Order diminution and its application in controller design using salp swarm optimization technique

Abstract

Order diminution (OD) or model order reduction (MOR), a very important field of System Engineering, has been explored by many researchers. Different methods are available for reducing the complexity of a control system, which are subsequently utilized to get a cost-effective controller. Model order reduction is done by either using classical methods or by using optimization techniques. In optimization algorithms, accuracy, complexity, and convergent rate are the main criteria for comparison in OD. This paper contributes a novel fast and more accurate OD (MOR) technique based on Salp Swarm Optimization. Further, the proposed method is applied to a time-delay system in four different manners. The effectiveness of the proposed technique is shown by reducing four benchmark systems, including a system with time delay and an 84th order system. Finally, the application of OD is shown by designing a reduced-based H-infinity controller for the 84th order system which results in a great saving of time (% 96%). The obtained results are comparable or better than those from the existing well-known order reduction techniques available in the literature.

An effective controller design strategy for higher order systems

“…Consider a unity feedback system with feed-forward transfer function G ( s ) G c ( s ) as shown in Figure 1. Let G(s) be the transfer function of the reduced-order model (Ahamed et al, 2022a, 2022b; Prajapati et al, 2020; Prajapati and Prasad, 2019, 2020, 2020b, 2022) for the original higher order plant to be controlled and G c ( s ) the transfer function of the proposed compensator to be designed in this section.

Figure 1.Feedback system.

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“…Furthermore, these methods had drawbacks such as non-uniqueness, pole clustering, gain adjustment and difficulty to maintain the dominant roots in the lower order system for non-minimum higher order plants. Ahamed et al (2022a, 2022b), Prajapati and Prasad, 2019, 2020, 2020b, 2022 and Prajapati et al (2020) have presented a number of reduction techniques to overcome these drawbacks, guaranteeing the stability of lower order models in addition to reproducing the behaviour of the original large-scale model for a number of higher order systems. These studies have shown that the reduced-order models produced by Mihailov stability, enhanced Pade approximation and truncation, improved generalized pole clustering, moment matching and salp swarm optimization approaches not only reflect the behaviour of the original large-scale model methods but also ensure the stability of the reduced-order models.…”

“…This study does not examine how this technique might be applied to higher order systems using reduced-order models. Using salp swarm optimization, Ahamed et al, 2022b employed a controller to a reduced third-order system. Although this technique could produce superior results, the optimization methodology is somewhat time-consuming and involves an iterative process.…”

A graphical technique of controller design and selection of lower and upper bounds in controller design using optimization techniques

“…By adjusting the parameter settings, a controller enhances the system's transient and steady-state performance. Till now, several controllers such as PID controller [1][2][3][4], cascade controller [5], fractional order PID (FO-PID) [6][7][8][9][10], proportional integral double derivative (PIDD) [11], dual proportional integral [12], tilt integral derivative controller [13], fuzzy-PID [14][15][16][17], state feedback control [18], adaptive neurofuzzy inference system [16], H-infinity controller [19,20], model predictive control [21], nonlinear model predictive control [22], adaptive model predictive control [23] have been developed. But the basic PID controller is widely used in all most all industries regardless of meaningful development in the control area during recent years because of its easy implementation, simple construction, working principle, and maintenance.…”

A novel hybrid of Nonlinear Sine Cosine Algorithm and Safe Experimentation Dynamics for model order reduction

“…Such endeavour has, nonetheless, been overshadowed by subsequent publication from Singh [13] in 2018, which successfully proposed the Sine Cosine Algorithm (SCA) as a superior MOR algorithm for high-order continuous structure against other efficacious order-reduction methods, including PSO, Elephant Herding Optimization (EHO) and Nelder-Mead Simplex Algorithm (NMSA), while maintaining an admirable operational simplicity. Moreover, optimization approaches, such as Harris Hawk Optimization (HHO) [14] and Salp Swarm Optimization (SSO) [15], have simultaneously emerged as exploitable algorithmic alternatives within modern academic and real-time MOR applications. With efficiency being established as a fundamental basis for the presumed effectiveness of the aforementioned MOR algorithms, estimating the precision of an order-reduced model would, therefore, be determined by the theoretical robustness of the specified optimization method.…”