## 6 Computational Study
### Experimental Design  
In our previous work [14], experiments have been described that demonstrate promising behavior of the proposed packet loss compensator. When used with a simple PD controller, performance was shown to be superior to that a simple derivative disabling technique with only a very modest increase in overheads. In this paper, the proposed compensator is investigated in more depth and is employed in conjunction with both the control buffering technique and controller design as proposed in Section 5. In these experiments, overhead and performance comparisons were made to the packet buffering and robust compensator as described in [23]. In this technique, once the plant parameters have been identified controller zeros are employed to cancel the process open-loop poles and integral action is used in the controller. The loop gain is selected to ensure a specific phase margin is achieved by carrying out a frequency sweep of the combined process, controller and buffer-induced delays to determine the critical gain. The frequency test interval is bounded by DC and the Nyquist frequency, and is divided into a grid  
Figure 4: Prototype test facility. of \(S\) test points; the larger the value of \(S\) the better the accuracy of the method but the higher the computational overhead as \(O(S\times(m+n))\) FLOPS are required along with numerous trigonometric and square root operations (although the former can be pre-computed at each frequency test point and stored in a table). For reasons discussed in [14] and elsewhere, systems with faster dynamics will be more susceptible to burst errors lasting a given temporal duration. In this case study, a servomotor was chosen as the process to control; this is a common choice for evaluating DCS performance [24]. The continuous-time dynamics relating the shaft speed to the armature voltage of the servomotor can be described by the transfer function:  
\[G(s)=\frac{2}{1+0.5s} \tag{18}\]  
In order to add further realism into the simulation, quantization corresponding to a 16-bit shaft encoder was employed, plus a small amount of zero-mean measurement noise (equivalent to \(\pm\) 1 encoder bit) was injected into the output of the simulation model. Note that although the nominal model given by Equation (18) was known in this case, the adaptive compensator and controller were \"cold-started\" with no prior knowledge of process parameters included. A fixed forgetting factor \(\lambda=1\) was employed by the identifier as no process parameter variations were expected. Identical noise sequences were employed in each of the described experiments that follow. The main objective of the experiments was to determine the ability of both schemes to compensate for the effects of burst errors. In order to numerically quantify this ability, the experiments were designed as follows. Firstly, the Robust Control (RC) scheme was applied to control the nominal model given by Equation (18) with a target phase margin \(pm=60^{\circ}\) selected, grid size \(S=100\) and sampling time \(T=0.1\) s employed. For reasons that will shortly be described, the sensor-controller and controller actuator buffers were set to a size of 10 samples each. The resulting closed-loop response was found to be well approximated by the following second order transfer function:  
\[G(s)=\frac{0.35e^{-s}}{s^{2}+0.8s+0.35} \tag{19}\]  
Next, the proposed Predictive Control (PC) method was employed using the same sample time of \(T=0.1\) s, with a design polynomial \(P(\mathrm{z})=1-1.9198\)\(\mathrm{z}^{-1}+0.9231\)\(\mathrm{z}^{-2}\), _i.e._, the discrete equivalent of the denominator of the transfer function given by Equation (19) using a sample time of 0.1 s. This gave approximately the same nominal closed-loop behavior between the two methods (save for the additional 1 second delay in the RC design). At this stage, two experiments were then carried out.