© 2019 Aliyu Bhar Kisabo, Aliyu Funmilayo Adebimpe and Sholiyi Olusegun Samuel. This open access article is distributed under a
Creative Commons Attribution (CC-BY) 3.0 license.
Journal of Aircraft and Spacecraft Technology
Original Research Paper
Pitch Control of a Rocket with a Novel LQG/LTR Control
Algorithm
Aliyu Bhar Kisabo, Aliyu Funmilayo Adebimpe and Sholiyi Olusegun Samuel
Centre for Space Transport and Propulsion (CSTP), Epe Lagos-State Nigeria
Article history
Received: 06-02-2019
Revised: 11-02-2019
Accepted: 11-03-2019
Corresponding Author:
Bhar Kisabo Aliyu
Centre for Space Transport
and Propulsion (CSTP) Epe
Lagos-State Nigeria
E-mail: aliyukisabo@yahoo.com
Abstract: This paper presents the design, simulation and analysis of a novel
LQG and LQG/LTR control algorithm for the pitch angle of a sounding
rocket. These improved LQG and LQG/LTR control algorithms stem from
the fact that a Riccati Differential Equation (RDE) rather than the popular
Algebraic Riccati Equation (ARE) is used to obtaining the Kalman gain in the
observer of the traditional Linear Quadratic Gaussian (LQG) control
algorithm. Thus, eight (8) different controllers were design, simulated and
analysed, three (3) of such controllers are novel and two out of these novel
controllers were able to recover completely the robustness lost in the traditional
LQG controller. All controllers synthesized were analysed using time response
characteristics of closed-loop system and compared with the LQR and LQG
control system. Using the LQR controller as the benchmark for best
performance and the LQG as the worst. This study shows an application option
that demonstrates optimal control system design in MATLAB/Simulink® and
the approach put forward here proves to be very effective.
Keywords: Rocket, LQG Control, LQG/LTR Control, Differential Riccatti
Equation
Introduction
Classical control system design is generally a trial-
and error process in which various methods of analysis
are used iteratively to determine the design parameters of
an “acceptable” system. Acceptable performance is
genrally defined in terms of time and frequency domain
criteria such as rise time, settling time, peak overshoot,
gain and phase margin, and band width. To meet the
demands of modern technology, different performance
criteria must be satisfied, in a complex multiple-input
multiple-out systems requirement. For example, the
design of a spacecraft attitude control system that
minimizes fuel expenditure is not amenable to solution
by classical methods. A new and direct approach to the
synthesis of these complex systems, called optimal
control theory, has been made feasible by the
development of digital computer.
The objective of the optimal control theory is to
determine the control signals that will cause a process to
satisfy the physical constraints and at the same time
minimize (or maximize) some performance criterion. In
certain cases, the problem statement may clearly indicate
what to select for a performance measure (Kirk, 1998).
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; Zhang et al., 2016; 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.
The first stage of any control system theory is to
obtain or formulate the system dynamics. There refers to
modeling in terms of dynamical equations such as
differential or difference equations. With such equations,
the system is called the plant. This aspect has been
addressed fully in Chapter One. In this Chapter, the
realized plant will be used to design and analyse Optimal
control algorithms (Brian and Moore, 1989) in
MATLAB/Simulink
®
.
This chapter is divided into five sections. Section two
presents the adotped mathematical model. In section
three, stability analysis was done for the rocket
mathematical model. Optimal Control theory was
introduced in section four hence, the design of LQR,
LQG and their two novel variants. Also, LQG/LTR was