# A Robust Control Algorithm of a Descent Vehicle Angular Motion in the Earth's Atmosphere
## 1 Introduction  
The descent and landing of spacecraft are one of the most important and crucial stages of their flight [1, 2]. The control methods at these stages of flight are significantly different due to the design of the spacecraft [3, 4, 5]. The control methods of the shuttle-type spacecraft reentry into the atmosphere are based on well-developed algorithms for aerospaceplane. Control methods for capsule-type spacecraft have been begun to be developed in Soviet Union era, and are continue to be actively improved (transport manned spacecraft \"Soyuz\"), to which this article is devoted.  
The works consider both uncontrolled movements (disturbed rotations in rarefied atmosphere [6], the search for stability conditions [6], predict resonance [7]), and trajectory following [8] and orientation of suborbital ships [9, 10], reusable launch vehicles [11], Earth landers [12, 13], Martian scientific laboratories [14, 15]. The applied management methods differ significantly from each other. These are pulse modulation [11], and sliding mode control [12], and control with forward and feedback [15, 16].  
The problem of increasing the landing accuracy requires research to improve the onboard lander algorithms. One of the ways to improve the accuracy of landing on the Earth is the development of new control algorithms for the stabilization of the angular position of the spacecraft when moving in the atmosphere, which should have advantages over existing algorithms that have actually found application at present [15], both in accuracy and in fuel consumption for control [17, 18, 19, 20]. This article is devoted to such research.  
It should be noted that the standard control of the capsule-type spacecraft orientation in the atmosphere [12, 13] is aimed at damping the angular velocities and tracking the programmed roll angle. In this case, the balancing position of the spacecraft at the other two angles (attack and glide) is maintained only due to the static stability of the spacecraft--the accuracy of such stabilization is low. It is required to improve accuracy without increasing fuel consumption.  
The disturbing forces and moments during the motion of the spacecraft in the atmosphere are stochastic. They largely depend on the shape and configuration of the spacecraft and are difficult to define. Therefore, if the control law depends on constantly changing aerodynamic parameters, the fuel consumption for maintaining a given orientation of the spacecraft will increase significantly. The aim of this work is to synthesize a universal (suitable for any type of spacecraft) controller that would ensure the fulfillment of higher requirements for stability and stabilization accuracy without increasing control costs, and at the same time would be robust, i.e., would not depend on the aerodynamic parameters of the spacecraft.  
We propose an approach to the synthesis of a controller based on the [PERSON]'s modal output control method, modified for dynamic systems with multiple inputs and outputs [21]. The novelty of the approach lies in the fact that due to the parameterization of the matrices with the desired spectra and the proper choice of the assigned poles, it is possible to achieve independence of the control channels for pitch, roll and yaw, both from each other and from the aerodynamic parameters of the spacecraft.