dc thruster controller implementation with integral anti-wind up compensation for underwater rov

8/7/2019 DC Thruster Controller Implementation with Integral Anti-wind up Compensation for Underwater ROV

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Journal of Intelligent and Robotic Systems 25: 7994, 1999.

1999 Kluwer Academic Publishers. Printed in the Netherlands.79

DC Thruster Controller Implementation withIntegral Anti-wind up Compensator for Underwater

ROV

JOHN N. LYGOURASElectronics and Digital Systems Laboratory, Department of Electrical and Computer Engineering,

67100 Xanthi, Greece

(Received: 26 May 1998; in final form: 30 October 1998)

Abstract. This paper presents the implementation and experimental results of different conventional

position control schemes for positioning an experimental model, the THETIS Underwater RemotelyOperated Vehicle (UROV). To achieve minimum response time and in order to avoid the so-called

Integral Wind-up phenomenon, Proportional-Integral (PI) plus integral antiwind-up compensation

is used. Hardware implementation of the design is described and experimental results of a digital

position control system over one direction using two dc thrusters fed by four quadrant (PWM-Driven)

transistor choppers are given. All control algorithms are implemented using a TIs Digital Signal

Processor (DSP). The actual position and orientation of the vehicle in a 3-D space is derived through a

combination of an ultrasonic scanning system, a direction gyrocompass, and a pressure depth sensor.

The vehicles use at the present stage of development is to perform water pollution measurements.

Key words: remotely operated vehicle (ROV), underwater technology, DC thrusters, integral wind-

up compensation, position control.

1. Introduction

In the past few years, the use of Remotely Operated Vehicles (ROV) has rapidly

increased due to the development of these vehicles to perform operations in deeper

and riskier areas where human divers cannot reach. Applications of ROVs include

ocean surveying, maintenance and construction of underwater structures, mainte-

nance of nuclear plants, water pollution measurements, etc. [16]. The design of

a high performance position control system for an ROV is of interest both from

the view of motion stabilisation as well as manoeuvring and tracking performance.

The dynamic response provided by such controllers should satisfy a set of strict

specifications in terms of speed, precision, overshoot, and interactions among the

controlled and/or uncontrolled coordinates. The controller should also be able to

cope with environmental disturbances, such as sea current and turbulence near

subsea structures, normally acting on the ROV.

Several ROV controlling methods have been proposed in the literature. It is

well known that conventional controllers with fixed gains do not guarantee high


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80 J. N. LYGOURAS

quality response of the overall system when significant changes occur in the vehicle

dynamics. Most of the controlling methods are designed on the basis to reduce

the inherent coupling between the vehicle response modes that naturally exist in

ROVs. The approach leads to a set of separate designs for the steering, diving, and

speed control systems. Simulations are then executed based on the dynamics of the

vehicle to illustrate the robustness and validity of the concept.

Among the variety of possible control strategies proposed in the relevant papers,

two of them, the conventional linear P-PIcontroller is preferable for its simplicity

and has been shown to give good results in position control, at least when the vehi-

cle parameters are constant and no external disturbance exists. On the other hand,

the state-feedback Variable Structure Control (VSC) algorithm gives better results

since precise modelling of the ROV is not needed and unmodelled perturbations

can be effectively rejected [7, 8]. Recently, neural network-based controllers for

Autonomous Underwater Vehicles (AUVs) have been proposed [9], and fuzzy

logic has been adopted to control the ballast of Unmanned Undersea Vehicles

(UUVs) [10]. Most of the above control schemes, however, are not implementedin real ROV models and their performance is verified only by simulation.

Although conventional controllers have some disadvantages as it was mentioned

above, they are preferable in many cases due to the simplicity of implementation. In

this paper, the P-PIcontroller with an integral antiwind-up compensator has been

used for position control of an ROV for every degree of freedom. It consists of an

inner velocity control loop and an outer positioncontrol loop. Another advantage of

the P-PIcontroller is its ability to reject step disturbances, i.e., to eliminate offset

provoked by step disturbance by means of the integral action of the inner loop [7].

