Pitch and flight path controller design for F-16 aircraft using combination of LQR and EA techniques

Abstract

In a linear regulator problem with a quadratic cost function, there are two weighting matrices which determine the feedback gain matrix, and thereby the closed loop eigenvalues and eigenvectors of the system. To find the weighting matrices leading to a desired eigenstructure, trial and error is a common approach. In spite of its simplicity, trial and error is too time-consuming and does not guarantee achieving expected results. In this regard, this paper presents a step-by-step algorithm for calculation of state and control weighting matrices in such a way that the pre-specified eigenstructure is generated with acceptable accuracy. Accordingly, once the designer chooses preferred eigenvalues and eigenvectors, the feedback gain matrix will be available uniquely. In design procedure, tracking of flight path and pitch attitude commands for an F-16 aircraft will be provided. To achieve this aim completely, the feedforward gain matrix necessary for getting a zero steady state error is calculated based on the mathematical model of the aircraft as well as the pseudoinverse matrix concept. Various simulations demonstrate that the resulted controller has good performance, gives the desired eigenstructure satisfactorily and also shows the expected robustness of a linear quadratic regulator.

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

“…d 1 ; d 2 ; d 3 and d 4 are the weightage function. The cost function (46) has four different terms. The integral square of the pendulum angle h t ð Þ is the first term, which is used to stabilize the IP leg at equilibrium.…”

“…Step 2 (calculation of objective function). Objective function (46) values of particles are calculated using the performance criteria for algorithm convergence.…”

“…LQR state feedback controller has been provided in the feedback of the IP in this work to achieve closed-loop stability and high performance. Also, guaranteed phases margin and gain margin and control weight matrices presented in the cost function can manage the error and control effort through state efficiently [46]. The optimally selected gain matrices significantly contribute to the efficiency of the controller [47].…”

Design and Virtual Simulation of an Optimal PID/LQRT-PSO Control System for 2WD Mobile Robots

“…In which case, the optimality of the resulting optimal LQR control might not be effective. The fourth class of optimal control design method is the LQR-PSO algorithm [13]- [16]. In this case, a prior optimization of weighting matrix Q and R is conducted.…”

System Identification and LQR Controller Design with Incomplete State Observation for Aircraft Trajectory Tracking

“…The full-state Linear-Quadratic Regulator (LQR) controller was successfully applied for trajectory tracking for various aircraft: fixed-wing [6,8,9], helicopters [10,11] and UAVs [12,13]. In case of incomplete state information, the LQG controller can be used instead.…”