To validate the robust stability of the flight control system of hypersonic flight vehicle, which suffers from a large number of parametrical uncertainties, a new clearance framework based on structural singular value (

In the past decades, clearance of flight control system has been paid great attention by the air force of many countries. Rational clearance improves not only the reliability and safety of flight control system, but also feedback valuable information to designers. Clearance methods split neatly into two types based on the different clearance principle. One is the so-called analytical-model-based method (AMBM) [

For hypersonic flight vehicle (HFV) whose maximum flight speed may reach to about 20 Mach, the principal criterion to validate is robust stability of its attitude control system because of the existence of uncertain coefficients. The uncertainties are mainly caused by the following three factors. First, the aerodynamic coefficients of HFV, obtained via wind tunnel test and computational fluid mechanics tools, often suffer from much more serious deviations than those of supersonic and subsonic vehicles. Second, it is still unknown how the external environment affects the HFV due to lack of flight experience. Finally, erosion and corrosion may damage the aerodynamic configuration of the vehicle and hence change the aerodynamic coefficients. Many advanced methods [

Among these model-based clearance methods mentioned above,

In order to reduce the computational burden of

In this work, we proposed a new clearance framework for robust stability clearance of the control system of HFV based on

The new clearance process.

The paper is organized as follows. In Section

The motion equations of the hypersonic flight vehicle are given as follows [

= attack, sideslip, and roll angle;

These aerodynamic coefficients are nonlinear functions of the deflection angles

Linearizing (

Suppose that a state feedback controller

Then, the closed loop system, as shown in Figure

Closed loop system of the attitude control of HFV.

It is clear that the stability of the system (

At a specific frequency point

According to definition (

When the number of uncertainties is large, the dimension of the searching space is also large. In order to cover the whole space uniformly, the number of particles of PSO (or analogy of other intelligent algorithms) should exponentially increase with respect to the number of uncertainties. Then, the computational burden will increase exponentially. Therefore, our aim is to find those

As we know, a system is stable if and only if all of its closed loop poles lie in the left half of the complex plan. Therefore, we define the nonlinear stability analysis function as follows:

All local SA methods need to calculate the differential or derivative; that is, they are based on the analytical model. However, the nonlinear function (

Consider the nonlinear model in the form

Denote

These functions in (

The variance of

The normalized sensitivity index is defined as

Because these global sensitivity indices are based on variance, enough samples are needed. The best and most widely used method is Monte Carlo (MC) simulations.

Supposing

The estimation below can be obtained [

It is worth noting that the input factors of the nonlinear model considered in Sobol’s method are limited to

Considering the nonlinear model (

The nonlinear model (

From (

The uncertain matrix

Substituting (

Generally, the whole clearance process can be summarized into the following.

establish the uncertain model of the attitude control system and normalize the uncertainties to

construct stability analysis function as (

generate the sample matrices

calculate output samples of the stability analysis functions (

calculate the SA index according to (

calculate the singular structure value according to (

In this section, a numerical example is given to reveal the effectiveness of the proposed method. Consider the nominal flight trajectory of a HFV depicted as Figure

Nominal trajectory of the HFV.

At the 9th point (

Then the system matrix of the closed loop system is

Calculate the global sensitivity indices of the function (

The global uncertainty sensitivity indices (

The global uncertainty sensitivity indices (

Dominant poles distributions for systems with one uncertainty.

Since

Structural singular value of the uncertain systems.

Structural singular value in low frequency interval of the uncertain systems.

The global sensitivity indices

GSA of all operation points.

Computational time of

In summary, GUSA provides a quantitative index for engineers to measure the effect of uncertainties on dominant closed loop poles. It is worth noting that the GUSA index is relative index. It means that we can order the effect of all uncertainties based on the GUSA index, but we cannot find a threshold value to ignore unimportant uncertainties. There is a tradeoff between precision and computational time when ignoring unimportant uncertainties. For instance, if we need to reduce more computational time, we can ignore one more uncertainty

In this paper, a new

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work is supported in part by the National Nature Science Foundation of China (nos. 61203081 and 61174079), Doctoral Fund of Ministry of Education of China (no. 20120142120091), and Precision manufacturing technology and equipment for metal part (no. 2012DFG70640).