## 5 Simulation Experiment
### Disturbance Suppression without Loading Force Command
#### 5.1.1 Suppression Performance  
In the proposed hybrid control scheme, the extraneous force is gradually eliminated by the composite methods. Therefore, four kinds of experiments are successively made to verify their corresponding suppressing effects. All experiments are conducted under the conditions that the motion disturbance input is 7 sin14\(t\) (mm/s), the force feedback loop is always closed and all perturbed parameters take their nominal values. 1. The original extraneous force is tested for comparison in the condition that the outer loop controller \(G_{\text{c}}(s)=~{}1\) and without the constant compensation term and DOB inner loop compensator. 2. The suppression by using the constant compensator. In this case, there is no DOB inner loop compensator and the outer loop controller \(G_{\text{c}}(s)=~{}1\). 3. The suppression by using the constant compensator combined with the DOB inner loop compensator. In this case, the outer loop controller \(G_{\text{c}}(s)=~{}1\). 4. The suppression by using the designed hybrid controller. The experimental results are drawn in the form of a Lissajous curve, and are depicted in Figures 16 and 17 because \(x_{\text{M}}\), \(x_{\text{L}}\) and \(F_{\text{L}}\) have the same frequency when the loading force command equals zero. In Figure 16, the curves of \(F_{\text{L}}\) and \(x_{\text{L}}\) to \(x_{\text{M}}\) have a clear physical meaning, and they illustrate the formation of the output force which is defined by Equation (1). In this case, the output force is the extraneous force. The smaller the spacing in the middle region of the curve of \(x_{\text{L}}\) to \(x_{\text{M}}\), the smaller the extraneous force is. In Figure 17, the curve of \(F_{\text{L}}\) to \(\dot{x}_{\text{M}}\) illustrates the relationship between the disturbance velocity and the extraneous force, and provides the information about when and how the extraneous force gets its maximum value. This curve is useful for evaluating the suppressing effect on the extraneous force. As seen from Figures 16 and 17 the original extraneous force is very big (up to 13,310 N, in Figures 16a and 17a). It is far beyond other disturbances in the loading system, and even more than some command loading forces. It is meaningful to suppress the extraneous force. After being compensated by the constant compensator, the extraneous force is decreased to 2688 N (decreased by 80%, in Figures 16b and 17a). This result is very close to the analysis result about the suppressing ability of the constant compensator in Section 3.1 (decreased by 84%). By using the constant compensator combined with the DOB inner loop compensator, the extraneous force is further reduced to 102 N (decreased by 96.2% from 2688 N, in Figures 16c and 17b). This result is close to our design in Section 4.2 where the designed \(Q\)-filter can attenuate the disturbance up to \(-42\) dB (decreased by 98.7%). With the designed hybrid controller, the extraneous force is restrained to 57 N (decreased by 99.6% from the original extraneous force, in Figures 16d and 17b). This implies that the proposed hybrid control scheme and controller are valid, and achieve excellent suppression of the disturbance force (less than 60 N) even with the largest motion disturbance. Notice that in Figures 16c,d and 17b, there are obvious burrs and peak values on the curves of \(F_{\rm L}\) to \(x_{\rm M}\) and \(F_{\rm L}\) to \(\dot{x}_{\rm M}\). The high burrs on the curve of \(F_{\rm L}\) to \(x_{\rm M}\) appear nearly at the maximum displacement, and the sharp peaks on the curve of \(F_{\rm L}\) to \(\dot{x}_{\rm M}\) occur around \(\dot{x}_{\rm M}=~{}0\). This implies there  
Figure 16: Relationship diagrams of \(F_{\rm L}\)–\(x_{\rm M}\) and \(x_{\rm L}\)–\(x_{\rm M}\) with disturbance 7 sin14\(t\) (mm/s), (**a**) original extraneous force case; (**b**) restrained by constant compensator case; (**c**) restrained by constant compensator with DOB case; (**d**) restrained by hybrid controller case.