Q2. What is the methodology of Hauser and Hindman (1995)?
The methodology of Hauser and Hindman (1995) applies to feedback linearizable systems, where the desired path is specified for the full state.
Q3. What is the first task of the maneuvering controller?
The first task is to reach and follow a desired path as a function of a scalar variable θ, left as an extra degree of freedom for the second task.
Q4. What is the reason for the flexibility of the design procedure?
This flexibility is due to the fact that θ → t − φ is required to be attained only asymptotically, rather than as an identity θ = t− φ.
Q5. What is the kinematics and dynamics of the ship?
The kinematics and dynamics is given byη̇ =R(ψ)ν (41) ν̇ =M−1N(ν)ν +M−1GT (42)where M = M> > 0 and T = [Tu, δ1, δ2]> is the control vector.
Q6. what is the control law for a container ship?
The control law is given byT =G−1M [−Kdz2 − P−12 R>(ψ)P1z1 −M−1Nν + σ1 + ν2υs(θ)] (46)and the update law for ω̇s is ω̇s = −λωs − 2µ1 £ z>1 P1η 0 d(θ) + z > 2 P2ν2 ¤ (47)The simulation are done for a container ship of length L = 175m, and the numerical values are taken from Appendix E.1.3 in (Fossen, 1994).
Q7. what is the control law in section 2?
2. assign θ to t − φ, that is, make the output y to oscillate with frequency 1 rad / s.The design in Section 2 results in the control law u=−2[x1 + x21 + x31 + x1x2 + x2−yd(θ)− y0d(θ)− 1 2 y00d (θ)] (2)where y0d(θ) = dyd dθ (θ) = cos(θ) and y 00 d (θ) = d2yd dθ2(θ) = − sin(θ).
Q8. where s is a bounded Cn1 signal?
From (33) it follows that ωs(t), and therefore yd(θ(t)), is dependent on the system state x(t) through the final tuning function τn.
Q9. what is the main idea of the design procedure developed in section 2?
To introduce the main idea of the design procedure developed in Section 2, the authors look at the strict feedback form systemẋ1 = x2 + x 2 1ẋ2 = u (1)where y = x1 is the output and u is the control.
Q10. What is the design procedure of section 2?
As defined in section one, the maneuvering problem is separated into two tasks, the geometric task and the speed assignment task.
Q11. What is the simplest way to determine the phase of a system?
Using the asymptotic formulation (17), on the other hand, allows for more flexibility, including the possibility to let θ̇ depend on the system state.
Q12. What is the design procedure of Section 2?
The recursive design procedure developed in this paper shows one solution to the maneuvering problem for nonlinear systems in vectorial strict feedback form.