## 1 Introduction
Machine learning techniques are one type of model-free tuning that may be used to properly tune the parameters of the FOPID controller without requiring previous knowledge of the dynamics of the system [15; 16]. Neural networks (NNs) were designed to tune the FOPID controller for numerous applications because of their capacity to tune more useful controller settings without requiring a thorough understanding of the system [16]. Although there are many methods for figuring out the FOPID parameters, as described in the aforementioned literature, robustness and stability must be taken into account. Also, figuring out the best controller gains is crucial. Through a tuning approach, the best controller gain values that meet these requirements can be found. Finding the ideal values, however, is the main objective. Numerous studies have examined the tuning of FOPID parameters using metaheuristic optimization methods [17; 18; 19]. These tuning techniques are actually offline systems and do not rely on the precise mathematical model that represents plants. In this sense, one of the following methods has been utilized to build the FOPID controller: hybrid optimization [20], fuzzy logic [21], particle swarm optimization (PSO) [22], or genetic algorithms [23]. Due to its quicker convergence, PSO-based design is one of the most popular among them, yet it frequently displays a local solution. On the other hand, the global solution achieved by genetic algorithms comes at a great computing expense. Consequently, additional efforts have been undertaken to suggest a different algorithm in order to attain both a global solution and speedier convergence. Different modified flower pollination optimization algorithms (MFPOAs) have been applied recently to solve many engineering optimization problems [24]. The classical flower pollination algorithm (FPA), which was developed to address global optimization based on the imitation of flower pollination, has proven effective in solving a number of optimization problems [25]. Sadly, however, due to its low convergence speed and inability to explore multiple regions within the search space during the optimization process, the classical FPA's performance still significantly suffers from stagnation in local minima, requiring multiple iterations to find better solutions within unpromising regions. In general, ten mathematical test functions were used to evaluate the classical FPA with a population size of 25, and the maximum iteration reached 10,840. This is regarded as a considerable rate to be consumed in order to get the required results. More details regarding the drawbacks associated with the classical FPA are discussed in [26; 27]. This paper adopted the MFPOA presented in [28]. The main benefit of the suggested MFPOA is that the algorithm converges more quickly while maintaining the same properties of the traditional FPA. The MFPOA is one of many nature-inspired algorithms that have been created recently for solving the optimization problem. This work makes use of the decentralized POPID controller design for higher-order systems that use the MFPOA. Because of its scalability, fault tolerance, modularity, design simplicity, etc., decentralized control is recommended. To establish the best FOPID controller gains, the MFPOA approach is used. For higher-order systems, the efficiency of the controller can be confirmed by taking parameter fluctuations and disturbances into account. The comparative results show that the suggested controller can meet design requirements with little overshoot and settling time, hence assuring robust stability. The main contributions of the present study are listed as follows:  
1. Loop interactions and coupling effects are decreased by creating decouplers with a simplified decoupling approach;
2. In order to obtain the best values of Ts, Tr, and Mp, a novel optimal FOPID controller is designed using an MFPOA method that places constraints on ITSE. This strengthens the system and improves the stability issues;
3.