Design of State Feedback LQR Based Dual Mode Fractional-Order PID Controller using Inertia Weighted PSO Algorithm: For Control of an Underactuated System

Abstract

Several control strategies are proposed and developed to enhance the performance of the various underactuated systems, particularly inverted pendulum. This paper presents the dual-mode fractional-order control with a reference model for pitch and angle control of an inverted pendulum. An inertia weighted PSO is utilized for optimal tuning of the FOPID parameters to ensure an optimal balance between local and global search. A cost function of this algorithm is framed based on the error between the reference model output and actual system output along with time-domain performance criteria. The reference model-based tuning improves the performance of the controller and steady-state error tracking. In addition, an optimal state feedback LQR is implemented using pole placement design in the feedback to stabilize and improve the robustness of the inverted pendulum. Compared to the conventional PID, the proposed structure illustrates the FOPID structure has significant performance improvement in both with and without disturbance conditions.

Intelligent FOPID and LQR Control for Adaptive a Quarter Vehicle Suspension System

“…The design steps are follows [32]: Solve the following equation for the matrix P [If a positiondefinite matrix P (n x n) matrix exists (Sure systems might not have a position definite matrix P), the system is stable, or matrix A-BK is stable]:…”

Design of a maximum power point tracking-based PID controller for DC converter of stand-alone PV system

“…In addition, among the evolutionary computation, the updated velocity and position for each particle in the swarm can be calculated using the current velocity and the distance from the particle best solution p besti and the global best solution g besti by employing Eqs. ( 9) and (10) [23,24]: Initialization parameters used for PSO are: population size = 30, maximum number of iterations = 2000, minimum and maximum velocities are 0 and 2, cognitive and social acceleration coefficient C1 = 2, C2 = 1.4, minimum and maximum inertia weights are 0.6 and 0.9. ( 8)…”

“…In [10], simulations show that the FOPID controller outperforms the PID controller in terms of performance, but the PID controller outperforms the FOPID controller in terms of position tracking under disturbance [10].…”