## 1 Introduction
Some proposed solutions are based on using a single closed-loop controller, while others employ complex control structures. Numerous IP tuning methods have been proposed so far [9; 34]. These techniques can be classified according to their IP model structure, i.e., tuning methods for ITD [20; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47; 48; 49; 50; 51; 52; 53; 54; 55; 56; 57; 58; 59; 60; 61; 62; 63; 64; 65; 66], for IFOTD [8; 32; 34; 67; 68; 69; 70; 71; 72; 73; 74; 75; 76; 77; 78; 79; 80; 81; 82; 83; 84; 85; 86; 87; 88; 89; 90; 91; 92; 93; 94; 95; 96; 97; 98; 99; 100; 101; 102; 103; 104; 105; 106; 107; 108; 109; 110; 111; 112; 113; 114; 115; 116; 117], for higher-order IPs with time-delay [108; 109; 110; 111; 112; 113; 114], and nonparametric tuning methods for IPs [1; 115; 116; 117]. First, we present the tuning methods for ITD. Controller designs based on the IMC tuning rules for PID controllers were proposed in References [62; 63; 64]. In References [36; 37], integral-proportional derivative (I-PD) control strategies were proposed. A two-degrees-of-freedom (2-DOF) PD-PI controller, that includes a second-order reference filter for improving tracking performance, was proposed in Reference [47]. A method for the auto-tuning of PID controllers based on closed-loop identification was proposed in Reference [38]. This method consists of the closed-loop identification of the model (after the reference or the disturbance step change), a performance assessment, and retuning of the PID controller. In Reference [39], a similar model-free PI/PID tuning method that uses a simple closed-loop reference step change (proportional control gain only) for obtaining the process model was proposed. In References [20; 57], a PID controller and three-state structure for achieving a time-optimal tracking response was proposed. Since this method uses an identification technique (least-squares-based) for the calculation of the process model during steady-state changes, it is not necessary to know the process model in advance. A modified smith predictor for the control of stable, integrating, and unstable processes that consists of a 2-DOF PID controller in series with a second-order filter, defined by the dead-time and an adjustable parameter, was proposed in Reference [42]. In Reference [54], a novel approach for tuning discrete-time PID controllers with higher-order derivatives with a special focus on noise attenuation filters was proposed. These controllers offer a third degree of freedom in control design devoted to the attenuation of measurement noise. In Reference [55], two integrated tuning procedures for the joint design of a PID controller in series with an \(n\)th-order binomial low-pass filter were proposed. The proposed higher-order controller represents an intermediate step between integer and fractional-order PID controllers. Then, in Reference [56], a derivation of higher-order PID controllers by generalising the Skogestad Internal Model Control (SIMC) method [8] for analytical model-based controller tuning was proposed. In Reference [59], robust and simple analytical 2-DOF PI/PID controller tuning rules based on the multiple dominant pole method (MDPM) were proposed. The method enables calculation of controller parameters while maintaining non-oscillatory closed-loop responses without overshoots. Note that the tuning methods for ITD can also be used for other types of IPs if the process can be modelled by the ITD model. This, for example, can be achieved by using a relay feedback identification method [37; 38; 41; 42; 43; 45; 46; 65; 101]. Next, the IFOTD tuning methods will be presented. In Reference [105], an analytical PID tuning method, where the tuning of parameters is based on maximum sensitivity (M\({}_{\text{S}}\)), was proposed. To reduce overshoots, a second-order reference filter is employed. Similar tuning rules were proposed by the same authors in Reference [106], where overshoots are reduced by cancelling some controller zeros and using fourth-order reference filtering.