## 4 Temperature Profile Control  
As discussed in previous sections, the analyzed drying method relies on a contact heat exchange between the cylinder and the tape. This implies a direct relationship between the dryness of the material and the drying temperature. Consequently, in order to be able to shape the dryness profile of cotton tape, it is necessary to facilitate the shaping of a transverse surface temperature profile along the cylinder generatrix. Taking into account the characteristics of heat exchange in the induction heated rotating cylinder (as analyzed in Section 2), a set of stationary inductors can be used to heat the cylinder surface. Figure 12 shows an example of a transverse profile of the surface temperature of a cylinder heated by six stationary inductors powered by a temperature controller with a set temperature value of 80 \({}^{\circ}\)C in a steady thermal state. Although the temperature profile can be shaped to some extent, there is significant irregularity in the temperature distribution. Obviously, the larger the number of stationary inducting units, the higher the uniformity of the temperature distribution at the cylinder surface. However, a larger number of dedicated power sources (HF generators) are also required, which is quite an expensive solution. Alternatively, a significant improvement in the uniformity of the temperature profile and much more flexible shaping can be achieved by the use of a movable inductor. This approach enables the generation of the required amount of thermal energy in any area of the cylinder, so that even highly demanding requirements can be fulfilled. As the heating and drying system becomes a two-degrees-of-freedom system, a two-loop control system is required. One of the loops controls the heating power, while the other controls the position of the inductors. A diagram of the system is shown in Figure 13.  
Figure 12: Temperature profile in the heat-steady state during temperature control with six inductors. Figure 13: Block diagram of a two-circuit temperature control system, where x—position along the forming cylinder, Tset(x)—temperature profile setpoint, T(x)—temperature profile, P(x)—heat power profile. in the form of the average value of the standard deviation of the temperature for each calculation step, expressed by the relationship  
\[\text{I}=\frac{1}{\text{n}}\sum_{\text{k}=1}^{\text{n}}\sqrt{\frac{1}{\text{m}- 1}\sum_{\text{i}=1}^{\text{m}}\!\left(\text{T}_{\text{k}}(\text{i})-\frac{1}{ \text{m}}\sum_{\text{j}=1}^{\text{m}}\text{T}_{\text{k}}(\text{j})\right)} \tag{10}\]  
where T--temperature; K--simulation step number; N--number of simulation steps; i, j--inductor position number; and M--maximum number of inductor positions. The values of the simulated quality index I are shown in Figure 16.  
As can be seen in Figure 16, the temperature profile-sensitive algorithm shows a clear advantage over the systematic algorithm due to the high uniformity of the obtained temperature distribution, which should also allow flexible temperature profiles and the related dryness profiles to be obtained. Figure 16: Values of indicator I calculated for different variants of inductor displacement and power supply. Figure 15: Inductor movement algorithm based on the temperature profile of the cylinder surface. Having a single inductor might be a quite significant limitation for industrial drying systems where large drying cylinders are normally used. In such cases, directing heat energy at only a single spot on the cylinder surface at a given moment may be insufficient to achieve the required temperature profile. Moreover, replacing a systematic algorithm with an algorithm taking into account the current temperature profile of the cylinder surface results in a significant degradation of the uniformity of the profile. This problem can be solved and the flexibility of the whole system can be increased significantly by using a set of independent inductors, located in such a way that the maximal area of the cylinder can be covered.