## 7 Comparison and Significance  
A measurable performance comparison analysis is required to be regulated as it is not persuasive enough to assess the performance of the controller by only error qualitative analysis. Specifically, thermoregulation can greatly vary from one to the other depending on the environment configuration and its thermal properties. We choose to compare our proposed system with the existing approaches, which do not consider the outdoor environment conditions. Thus, the input parameters used by the fuzzy controller are modified and the testing process is performed, which relies on the following steps:  
* Test the proposed approach under the fixed inside and outside temperature set point in beginning;
* Compute the steady stable temperature reached, which is used as the set point to compute the error as well as the related performance indices. For instance, the steady stable temperature was 25.03, which can be seen from the test result shown in Figure 12;
* Test the existing approach to reach the computed set point under the same environmental conditions;
* Compute the related performance indexes.  
In order to adjust the controller parameters to produce an optimal controlled response, we need to decide what constitutes a good response. In fact, many different measures that can be used to compare the quality of controlled responses. Three commonly performance indices are used in the comparison process: _ISE_ is the integral square error over time, which will penalize large errors since the square of a large error can be much bigger. Control systems specified to minimize _ISE_ will tend to eliminate large errors quickly, but will tolerate small errors persisting for a long period of time; _IAE_ represents the integral of the absolute value of error, it doesn't add weight to any of the errors in a systems response and tends to produce slower response than _ISE_ optimal systems but usually with less sustained oscillation; and the _ITAE_ integrates the absolute error multiplied by the time over time to weight errors that exist after a long time much more heavily than those at the start of the response.  
Figure 12: Measured indoor temperature on 24 June 2017.  
_ITAE_ tuning produces systems that settle much more quickly than the other two tuning methods. The error signal \(e\) (\(t\)) in a control system is given by the Equation (12):  
\[e\) (\(t\)) = r (t)-c (t), \tag{12}\]  
where \(r\) (\(t\)) is the input signal while \(c\) (\(t\)) represents the output signal. The performance indices can be calculated according to Equations (13)-(15). We consider the time function on an interval within \(t_{0}<t\)\(<t_{0}+T\), where \(t_{0}\) is the starting point while \(T\) denotes the ending point. The \(\int_{0}^{\infty}()dt\) represents the integration over \(t\) from \(t_{0}\) to \(t_{0}+T\):  
\[ISE=\int_{0}^{\infty}[e(t)]^{2}dt, \tag{13}\]  
\[IAE=\int_{0}^{\infty}|e(t)|dt, \tag{14}\]  
\[ITAE=\int_{0}^{\infty}t|e(t)|dt. \tag{15}\]  
All the measures require a fixed experiment to be performed on the system (i.e., a fixed set point or disturbance change) and the integrals are evaluated over a fixed time period usually until a time long enough for the responses to settle. The experiment results are summarized in Table 9 and it can be seen that the proposed approach improves the controller performance by 4.1% according to ISE and by 16.1% on the basis of ITAE index. The results demonstrate that the proposed approach considering the outdoor environment condition shows more excellent performance than the existing approach only taking into account indoor thermal conditions.