Lateral Movement with a given yaw angle

Block appearance in REPEAT VISION

  In the absence of disturbances in the lateral direction, the missile trajectory coincides with the firing plane and, unless there are any special considerations, the program value of the yaw angle should be assumed to be zero. The yaw mismatch angle will be related to the angle of rotation of the controls by means of the static coefficient of the control system — K\(_{0\psi}\) obtaining (1):

(1)\[\delta_{y_1}=k_{0\psi}\cdot \psi\]

 Используя балансировочную зависимость запишем (2),(3), (4), (5), (6), (7), (8)и (9):

(2)\[\frac{б\cdot \nu^2}{2}\cdot S \cdot lm^{\beta}_{y_{1}} \cdot \beta_{\delta} + Z^{\delta}_{p_1} \cdot y_1 \cdot l_p \cdot \delta_{y_1}=0 \]

 Hence (3):

(3)\[\beta_\delta=-\frac{2\cdot Z^{\delta}_{p_1}\cdot y_1 \cdot l_p \cdot \delta_{y_1}}{б\cdot \nu^2 \cdot S \cdot lm^{\beta}_{y_{1}}}=-\epsilon_{\psi} \cdot \delta_{y_1}\]

(4)\[\psi= \Psi + \beta\]

(5)\[\beta_\delta=-\frac{\epsilon_{\psi \cdot k_{0\psi} \cdot \Psi}}{1+\epsilon_{\psi \cdot k_{0\psi}}}\]

(6)\[Z*=Z=-Z^{\beta}\cdot \beta_{\delta}\]

(7)\[\dot{\Psi}=\frac{(P+Z^{\beta})}{m\cdot \nu \cdot cos \theta}\cdot \beta_{\delta}\]

(8)\[\dot{\Psi}=\frac{\epsilon_{\psi} \cdot k_{0\psi} \cdot (P+Z^{\beta})(\Psi_{np}-\Psi)}{m\cdot \nu \cdot cos \theta \cdot (1+\epsilon_{\psi} \cdot k_{0\psi})}\]

(9)\[\dot{z_3}=-\nu \cdot cos\theta \cdot sin\Psi\]

 As a result, we obtain a system of equations that approximates the balanced flight of a guided missile in the lateral direction.

1.  Properties

Property	Default Value	Description	Units of measurement
AD length	2	-	m
Distance from the center of pressure of the controls to the center of mass of the AD	2	-	m
Initial angle of trajectory rotation	2	-	degree
AD surface area required to determine the moment My1	2	-	m\(^2\)
Initial values for lateral displacement	2	-	m

2.  Inputs and outputs

Parameters	Input/Output	Description	Units of measurement	Port type
\(v\)	Input	AD speed module	m/s	Automation
Theta (\(\theta\))	Input	Flight-path angle	rad	Automation
P	Input	AD engine thrust vector in the coordinate system	N	Automation
Z\(_{betta}\)	Input	Lifting force in half-speed coordinate system	N	Automation
M\(_{ybetta1}\)	Input	Moment projection on the Y1 axis in the related coordinate system	N\(\cdot\)m	Automation
Z\(_{p1}\)	Input	Sum of forces generated by controls in a related coordinate system	N	Automation
m	Input	AD mass	kg	Automation
Q	Input	Velocity head	N/m\(^2\)	Automation
Psi_prog \(\psi_{prog}\)	Input	Program yaw angle value	rad	Automation
\(K_{0psi}\)	Input	Control system factor	rad	Automation
Psi \(\Psi\)	Output	Trajectory rotation angle	rad	Automation
Z\(_z\)	Output	Lateral offset	m	Automation
psi \(\psi\)	Output	Yaw angle	rad	Automation
betta \(\beta\)	Output	Gliding angle	rad	Automation

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