A novel design methodology on cascaded fractional order (FO) PI-PD control and its real time implementation to Cart-Inverted Pendulum System

Mondal, Reetam; Dey, Joykrishna

doi:10.1016/j.isatra.2022.04.015

Cited by 25 publications

(16 citation statements)

References 18 publications

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“…The linear model of the pendulum system according to the two outputs as in Figure 8 has transfer functions [29,30] as follows:…”

Section: Extension and Real-time Implementation Of Fo Imc On Higher O...mentioning

confidence: 99%

“…The maximum limit of force (F) that can be applied is

\pm 20 normalN

, the value of which depends upon the restricted value of the DC motor voltage (within the span of

\pm 2.5 normalV

) [25, 26]. The pendulum with the bob of mass

m

has a stick length of

l

, cart viscous friction

b

, moment of inertia I, and acceleration due to gravity

g

, the magnitudes of which are adopted from Mondal and Dey [29, 30]. Here, linearization is carried out around the equilibrium point

((), x, \overset{x}{true}, θ, \overset{θ}{true}) = ((), 0, 0, 0, 0)

with Taylor approximation of the nonlinear functions to obtain the linear equations of motion.…”

Section: Extension and Real‐time Implementation Of Fo Imc On Higher O...mentioning

confidence: 99%

“…In the design approach, the minimum number of steps required is indicated explicitly to guarantee the tuning of the FO controller for an improved closed loop performance reaching the exact values of stability margins at a selected gain cross‐over frequency

((), {ω_{cg}}^{'})

. Additionally, the real‐time implementation of the FO‐IMC is also executed, and the performance of which is found out to be adequately satisfactory for highly nonlinear NMP unstable cart‐inverted pendulum system as well [25–30]. The validity of the proposed approach is ratified through the plot of sensitivity function assuring satisfactory gain margin (GM) and phase margin (PM) leading to robustness to various plant uncertainties concerning to reference tracking and disturbance rejection.…”

Section: Introductionmentioning

confidence: 99%

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Fractional order internal model control of non‐minimum phase and time‐delayed plants

Mondal

Dey

2023

Asian Journal of Control

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Several applications on fractional order (FO) control have gained considerable significance in the recent years, which led to the evolution of novel tuning strategies of the generalized order FO controllers. Some of the methods in available literatures are based on constrained minimization optimization techniques or analytical method defined only for specific plants. They are valid only for some special model cases. On the contrary, in this technical note, a generalized non-integer order internal model control (IMC) framework is realized for any order non-minimum phase (NMP) plants with right half plane (RHP) zero as well as time delayed plants having any finite relative order. Its parameters are graphically interpreted satisfying the frequency domain design stipulations for single input and single output (SISO) higher order linear time invariant (LTI) plants. The performance of the same on a bioreactor fermentation process for its temperature control is found to have outperformed in contrast to its integer order (IO)-IMC. It is therefore inferred here that this new approach pledges to impart unique solution of the controller parameters, formulating a highly efficient tool outperforming the existing paradigms. Simulation and real time experimentation are presented to validate the method put forward providing satisfactory performance in reference tracking, disturbance rejection, and robustness to various plant parameter perturbations. K E Y W O R D S fractional order (FO) control, internal model control (IMC), non-minimum phase unstable plants, time delayed plants

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“…The linear model of the pendulum system according to the two outputs as in Figure 8 has transfer functions [29,30] as follows:…”

Section: Extension and Real-time Implementation Of Fo Imc On Higher O...mentioning

confidence: 99%

“…The maximum limit of force (F) that can be applied is

\pm 20 normalN

, the value of which depends upon the restricted value of the DC motor voltage (within the span of

\pm 2.5 normalV

) [25, 26]. The pendulum with the bob of mass

m

has a stick length of

l

, cart viscous friction

b

, moment of inertia I, and acceleration due to gravity

g

, the magnitudes of which are adopted from Mondal and Dey [29, 30]. Here, linearization is carried out around the equilibrium point

((), x, \overset{x}{true}, θ, \overset{θ}{true}) = ((), 0, 0, 0, 0)

with Taylor approximation of the nonlinear functions to obtain the linear equations of motion.…”

Section: Extension and Real‐time Implementation Of Fo Imc On Higher O...mentioning

confidence: 99%

((), {ω_{cg}}^{'})

Section: Introductionmentioning

confidence: 99%

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Fractional order internal model control of non‐minimum phase and time‐delayed plants

Mondal

Dey

2023

Asian Journal of Control

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“…The fractional order control principles, when implemented in IP platforms, came up with accurate regulation in pendulum angle control within inner primary loop and in cart position within outer secondary loop [9]. The robust and optimal control principles are combined to get the fractional order PI λ D µ control.…”

Section: Major Milestonesmentioning

confidence: 99%

Survey on Robust Control Applications in Inverted Pendulum Systems

Johnson¹,

Aziz²,

Parvathy³

et al. 2022

IJEAST

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The Inverted Pendulum (IP) systems are the benchmark problems in control literature. The general control strategy is the feedback control system, which can be used to measure continuously the angle of the pendulum, thereby commanding the cart to move to and fro so that the pendulum will be balanced in the upright position. Though there are control simulations with experimentation available, about half century back, the robust control studies with IP have gained remarkable attention only in the last two or three decades. The robust techniques like 𝑯∞, µ-Synthesis, SMC, LTR, Lyapunov approach etc. are mentioned here. Control experimentation with IP related studies based on robust point of view is very essential since the growing importance of robust techniques in control system community. The proposed paper is a brief survey of the so called literature mentioned in the past three or four years.

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“…Controller structures can be basically examined as linear and non-linear controllers. Linear controllers used in IPS can be summarized as proportional integral derivative (PID) [9], PI, PD [10], Linear-quadratic regulator (LQR) [11,103,104], linear-quadratic-gaussian (LQG) [104], 𝑯 𝟐 and 𝑯 ∞ optimal control [12], etc. The PID controller commonly used in IPS control shows excellent performance due to its robustness in different operation conditions.…”

Section: Introductionmentioning

confidence: 99%

Comprehensive Review of Different Pendulum Structures in Engineering Applications

Hazem

Bingül

2023

IEEE Access

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For years, the pendulum system has been the most popular experimental setup for education and research in robotics and control theory. This paper examines the different kinematic and dynamic structures of pendulum systems, which are frequently used in literature, considering their usage in various engineering fields. Each pendulum system resembles a real physical system, allowing for a deeper understanding of the system's behavior. While each pendulum has its own advantages and disadvantages, they are subjective and depend on the field of application and method of use. This paper aims to review and simplify the understanding of the various pendulum systems used in research and applications, presenting a summary of the general properties of pendulum systems to the researcher.INDEX TERMS Pendulum systems, robotics, control theory and engineering modelling,

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A novel design methodology on cascaded fractional order (FO) PI-PD control and its real time implementation to Cart-Inverted Pendulum System

Cited by 25 publications

References 18 publications

Fractional order internal model control of non‐minimum phase and time‐delayed plants

Fractional order internal model control of non‐minimum phase and time‐delayed plants

Survey on Robust Control Applications in Inverted Pendulum Systems

Comprehensive Review of Different Pendulum Structures in Engineering Applications

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