Missile attitude control via a hybrid LQG-LTR-LQI control scheme with optimum weight selection

Abstract

Abstract-This paper proposes a new strategy for missile attitude control using a hybridization of Linear Quadratic Gaussian (LQG), Loop Transfer Recovery (LTR), and Linear Quadratic Integral (LQI) control techniques. The LQG control design is carried out in two steps i.e. firstly applying Kalman filter for state estimation in noisy environment and then using the estimated states for an optimal state feedback control via Linear Quadratic Regulator (LQR). As further steps of performance improvement of the missile attitude control system, the LTR and LQI schemes are applied to increase the stability margins and guarantee set-point tracking performance respectively, while also preserving the optimality of the LQG. The weighting matrix (Q) and weighting factor (R) of LQG and the LTR fictitious noise coefficient (q) are tuned using Nelder-Mead Simplex optimization technique to make the closed-loop system act faster. Simulations are given to illustrate the validity of the proposed technique.

Pitch Control of a Rocket with a Novel LQG/LTR Control Algorithm

“…A lot of work has been done in the area of optimal controller design for aerospace vehicles (Jianqiao et al, 2011;Das and Halder, 2014;Moshen Ahmed et al, 2011;Liu, 2017;Nair and Harikumar, 2015) but non derives it Kalman gain from a diffferential reccati equation as we will demonstrate in this study. Also, in previous works, the synthesied LQG/LTR (Barzanooni, 2015;Barbosa et al, 2016;Ishihara and Zheng, 2017) did not restore completely the robustenses of the LQR or that of the Kalman filter.…”

Transformation of LQR Weights for Discretization Invariant Performance of PI/PID Dominant Pole Placement Controllers

“…Although we proposed here a novel way for discrete LQR based digital PI/PID controller design with a discretization invariant transformation between continuous and discrete times, there are also a few limitations of the presented approach, as outlined below:  The design is based on fixing the weighting factor R = R first between the continuous and discrete time versions and then deriving the transformation between the respective   , QQ matrices, unlike the simultaneous LQR weighting matrix and weighting factor   , QR tuning as reported in [40], [22]- [24]. This is a widely used analytical approach for LQR based PID controller design for SISO systems [12], [20], [19], [39], as the R = R matrix are mere constants which greatly helps in the analytical derivation rather than including it in the expressions for the PI/PID controller gains.…”

“…weighting matrix and Riccati matrix solution   , QP from (15), (20)-(21) for the second order, (42)-(44) for the first order integrating and (62)-(64) for the first order generalized system structures, with a fixed weighting factor R , using the dominant pole placement based PI/PID controller tuning method and CARE (11) as an extension of the works reported in [12], [20], [19], [39]. This is fundamentally different approach where we aim to derive analytical expressions for the LQR weighting matrices and Riccati matrix solution to meet given closed loop performance specifications, compared to the traditional approaches of LQR weight tuning to optimize for certain control performance objectives [40], [22]- [24]. Using the expressions of   , QP from (15), (20)- (21) for the second order, (42)-(44) for the first order integrating and (62)-(64) for the first order systems are plugged into the CARE (11) solver to find out the PI/PID controller gains in Table 2 for the test-bench processes in Table 1, while considering the weighting factor as 1  R .…”

“…Within the LQR framework, the multiobjective optimum weight selection in the presence of large process delay has been addressed in [23] using two different transformations of the continuous time Riccati equation. The optimum weight selection has also been extended for the noisy tracking (integral) problem using linear quadratic Gaussian (LQG) control with loop transfer recovery (LTR) for improved stability margins [24]. Also, optimal statefeedback PD controller design has been previously studied with minimum norm controller gain to reduce noise amplification in [25], [26], [27].…”

A Novel SHLNN Based Robust Control and Tracking Method for Hypersonic Vehicle under Parameter Uncertainty

“…In order to reduce the impact of model parameters perturbation on the system, a mixed 2/ ∞ control was proposed using fuzzy singularly perturbed model with multiple perturbation parameters [19]. A new strategy for missile attitude control using a hybridization of Linear Quadratic Gaussian (LQG), Loop Transfer Recovery (LTR), and Linear Quadratic Integral (LQI) control techniques was established [20]. However, it will result in relatively conservative results and will undermine the performance robustness of the system, due to the robust LQG control to maintain the minimum performance index.…”