## 1 Introduction
In addition, PI and PID controllers without adequate anti-windup protection, which prevents unwanted integration due to control limitations (windup phenomenon), are generally not useful in practice [9]. Compensation for constant disturbances is encountered in practically every control task and includes not only compensation for physical external influences but also internal disturbances resulting from simplified models of possibly time-varying processes. Machine or process health monitoring and fault diagnosis help to operate the systems safely and efficiently. In addition to compensation, this also requires explicit reconstruction of disturbances. There are many control approaches, such as simple PI and PID controllers, that are able to compensate for faults but do not provide explicit information about their values. The design of a high-quality controller requires a sufficiently accurate method of process identification. While there are a number of approaches that directly provide the transfer function of the given system (3), such as [PERSON]'s identification method [10], their practical application encounters a number of problems caused by measurement noise, non-linearities of process, quantization of signal levels, etc. Therefore, simpler methods can be useful as they can calculate the individual parameters of the transfer function step by step graphically and numerically [11]. However, the question remains whether the necessary identification of the process can be further simplified. For example, the process identified by the method of [PERSON] and Nichols [12] can be approximated by an integral plus dead time (IPDT) model [13]. Another question is whether the design of a PID controller based on two different values for the maximum sensitivity, which was applied in [8], sufficiently fulfils the requirements of practice and allows fine tuning of the controller settings. The numerous aspects of POCD have even led to the inclusion of inverse-response systems in interactive open-source software tools for control loop analysis [14]. The tools offer simulations under different conditions and can thus compensate for the missing aspects of the design methods under consideration. PI and PID controllers are proclaimed as the most commonly used solutions in practice [15]. Although this statement is generally correct, it can be slightly misleading as the first controllers with the integrating and derivative terms were called automatic reset and hyper reset controllers, respectively, [16]. These control realizations do not contain an explicit integrator, but instead a filter in a positive feedback loop. It turns out that these controllers especially can easily fulfill POCD requirements. Several recently published papers (see, e.g., [17; 18]) have shown that the essential idea of these historical and still-existing in industry automatic reset controllers (ARCs) is the use of a positive feedback from the controller output (see Figure 1). The problem is that the implementation has been neglected for a long time. To explain the nature of AR, a model-based approach can be used, formulated for an integral process model describing an input-output behavior with a differential equation \(\dot{y}=K_{\mathrm{s}}u+d_{i}\), whereby \(\dot{y}=dy/dt\). The reconstructed value of the constant input disturbance \(\hat{d_{i}}\) of such a system can be calculated as the difference between the estimated input of the process \(\hat{u}=\dot{y}/K_{\mathrm{s}}\) and the output of the controller \(u\) as \(\hat{d_{i}}=\dot{y}/K_{\mathrm{s}}-u\). To perform the entire calculation, the reconstructed disturbance must be supplemented with a low-pass filter (see Figure 1)  
\[F_{\mathrm{R}}(s)=\frac{1}{1+T_{i}s} \tag{5}\]  
If you choose the time constant \(T_{i}\) to be greater than the time constant of the closed-loop transients, the first term \(\dot{y}/K_{\mathrm{s}}\) can be neglected near to steady states and the disturbance value can simply be calculated as \(\hat{d_{i}}=-u\).