## 5 Discussion  
The evaluation of the filtered PID controller [8] and \(PD_{n}^{m}R\) controllers depends on whether the measurement noise is taken into account. For example, the evaluation according to Figures 3 and 5 (without measurement noise) would be completely different from the evaluation according to Figure 6 (with measurement noise). The latter results are closer to the POCD requirements as they correspond better to reality. Realistic evaluation is very important for controller design, so we briefly summarize the changes introduced by this article:  
* Instead of parallel filtered PID controllers based on heuristic optimization and knowledge of the exact process model [8], the article proposes the use of HO-AR controllers with odd values of the derivative degree \(m\in[1,7]\), whose parameters are tuned based on a simplified IPDT process model;
* Instead of \(n=m=1\) in the original article [8], not allowing for modification of the noise attenuation, it is recommended that \(n>m>1\) (ideally \(m=3\) and if possible at least \(n=m+2\)) be used to better attenuate the measurement noise;
* A substantial increase in control performance (reduction in excessive controller effort in the range of \(10^{3}\) and also reduction in the output wobbling) can be achieved by choosing \(m\geq 3\);
* While [8] optimized the total variation \(TV_{u}\) of the control signal \(\sum_{i}|u_{i+1}-u_{i}|\) considering both the setpoint and disturbance responses, the present article only considers the excessive increments in the process input and output signals (16) during disturbance step changes;
* From the point of view of the POCD, no further optimization of the \(PD_{n}^{m}R\) controller is required apart from the selection of the tuning parameters \(m\), \(T_{em}\), and \(n\);
* The structure of the HO-AR controllers used is based on the IPDT process model [17; 35]. Therefore, the step response of the given non-minimum phase process is directly approximated by the IPDT model, which greatly simplifies the experimental identification of the process;
* Thanks to the nature of such an IPDT approximation of the measured step response and the controller design used, the whole procedure can be described as a generalization of the Ziegler and Nichols method [12] for HO-ARCs and inverse response processes;
* By using ultra-local integral models, the presented controller design is similar to some alternative approaches, such as active disturbance rejection control (ADRC) [36; 37; 38; 39; 40; 41; 42] or model-free control (MFC) [43; 44], which differ mainly in the type of disturbance observer used;  
Figure 10: Setpoint and disturbance step response of constrained \(PD_{n}^{m}R\) controllers with the minimal values of \(T_{e}\) (20); \(u\in[-0.52,0.52]\) for setpoint responses and \(u\in[-1.02,0.02]\) for disturbance responses), \(n=m+2,T_{f}=T_{e}/n\); \(F_{p}(s)\) (A7) is set with \(p=0\) (full curves), \(p=1\) (dotted); \(T_{s}=0.001\).  
* An additional advantage of the new approach is that HO-AR controllers offer easier adaptation to technological requirements, allow reconstruction of input disturbance, ensure high-quality transients even in systems with limited control signal, and thus, better fulfil all POCD requirements.