“…Thus, the function of θ ̇ can be rewritten as θ ̇= q + (𝑐𝑜𝑠Ф − 1)q − 𝑠𝑖𝑛Ф𝑟 = q + 𝑑 θ1 (40) Where 𝑑 θ1 is the external disturbance of this system and 𝑑 θ1 = (𝑐𝑜𝑠Ф − 1)q − 𝑠𝑖𝑛Ф𝑟. Take the derivative of both sides with respect to t: θ ̈= q̇+ 𝑑 θ1 ̇ (41) Substitute (33) Therefore, the desired state-space vector of the attitude angle control system can be defined as 𝑋 = (𝛹, 𝛹 ̇, θ, θ ̇, Ф, Ф ̇)𝑇 ∈ 𝑅 6 (47) The output vector of this system can be defined as 𝑌 = (𝛹, θ, Ф) 𝑇 ∈ 𝑅 3 (48) Letting 𝑥 1 = 𝛹, 𝑥 2 = 𝛹 ̇, 𝑥 3 = θ, 𝑥 4 = θ ̇, 𝑥 5 = Ф, 𝑥 6 = Ф ̇. The related state-space function can be obtained as where 𝐷 𝛹 is the total uncertainty of the yaw angle controller, which can be expressed as 𝐷 𝛹 = ∆𝑎 𝛹1 𝑥 2 + ∆𝑎 𝛹2 𝑈 2 + 𝑑 𝛹 (51) In the process of recursion, the sliding mode surface and adaptive law need to be introduced to determine the control effect of the controller.…”