An experimental model, 1.4 m long underwater ROV using DC thrusters (com-

bination of DC motor with a propeller) has been constructed. The model is a

remotely controlled submersible vehicle, rectangular in shape and composed of

a Ferrum-Aluminum framework which encloses and supports all components. The

configuration of the vehicle is of an open-frame type with buoyant material on its

top. The water flow around the vehicle of this type is complex, and it is very difficult

to estimate its hydrodynamic characteristics by computation. So, hydrodynamic

tests provide the only way to determine the derivatives which are necessary for the

evaluations of manoeuvrability.

2. ROV Model Structure

The ROV system can be described by the following equation:

FM

=

Mij

uvv

+

Aij

urr

, (1)

where F, Mare the external forces and moments, Mij is the basic inertia matrix of

the vehicle, Aij is the added inertia matrix (including the added moments of inertia

and cross coupling terms such as force coefficients due to angular acceleration), uv


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DC THRUSTER CONTROLLER FOR UNDERWATER ROV 81

and wv are the linear and angular velocity of the vehicle, respectively, and ur, wrare the linear and angular velocity with respect to the fluid, respectively.

This is the general model for the ROV system. In fact the model is similar in

structure to the models for objects which are not underwater. The main difference

is caused by the presence of the additional mass and the drag forces for underwater

vehicles. The external force is given as the sum of the hydrodynamic force Ff, grav-

ity force Fg, thrust Ft and the tension Fc of the tether cable at the cable termination

point. Thus:

F= Ff+ Fg + Ft + Fc = Ff+ Fb + Fw + Fti + Fc, (2)

where Fb is the buoyancy, Fw is the weight force of the vehicle, and Fti is thrust

of the ith thruster. The general ROV model is simplified by many authors not

considering, for example, the cable tension Fc (considering the influence of the

cable on ROV as disturbances) since the forces and the torques arising from the

cable are difficult to specify. However, if the external forces due to the cable are to

be considered, a number of force models can be found in the literature [11].

When the dynamics of the ROV and the thrusters are considered, a complex

nonlinear system is obtained, even when the craft dynamics is assumed to be linear

(for instance, hover), due to the nonlinear features of the thrusters at low speed op-

eration. Thus, when a control system for the thrusters of an ROV is to be designed

one must take into account all the existing nonlinearities.

To apply linear control theory, it is necessary to obtain a linear model for the

ROV. The nonlinear model describing an ROV can be written as follows [12, 13]:

x = f (x,u), (3)

where x is a state vector, and u is the input, which are forces and moments pro-

duced by the thrusters. Given an operating point: x0 = (u0, v0, w0, p0, q0, r0)T

with inputs: Th = (t10, t20, t30, t40, t50, t60)T, a small variation around this can be

approximated by a linear model usually written as:

x = (f/ x)

x=x0u=u0

x + (f/u)

x=x0u=u0

u (4)

where x0 and u0 are nominal output and input which satisfy:

x0 = f (x0, u0). (5)

For the ROV model, the state is defined by x1 = [u v w p q r]T and x2 =

[, , ]T, hence,x1x2

=

f1(x1, x2, u)

f2(x1, x2)

, (6)

where u, v and w denote the three components of the absolute translational velocity

in the Oxyz system attached to the centre of the mass of the vehicle, p, q and


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82 J. N. LYGOURAS

r denote the three components of the absolute angular velocity Win the Oxyz

system and , and are the Euler angles.

