1 INTRODUCTION
When navigating a fast ferry in the seas, the vertical
movements including heave and pitch motions induced by
wave can cause vertical accelerations. Excessive vertical
accelerations may make passengers seasick, and even
constitute a great threat to safety of the vehicle. In order to
effectively control and decrease the vertical accelerations
associated with heave and pitch motions, shipbuilders
usually use active control surfaces as actuators
[1,2]
. The
most commonly used moving actuators are flaps at the
transom and T-foil near the bow. By the design of the
multivariable vertical motion controllers, flaps and T-foil
can be used to counteract the wave induced vertical
accelerations, thus to prevent seasickness.
During the design of the vertical motion controllers for
fast ferries, the linear plant models are often used in current
literatures. Reference [3] gives a classic PD controller, and
uses the motion sickness incidence (MSI) as the
performance index to optimize the controller parameters.
Reference [4] uses the quantitative feedback theory (QFT)
methodology to the design of a multivariable robust
controller. Whereas it can be seen from the simulation
results, this approach greatly sacrifices the MSI (compared
with the PD results) to maintain the robustness. Reference
[5] use different controllers (PD, first order filter and
second order filter) for a high speed ferry, and then presents
a comparative study of the results. Reference [6] design a
multivariable PD controller for a high speed craft, and then
use the ȝ-analysis for robustness analysis of the system.
Since the nonlinearity of the actuators is neglected in the
above references, if controller parameters are improperly
selected, the actuators may reach saturation point. At this
This work is supported by National Natural Science Foundation under
Grant 61304076 and Fundamental Research Funds for the Central
Universities under Grant HEUCFX041501.
time, the closed-loop performance of the linear system
cannot be used to check and access the simulation results.
In view of this, a multivariable PD controller for the fast
ferry is firstly designed in this work, and then the worst
vertical acceleration (WVA) is used for the H
2
norm index
to optimize the controller parameters. In order to access the
performance of the whole system which includes the
nonlinearity of the actuators, an evaluation method based
on the describing function and on the notion of “variance
gain” is proposed in this work. In this evaluation approach,
the closed-loop system is fed with a finite set of N pure
sinusoidal signals, and then the describing function and
variance gain are computed in N points to approximate the
frequency response function. This evaluation approach
provides, in the frequency domain, a clear picture of the
closed-loop performance on the vertical acceleration
(comfort objective). This frequency domain closed-loop
performance computation approach inherently provides a
quantitative estimate of the degree of Input/Output
non-linearity of the closed-loop system, and it can also be
used to access the simulation results of the system.
2 THE PROCESS MODEL
Fig.1. The process model of the plant
As shown in Fig.1, the process model of the fast ferry is
composed of actuators (flaps and T-foil), ship and wave
[1]
.
There are two control inputs in Fig.1: the set-point of the
flaps position u
F
and the set-point of the T-foil position u
T
.
On Performance Evaluation Method and Optimal Control for Vertical Dynamic
of a Fast Ferry
Liu Yan-wen Zhao Zheng
College of Automation, Harbin Engineering University, Harbin 150001, China
E-mail: zhwlyw@163.com
Abstract: To decrease the vertical acceleration associated with pitch and heave, a multivariable PD controller is firstly
designed in the paper, then parameters of the controllers are optimized according to the H
2
norm of the worst vertical
acceleration (WVA) output. The non-linearity of the actuators (flaps and T-foil) is considered and included into the
simulation process. In order to assess the closed-loop performance of the nonlinear system, an evaluation method based
on the describing function and the variance gain is proposed. This evaluation approach provides, in the frequency
domain, a clear picture of the closed-loop performance on the vertical acceleration. By using this evaluation approach to
a specific example, it is indicated that this frequency domain closed-loop performance computation approach can more
reasonably explain the simulation results of the system. This evaluation method can not only be used to quantitatively
access the WVA reduction percentage, but also can be used to estimate the degree of Input/Output non-linearity of the
closed-loop system.
Key Words: Multivariable PD Control, H
2
Norm, Describing Function, Closed-loop Performance
Process
Model
u
F
u
T
heave
itch
1630
978-1-4799-7016-2/15/$31.00
c
2015 IEEE