Mathematical Problems in Engineering

Volume 2015, Article ID 923156, 11 pages

http://dx.doi.org/10.1155/2015/923156

## Coordinated Control of Pressure Difference and Rising Velocity for Stratospheric Airship with Thermal Effects

Department of Automation, Xiamen University, Xiamen 361005, China

Received 2 March 2015; Accepted 27 May 2015

Academic Editor: Jose J. Muñoz

Copyright © 2015 Luhe Hong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Ascending control of stratospheric airship is a challenging control problem, especially if both the rising velocity and the pressure difference between the inside and outside of the airship are required to be controlled simultaneously during ascending. In this paper, a coordinated scheme to control pressure difference and rising velocity of stratospheric airship with vector thrust is presented. With the control scheme, the airship maintains the pressure difference by exhausting air with feedback control. At the same time, the supplemental thrust is generated to compensate the buoyancy fluctuation caused by exhausting air so that the airship’s vertical velocity can track a given reference trajectory. Simulations show that the coordinated control scheme ensures that the airship rises to the altitude of 20 km steadily and rapidly while the pressure difference is always in the safe range. Furthermore, the control scheme is robust enough to the thermal disturbance caused by solar radiation and other thermal processes, which is calculated with partial differential equations.

#### 1. Introduction

Stratospheric airship, a low-speed near space aerocraft, mainly relies on static buoyancy to ascend and maintain itself in working height [1]. Because of its unparalleled advantages such as low power consumption, high security, and large shipping capacity, the prospect of airship has drawn increasing concern around the world, while airship technology has become a cutting-edge and hot issue for academic research [2].

Rising to the resident height safely is a prerequisite for stratospheric airship to work properly [3]. During ascending, the stratospheric airship exhausts inner air continuously to guarantee that the pressure inside the airship is slightly greater than the atmospheric pressure outside. If the internal pressure is not enough, the airship balloon may be deflated by external atmospheric pressure, resulting in an overall structural deformation. If the internal pressure is too large, the balloon may be in excessive tension even rupture. Therefore, to control the pressure difference between inside and outside of the airship is extremely important throughout the whole process of ascending [4].

From the perspective of control theory, pressure difference control during ascending is a difficult problem. It requires simultaneously high accuracy, rapidity, and robustness. First, the pressure difference of airship must be guaranteed in a very limited safe range. For example, a typical value of the internal pressure greater than the external pressure is about 300 Pa~600 Pa [5], which means the allowable maximum fluctuating value is only 300 Pa and less than 3 of the internal pressure of airship on the ground. To guarantee the pressure difference is always in the safe range, the control approach must be highly accurate. Second, in practice, the airship must have an appropriate increasing velocity, which leads to quickly decreasing the atmosphere pressure outside of the airship. For instance, if the airship has altitude 1 km and rising velocity 1 m/s, its external atmosphere pressure decreases by approximately 11 Pa per second. To maintain pressure difference in the safe range, the internal pressure must be adjusted quickly enough. Third and most important, in rising process there exist nonignorable unmodeled dynamics. Thermal effects, such as solar radiation and force convection, can significantly affect the internal pressure of the airship and the pressure difference. Unfortunately, these thermal effects are too complicated to be modeled with precise and brief mathematical models used for online control. So, the pressure difference control has to view these thermal effects as unmodeled dynamics and to be robust enough.

In the current literature, the pressure difference control during ascending has not been carefully addressed. Seldom research considers pressure difference, rising performances, and thermal effects simultaneously. Affected by low-altitude airship, many researchers focus only on the flight dynamic performance, such as Zheng et al. [6], Bestaoui and Kahale [7], Zhang et al. [8], and Mueller et al. [9]. In [10, 11], two approaches are used, respectively, to control the pressure difference during ascending while the rising performances such as velocity and smoothness are not guaranteed. A coordinated control scheme of pressure difference and height of stratospheric airship was proposed by Wu et al. [4], but with the scheme the airship may oscillate in the vertical direction. On the other hand, Guo and Zhu [12] and Shi et al. [13] considered the thermodynamic interference during airship ascending, while the pressure difference and flight dynamics were not considered.

This paper presents a new ascending control scheme for stratospheric airship which has vector thrust. By exhausting air and the vector thrust, the pressure difference and rising velocity of the airship are coordinately controlled so that the airship can rise to the resident height steadily and rapidly. In the scheme, the priority is given to control pressure difference by exhausting air with feedback. Then a controller is designed by pole placement method to adjust the thrust to compensate the rising velocity change caused by exhausting air and to track a given altitude-velocity reference. A thermal model of the airship is established to estimate thermal effects caused by direct solar radiation and other disturbances and to verify the robustness of the control scheme. Simulations show that, with the coordinated control, the airship can rise to the altitude of 20 km within 8 hours against thermal disturbance. During ascending, the pressure difference is always controlled in the range of 340 Pa~420 Pa while the airship does not oscillate in the vertical direction.

The remainder of the paper is organized as follows. Section 2 presents the airship features. In Section 3, the mathematical models of environment and airship are established. In Section 4, the corresponding coordinated control strategy is given. Section 5 gives the simulation results and analysis while Section 6 is for concluding remarks.

#### 2. Airship Features

According to the different structures, traditional airships can be divided into three types: blimp airship, semirigid airship, and rigid airship. This paper investigates semirigid airship. A rigid dragon skeleton, which can maintain good structural shape and withstand a certain twisted moment, is designed in the lower part of the airship. Airship hull is designed as water droplets form, synthesized based on ellipsoid approximation, and it is the same minor axis length between two ellipsoids. The lengths of the short axis and the two long axes are denoted as , , and , respectively. The total length of airship is . Inside airship, there are helium bags and air ballonets. Some exhaust valves and inspiratory valves controlled by onboard computer are equipped in the air ballonets. Thrust devices equipped in the abdominal and tail of airship are also controlled by onboard computer. The overall structure schematic diagram of airship is shown in Figure 1.