Considering an input of the form:

u = u0 + u (7)

where u0 is the nominal input, and u is the difference between the actual and

nominal, we can evaluate x0 = f (x0, u0). Then, nominal input and nominal state

should satisfy the ROV nonlinear model, namely

x0 = f (x0, u0), (8)

so x0 can be obtained through the above equation. In this case, the range in which

the linear model coincides with the nonlinear one can be investigated. Based on the

simulation results of linear velocities of the ROV given in [11], this range can be

limited as follows: ifU10, W10, q10 and Un, Wn, qn, the velocity u, w and q from the

linear model with zero inputs as the nominal one and the ones from the nonlinearmodel, respectively, the ROV nonlinear model can be approximated by a linear one

with satisfactory precision, i.e., U10 = Un and q10 = qn if

Un < 0.5 m/s, wn < 0.02 m/s and qn < 0.03 rad/s

and W10 = Wn and q10 = qn if

Un < 0.01 m/s, wn < 0.2 m/s and qn < 0.012 rad/s

if the above conditions are satisfied, the nonlinear model can be approximated by

the linear one with satisfactory precision.

There are practical reasons why the dynamic models of DC motors cannot

be applied directly to model the motors of the DC thrusters. Although many of

the characteristic parameters are provided by the motor manufacturer, there are

parameters (e.g., the moment of inertia of the load, frictional torque, the dumping

constant, the drag forces, the gravity and buoyancy forces and moments) that must

be obtained experimentally after the motors are built into the vehicle.

Underwater vehicles are generally equipped with thrusters which consist of a

propeller driven by a torque source . In normal operation, the rotational velocity

of the propeller n and the advance velocity of the vehicle, VA, are both positive (first

quadrant operation). The load torque Q from the propeller and the thrust force T

are then usually written as:

Q = D 5KQ

(J0

)n|n|, (9)

T= D 4KT(J0)n|n|, (10)

where is the mass density of water, D is the propeller diameter, KQ and KTare the torque and the thrust coefficients of the propeller and J0 is the advance

ratio: J0 = VA/nD . If both n and VA are negative (fourth quadrant), the thruster


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characteristics are quite similar to those in the first quadrant. In general, however,

the thrust and torque coefficients are not equal in these two quadrants (i.e., sym-

metrical), since positive thrust is usually greater than negative thrust. It is assumed

that an algebraic relation, although complicated, exists between the thrust Ti of

propeller i and the physical input. Therefore, the thrust will be chosen as input in

the system:

ui = Ti. (11)

This means that the system will be linear in the inputs. In order to adjust the output

torque of each thruster the motors speed must be controlled.

The control system for the ROV thrusters has to consider two aspects. The

first one is related to the nonlinear character of its dynamics, as it is described by

Equations (9) and (10). The influence of the nonlinear term |n|n is reflected in time

responses of the thrusters to different amplitude step functions. For larger inputs

the response is more rapid so that at hover, where the nominal force required is

minimum, the time response of the thruster is higher. The second aspect is related

to the operating condition of the thrusters at hover.

One major problem that dc motors introduce, when driven by low input voltages

directly or using a PWM driver circuit, is that of dead-band nonlinearity. Consider-

ing as static this nonlinearity, it is cancelled in our application by specially designed

logarithmic networks. These circuits are designed in a way to present a nonlinear

transfer characteristic, symmetric to the axis y = x, to the static nonlinearity of

the dc motor. When such a circuit is connected in series with the dc motor driver

circuit, the dead-band nonlinearity of the motor is cancelled [14].

3. Position Control System Using DC Thrusters

There has been a lot of research work on the analysis of position controllers using

brush dc servomotors [1517] using either conventional or modern control tech-

niques. The basic requirements in a position control system are the properties of

small overshoot and fast settling time to a step input change. Commonly, several

combinations of P (Proportional), I (Integral) and D (Derivative) terms are used. In

the sequel the implementation of a position controller of the underwater vehicle,

based on the information derived from suitable sensors is described. The control

system is responsible for the overall system performance because it determines

the movement on a specific trajectory path. This trajectory is determined either

manually or automatically by the trajectory planning algorithm of the vehicle. The

vehicle is controllable through brush DC thrusters and is capable to move in the 3-

D space and to turn around the z axis. The position control of the vehicle in space

is achieved through the torque control of its thrusters.

