1 Introduction
High angle of attack missile in flight, there is a serious inter-channel pneumatic coupling. Engineering design, usually a small random disturbance coupling term as treated, but when the coupling effect is large, the control system is easy to lose stability, thus coupling effect between channels must be considered, and its decoupling. In recent years, with the development of control theory, various decoupling control emerged, such as decoupling feature configuration, self-tuning decoupling, linear quadratic decoupling, singular perturbation decoupling, adaptive decoupling, intelligent decoupling, H∞ decoupling, decoupling variable structure, of which reference [4] multivariate frequency domain method, the MIMO system into a series of coupled SISO system, then the classical frequency domain method are designed, implemented a BTT missile autopilot decoupling, [5] the structure wherein output feedback configuration, reasonable allocation of the eigenvalues of the closed loop system, the feature vector, obtaining the feedforward output feedback controller, a three-channel solution to achieve missile coupled, [6] variable structure control and robust control, dynamic decoupling system.
The high angle of attack the missile in flight, the missile is subjected to external disturbances and uncertainty parameters are all very large, decoupling using the general method is difficult to ensure real-time control system requirements, since H∞ mixed sensitivity own merits, where It proposed a design method based on H∞ mixed sensitivity decoupling controller. Decoupling H∞ mixed sensitivity controller is involved in a closed loop system is coupled to the non-ideal mixed sensitivity to design, so as to achieve the purpose of decoupling. In H∞ mixed sensitivity controller design, the need to select the weighting function, to reach the purpose of decoupling. An advantage of this method is that the decoupling control: Because of the advantages H∞ mixed sensitivity controller itself, so that the decoupling controller robust stability and anti-jamming capability.
2, high angle of attack simplified mathematical model of a missile re-entry
Missile dynamics is described by a set of nonlinear equations variable coefficients. Due to elastic vibration factors, the liquid sloshing, and the like swing engine, the equation is very complex. In order to analyze the various equations of motion of missiles, missile control systems, and calculation designed to provide convenient, we use small perturbation simplification. Consider rigid motion and elastic vibration of the missile, it is assumed yaw, roll channel standard trajectory parameters is zero, i.e., to obtain the following equation of motion based elastomer small perturbation assumption. Small perturbations projectile motion equation and the equation of vibration of the elastic movement of the rigid posture elastomer composition. Formula (1) to (3) is a simplified mathematical model.
(1) a method of rigid-body motion pitch channel to equation:
Wherein, αWP, αWQ are stable because the wind, wind shear effect of the additional angle of attack is formed; My, Mx structural disturbance torque; [delta] is the angle of heading trajectory; ballistic sideslip angle beta]; ballistic yaw angle [Psi]; δψ actual yaw steering angle trajectory; structural disturbance force Fx.
(2) a transverse passage yaw rigid motion equation:
Wherein, βWP and βWQ missile are additional side slip angle due stable wind, wind shear effect formation; qiψ yaw - generalized coordinates transverse modes i-th channel (not including rigid body modes) corresponds.
(3) rolling path elastomer equation of motion:
Wherein, γ is the trajectory sliding angle; steering angle [delta] r is the rolling trajectory.
3, the mathematical model coupled elastomers
Seen from the simplified model of the three channels, the parameters (δ, γ) elastomer motion equation of yaw channels contained in the rolling passage, projectile motion equation of the rolling passage of variable yaw channel (δ, ψ containing, beta] ). The mutual coupling of the tilt a normal channel (1), the yaw channel (2) with the rolling channel (3) simultaneous, the composition of a two-input, two output multivariable system, taken as a state vector [β ψ ψ γ γ] T, the control input u = [δψc δγc] T, measurement output as r = [ψc γc] T, to obtain an elastomer state space equation of motion is expressed as:
△ A, △ B parameters such as a high-frequency elastic vibration part due to uncertainty
By the formula (5) can be seen, S (s) + T (s) = I, it is a unit matrix. Selecting an appropriate weighting function of S (s) and T (s) for frequency-domain shaping, i.e. at low frequencies to reduce the gain of the sensitivity function primarily, but at high frequencies to reduce the gain based Complementary sensitivity function, so that after frequency-domain shaping system satisfies:
Wherein, Ws (s) weighted to reflect the performance of the anti-jamming system, WT (s) is weighted to reflect the robustness of the system.
4.2 Decoupling controller design problem
By the formula (5) that the closed loop transfer function T (s) for the system shown in FIG. To this end T (s) may be shaped as desired purpose diagonal matrix to achieve decoupling. [4] gives the H∞ mixed sensitivity problem H∞ shaped as a standard herein is to be derived on this basis, and selecting the appropriate weighting function to achieve the purpose of decoupling. FIG 2 is a block diagram illustrating sensitivity mixed H∞. In FIG. 2, z1, z2 performance evaluation is output. uS, uT, respectively Ws (s) and WT (s) input, yG output G (s) is.
Is G0 (s), WS (s), WT (s) of the state space are implemented:
Figure 2 shows, the system P (s) is input d, u, output z1, z2, y. Provided x0, xS, xT is G (s), WT (s), WS (s) of the output state. Can be deduced from Figure 2: yG = C0x0 + D0uyuT = yg, us = d-yG, then:
Setting x = [x0 xS xT] T, z = [z1 z2] T, the definition of the virtual output signal zp = F1x + F2dF3u, the virtual input signal dp = zp, and consider the formula (7), to give the generalized plant P (s) extended after the realization of the state space is:
Formula (8) parameter uncertainties △ A, △ B1 and B2 satisfy the following relation △:
In this way, the robust controller design of uncertain systems into a standard H∞ design problem.
As can be seen from the standard H∞ design problem, a weighting function involved here WS (s), WT (s) of choice, taking into account the invariance decoupling system, WS (s), WT (s) should be a diagonal matrix, form as follows:
Wherein, WSj (s), WTj (s) (j = 1, ..., m) are
4.3 Principles of the selected weighting function
And of S (s) and T (s) for frequency-domain shaping. At low frequencies to reduce the gain of the sensitivity function primarily, but at high frequencies to reduce the gain of the complementary sensitivity function based. At low frequencies such that S (jω) is located in a gain curve VS (jω) or less, and in the high frequency band such that T (jω) located VT (jω) or less.
5, simulation example
The selection principle condition of formula (5), (6) the sensitivity function S, the complementary sensitivity function T and satisfy the formula (10) and the weighting function, the weighting function can be obtained Ws and complementary sensitivity function of the sensitivity (S), WT (s):
By its simulated frequency-domain shaping, molding the mixed sensitivity as shown in FIG. , By appropriately selecting the weighting function of S and T, the frequency-domain shaping of Figures 3a and 3b shows that the sensitivity and complementary sensitivity singular value curve full frequency segment S and singular value T is less than the singular values of its weighting function matrix inverse , singular value satisfies requirements, but also to satisfy the formula (6) requirements, the system can be robust and have good anti-jamming capability, decoupling conditions, to achieve the purpose of decoupling.
6 Conclusion
For the case where there is a large missile coupling high angle of attack during reentry and yaw channels rolling path, the method H∞ mixed sensitivity decouple decoupling control, and selected based on the sensitivity of the weighting function hybrid coupling controller the weighting function to better take into account the sensitivity of the complementary shaped and decoupling system, to overcome conservative system design. Simulation results show. The decoupling method allows decoupling system has good stability and robustness.
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