Design of an integer order proportional–integral/proportional–integral–derivative controller based on model parameters of a certain class of fractional order systems

Abstract

In this study, we deal with systems that can be represented by single fractional order pole models and propose an integer order proportional–integral/proportional–integral–derivative controller design methodology for this class. The basic principle or backbone of the design methodology of the proposed controller relies on using the inverse of the fractional model and then approximating this fractional controller transfer function by a low integer order model using Oustaloup filter. The emerging integer order controller reveals itself either in pre-filtered proportional–integral or proportional–integral–derivative form by emphasizing on the dominancy concept of pole-zero configuration. Parameters of the proposed controllers depend on the parameters of the single fractional order pole model and the only free design parameter left is the overall controller gain. This free design parameter is determined via some approximating functions relying on an optimization procedure. Simulation results show that the proposed controller exhibits either satisfactory or better results with respect to some performance indices and time domain criteria when they are compared to classical integer order proportional–integral–derivative and fractional order proportional–integral–derivative controllers. Moreover, the proposed controller is applied to real-time liquid level control system. The application results show that the proposed controller outperforms the other controllers.

A study on a new criterion for minimum-energy perfect control in the state-space framework

“…12,13 For instance, an application of various nonsquare parameter/polynomial matrices in the inverse model–based control algorithms, including the minimum variance/perfect control procedure, makes such control laws more robust. 14–16 In particular, it can be observed in case of multivariable systems, having different numbers of input and output variables. 17,18 For such plants, the use of so-called degrees of freedom of nonunique right inverses gives quantifiable minimum-energy benefits, in opposite to the unique T - inverse , for which the said control algorithm often does not exist.…”

Optimal fractional‐order controller design using direct synthesis method

“…Grünwald–Letnikov approximation, which utilises small step size h in (2) is one of the most frequently used approximations in the time domain [37, 38]. On the other hand, the most commonly used approximation in the frequency domain is the Oustaloup filter in which an integer‐order transfer function with zero‐pole couples is employed [15, 21, 38, 39]. This approximation is given by where N is the order of filter.…”

“…On the other hand, in terms of system identification aspect, real‐time systems such as twin‐rotor helicopter [20], liquid level system [21], heat flow platform [22, 23] etc. might be modelled both by the fractional‐ or integer‐order structure.…”

Improvements of torque ripple reduction in DTC IM drive with arbitrary number of voltage intensities and automatic algorithm modification

“…There exist three more cases with regard to the class of controllers and system models in the usage of fractional calculus, i.e. integer-order control for fractional-order models [2] and fractional-order control for integer-order models [3][4][5][6][7] and fractional-order models [8,9]. The behavior of real-time systems are often expressed using higher-order differential equations.…”