The measured sensor signals used for position control feedback are depth, ori-

entation, and distance from surrounding objects by means of an ultrasonic scanner

system [18]. This system provides the capability to scan the 3-D space around the


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84 J. N. LYGOURAS

(a)

(b)

Figure 1. (a) The THETIS ROV propeller placement and (b) the Position Error Transforma-

tion (PET) technique to drive the system.

vehicle and to represent the scanned profile on the controlling computer screen.

The scanning ultrasonic tranceiver can be stopped in any desired direction if an

obstacle has been detected. The actual position in the 3-D space of the ROV can be

derived using combined information of the above sensors.

In Figure 1(a) the THETIS ROV considered is equipped with four propellers

(p1, p2, p3, p4) which allow us to control the vehicle on the horizontal plane

(xh, yh), the depth zh, and the heading . The remaining degrees of freedom (pitch


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and roll angles) cannot be directly controlled. However, the system uses passive

stability keeping the metacentric height of the vehicle sufficiently large resulting in

small pitch and roll angles.

The ROV control inputs, denoted as uj (j = x , y , z , ) are the signals that

are applied to the command unit of the ROV propellers. In manual control, those

inputs are produced by the tele-operator through a joystick. Using the Position

Error Transformation (PET) technique to drive the system, (Figure 1(b)) the posi-

tion error and the ROV velocity measured in inertial coordinates are transformed

to body coordinates and the controller gives directly the ROV control inputs uj .

Assuming that and are zero, the position error in body coordinates is given by

the following transformation:

[ex ey ez]T = Tz()(Pref P), e = ref , (12)

Tz() = cos sin 0

sin cos 0

0 0 1 . (13)

A block diagram of the digital position control system is shown in Figure 2. It is

composed of the power circuit, the controlled thruster, the controlling DSP, suitable

sensors and the appropriate interface. Using the ultrasonic scanning system the

actual distance of the vehicle from the surrounding environment is displayed. If a

stable target is detected, the vehicle is capable of keeping a constant distance xdfrom it. The respective thrusters are then actuated in a direction so that to make the

position error xd xr zero. In the same way the heading r is read from a gyroscope

and the respective thrusters P1 and P2 can be actuated to turn the vehicle about the

z axis.

Figure 2. Ultrasonics, depth sensor, and a gyrocompass-based ROV position control system.


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86 J. N. LYGOURAS

Table I. Thrusters specifications

Type DC motor

Input DC 25 V, 6 A main power and

DC 12 V for electronic module

Output 120 W at 3000 rpm

Output torque 1.6 Nm

Control method Output torque control via PWM

Size 80 mm (diameter) 150 mm

Propeller diameter 10 cm, two-blade

The power circuit that allows us to control the vehicle on the horizontal plane

(xh, yh) consists of two dc thrusters P1 and P2 which can be operated together

or separately driven by four quadrant choppers and using the PWM technique.Four-quadrant operation is necessary for accelerating and braking the motors in

both directions. The choppers operate at a fixed frequency of 10 KHz with a vari-

able duty cycle controlled by an input voltage (10 V < Vin< + 10 V). Specially

designed D/A converters are used to convert the desired control word into the

corresponding input voltage for the chopper. The characteristics of the thrusters

used in our experiments are listed in Table I.

We have made the following assumptions on the position control system:

The whole system is a linear system.

The time response of back emf of the motor is considered very slow vs. time

response of the current loop, thus it has been omitted. The time delays of the chopper (bridge) and ultrasonic transceiver (when it

measures the distance of a stable target) have also been omitted.

4. PI Controller Implementation with Integral Antiwind-up Compensator

The implemented control scheme is shown in Figure 3(a). According to the PET

presented in the previous paragraph, an algorithm was implemented to control the

four DC thrusters for positioning the vehicle in each direction. Three different

position control schemes have been implemented and tested, more thoroughly the

following:

Position and velocity feedback with P and PIcontrollers, respectively,

Position, velocity and current feedback with P, PIand PIcontrollers, respec-

tively, and


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(a)

(b)

Figure 3. The implemented position control schemes: (a) position and velocity feedback and

(b) integral antiwind-up compensator.

