of the process.

The process closed-loop responses for all the process models tested in this chapter (*GP1* to *GP6*) revealed that the proposed method can significantly improve the disturbance-rejection performance of the lower-order processes with smaller delays, while the improvement of the higher-order processes and/or processes with higher delays is not so significant. Therefore, the application of the method for lower-order processes with smaller delays might be beneficial in practice.

**7. Conclusions**

**Table 8.**

function if it is known.

stood and defined by the user.

the DE-MOMI and ADRC methods.

**Acknowledgements**

systems in emobility.

**63**

method.

In the chapter, it was shown that the disturbance rejection performance of the PID controller can be improved by adding a simple disturbance estimator (DE). The disturbance estimator consists of the process model and the inverse process model with DE filter. The advantage of the proposed approach is that the DE parameters can also be obtained directly from the nonparametric process data (time response of the process) without prior process identification. The same is true for the PID controller parameters, which are obtained using the MOMI tuning method. Of course, all PID and DE parameters can also be calculated from the process transfer

**Process experiment DE-MOMI MOMI DRMO AH ADRC** GP5 tracking 0.216 0.217 0.526 0.336 0.256

*Improving Disturbance-Rejection by Using Disturbance Estimator*

*DOI: http://dx.doi.org/10.5772/intechopen.95615*

GP6 tracking 8.66 8.66 12.34 11.06 12.32

*The calculated IAE values for tracking and disturbance rejection (DR) responses for the processes (39).*

DR 0.017 0.186 0.055 0.020 0.019

DR 7.80 8.42 8.79 8.89 8.83

The proposed solution, called DE-MOMI method, has been tested on several different process models. It was shown that the control performance of the DE-MOMI method was significantly improved compared to similar MOMI and DRMO methods, especially for lower order processes with smaller time delays. In contrast, the improvements were noticeable but not as significant for higher order processes or processes with larger time delays. The additional advantage of the proposed method was that the tracking performance remained similar to that of the MOMI

The controller noise was controlled by the high frequency noise factors KPIDn and KDEn. The advantage of using these factors is that they can be easily under-

The DE-MOMI method was also compared with some other non-parametric disturbance-rejection methods including the ADRC method. The results showed that the DE-MOMI method has either comparable or better control and tracking performance than the other tested methods. Nevertheless, it should be mentioned

Future research activities could therefore focus on combining the advantages of

The authors gratefully acknowledge the contribution of the Ministry of Higher Education, Science and Technology of the Republic of Slovenia, Grant No. P2-0001 as well as the support by the grants APVV SK-IL-RD-18-0008 Platoon Modelling and Control for mixed autonomous and conventional vehicles: a laboratory experimental analysis and VEGA 1/0745/19 Control and modelling of mechatronic

that the ADRC method uses a somewhat simpler control structure.

**Figure 14.** *The closed-loop responses on the process* GP5*, when using the MOMI, DRMO and DE-MOMI method.*

**Figure 15.** *The closed-loop responses on the process* GP6*, when using the MOMI, DRMO and DE-MOMI method.*


*Improving Disturbance-Rejection by Using Disturbance Estimator DOI: http://dx.doi.org/10.5772/intechopen.95615*

**Table 8.**

**Figure 14.**

**Figure 15.**

**62**

*The closed-loop responses on the process* GP5*, when using the MOMI, DRMO and DE-MOMI method.*

*Control Based on PID Framework - The Mutual Promotion of Control and Identification…*

*The closed-loop responses on the process* GP6*, when using the MOMI, DRMO and DE-MOMI method.*

*The calculated IAE values for tracking and disturbance rejection (DR) responses for the processes (39).*