Position and velocity feedback with P and PIcontrollers, respectively, plus an

integral antiwind-up compensator.

A severe problem in analogue controllers including an I-term is the so-called

integral wind-up phenomenon, caused by persistent offset between the mea-

sured and set values. This saturation-type nonlinearity is not considered in most

conventional methods of analysis and design of position controllers, though such

nonlinearity practically exists in the current reference input node. The effect of this

is to lengthen the system settling time and to cause large overshoots. Fortunately, it


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88 J. N. LYGOURAS

is simple to include mechanisms for the exact adjustments of the integral term into

digital controllers.

To overcome the integral wind-up problem of the speed controller with PI-

action, integral antiwind-up compensation is used and extensively tested. Accord-

ing to this technique, the controller employs the PI-action when the magnitude of

the velocity error is smaller than a prescribed value. Otherwise, the controller gen-

erates the maximum permissible control signal with the integrator being forced to

reset. The design, which is experimentally verified, proves that the speed controller

of this type provides a fast settling time property with small overshoots regardless

of the magnitude of the reference input signal. In this way, the integral wind-up is

prevented and also the maximum ratings of hardware components are utilized.

The purpose of the speed control loop is to reduce the effects of hydrodynamic

and drag forces and also to compensate for the load carried by the thruster. The

vehicles actual speed is obtained by numerical differentiation of the translational

displacement along the axis during a fixed time interval. The required position

and velocity accuracy depend on the specific application. Although this methoddoes not provide so accurate results, since position measurements can be noisy,

it is the simplest way since it is difficult to derive the linear and angular speed

of the vehicle in all directions. Moreover, the accuracy achieved by the ultrasonic

scanning system (1 cm) is enough for our application. The number representing the

speed for the ith sampling period is given by:

v(i) = KuF[u(i) u(i 1)]

t, (14)

where KuFis the feedback gain of the speed.

The implementation of the PI-controllers for the speed control and current con-

trol loops is achieved by using the incremental trapezoidal integration algorithm

which computes the integrals of the errors with an increased accuracy:vu = vu1 + vu (15)

vu = Kx

eu

1 +

T

2Ti

eu1

1

T

2Ti

(16)

The gain of the outer position controller has been estimated using the Zigler

Nichols technique operating the system only with the position control loop. The

selection of time constants of the PIcontrollers is based on the conventional analy-

sis.

The transfer function of this type of controller is given by the following equa-

tion:

u(t) =

Ku(eu(t) + (1/Tu)I), for eu(t) k,Emax and I= 0 for eu(t) > k,

Emax and I= 0 for eu(t) < k,

(17)

where

u(t) is the output of the controller,


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eu(t) is the speed error,

Emax is the maximum allowable voltage to the thruster,

Iis the integrators output = t

0eu(t) dt,

Ku is the forward velocity gain, Tu is the integration time constant,

k is a user defined small positive number.

The above algorithm describes the bang-bang control action which in a block

diagram is shown in Figure 3(b). The desired speed here is compared with the

actual speed resulting from differentiation of the distance signal derived from the

ultrasonic scanning system. If the absolute value of the error is less than or equal

to the prescribed value k then the error is given via the PIcontroller to the motor.

When the error is greater than k, then the maximum allowable voltage is given

to the motor while keeping the integrator reset. From the implementation of the

above control algorithm two significant advantages are resulting. The first one is

the minimization of response time of the system while keeping the overshoot low,and the second is avoidance of the so-called Integral Wind-up phenomenon. The

threshold k used in the PIspeed controller is experimentally determined as in the

other relevant applications.

5. Experimental Results

The modelling, design and control of an open-frame underwater remotely operated

vehicle have been described in this paper. Under the assumption that the linear

velocity of the vehicle along the axis of motion is low, the ROV model can be

considered as linear. This assumption is not far away from reality since the velocity

of this kind of vehicles is rarely higher than 0.5 m/s. The flow round the vehicleof this type is complex, and it is difficult to estimate its hydrodynamic charac-

teristics by simulations. So, hydrodynamic tests were conducted to determine the

derivatives which are necessary for the evaluations of manoeuvrability. Since the

thruster parameters are unknown, experimental data are acquired to identify the

continuous-time model. The order of the model is chosen to ensure acceptable ac-

curacy, without increasing the complexity of the controller. Velocity step response

of the dc thruster was made to identify the transfer function from pulse width to

velocity. Velocity measurements are taken every 5 ms. The dominant time constant

of the motor is found to be 120 ms. The motor exhibits nonlinear saturation at the

maximum velocity (4000 rpm in no load conditions, 1500 rpm inside the water)

and a frictional dead zone at small command inputs (|Vin

| < 2.0V).

The above described control schemes in Figure 3 have been experimentally im-

plemented and extensively tested. The ROV system has been tested in a water-pool,

in the laboratory of Hydraulics. Artificial water-pool bed profile on the controlling

computer screen, using the ultrasonic scanning system, is illustrated in Figure 4.

This image enables the user to know the distances of the objects surrounding the


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90 J. N. LYGOURAS

Figure 4. Artificial water-pool bed profile on the controlling computer screen, using the

ultrasonic scanning system.

vehicle on a plane including the X-axis and rotated at an angle relatively to the

x-z plane. The scanning transceiver can be rotated round the x axis and in this way

it can scan the space around the vehicle over almost a hemisphere. The two-way

scanning time for the ultrasonic transducer is about 1.0 s.

Step input response is taken moving the vehicle longitudinally along the x axis.

Nonlinearities in the control system (motor saturation and position quantization)

have been neglected in the controller design. The nonlinearity caused by friction

and moment of inertia of the rotor (dead-band nonlinearity) is cancelled using the

circuit described in reference [14] with very satisfactory results. Controller gains

have been selected to satisfy the design goals of minimum overshoot and settling

time. Experimental results showing the response of the P-PIcontroller to step

inputs in the x direction are shown in Figure 5. Obviously, the last response is

a better one since it has the minimum response time and smaller overshoot. The

satisfying system response is achieved with small overshoot while no disturbances

exist.

6. Conclusions

The position controller using PIplus integral antiwind-up compensation has been

implemented and successfully tested for control of the thrusters of the constructed

ROV. Initial experimental results have been presented in this paper. This control

law is simple and can be very easily implemented. Even though the presented ROV

is essentially an experimental, test-bed vehicle, it is still capable of performing


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(a)

(b)

Figure 5. Step input response of the three tested configurations: (a) large signal step response

for the case where position and velocity feedback is used with P and PIcontroller, respectively.

Here, Kx = 13, Ku = 1.1 and Kx = 21.5, Tu = 20; (b) position, velocity and current

feedback with P, PIand PIcontrollers, respectively. Here Kx = 10, Ku = 1.1, Tu = 30,

Kc = 1, Tc = 70 and Kx = 12, Ku = 1.0, Tu = 25, Kc = 1.1, Tc = 60 and (c) position and

speed feedback with P, PIcontrollers, respectively, with integral antiwind-up compensation.

Here, Kx = 15, Ku = 0.8, Tu = 5 and n = 0.55 V.

various shallow water tasks. It is equipped with a B/W video-camera and other

suitable sensors and its primary use, at the present stage of development, is to

perform water pollution measurements. It is a low-cost, efficient and reliable ve-

hicle which can prove a good subsea support system for underwater site surveys

(wrecks, coral, shells, pipelines, etc.), in heavily polluted water up to 100 m deep.

It can also be used for surface monitored underwater tasks as well as diver support,


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92 J. N. LYGOURAS

(c)

(d)

(e)

Figure 5. (Continued.)


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Figure 6. The constructed THETIS ROV.

thus improving diver efficiency and safety. A photograph of the constructed ROV

is shown in Figure 6.

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dc thruster controller implementation with integral anti-wind up compensation for underwater rov

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