chapter 4 performance estimation of wrim with...

69

CHAPTER 4

PERFORMANCE ESTIMATION OF WRIM WITH FLC AND

PID CONTROLLERS

4.1 INTRODUCTION

This chapter describes the Fuzzy Logic Controller (FLC) and PID

controller used for closed loop operation and the performance estimation of

WRIM. The design procedure of the Fuzzy Logic Controller is presented in

Section 4.2. The PID controller designed in chapter 2 is also utilized in this

chapter. Simulation model of the developed system is presented in section 4.3.

The performance of the WRIM is estimated using MATLAB/simulink with FLC

on stator side inverter and PID controller on rotor side inverter and vice versa.

The simulation results for Fuzzy-PID and PID-Fuzzy combinations are presented

in section 4.4 and 4.5 respectively. The motor and controller performance has

been analyzed and the results are summarized in Table 4.4.

4.2 DESIGN OF FUZZY LOGIC CONTROLLER

Unlike digital logic, the Fuzzy Logic is a multivalued logic. It deals with

approximate perceptive rather than precise. The effective and efficient control

using fuzzy logic has emerged as a tool to deal with uncertain, imprecise or

qualitative decision making problems. Fuzzy Logic derived from fuzzy set

theory. Fuzzy logic was first proposed by Lotfi Zadeh in 1965. Recently the

Fuzzy Logic is utilized in many applications, such as adjustable speed drive,

aircraft engines, helicopter control, missile guidance, automatic transmission,

wheel slip control, auto focus cameras, washing machines, railway engines for

smoother drive and fuel consumption and many industrial processes. Many

literatures say that the Fuzzy Logic Control provides better results than the

conventional PID controllers.

70

Fuzzy set theory represents the human reasoning with knowledge that is

almost impossible to represent in quantitative measures or for that control plants

that are hard to control or ill defined. Fuzzy inference system models the system

using if-then rules. Fuzzy set theory proposes the membership function at range

of numbers (0, 1) or False or True membership function. This theory provides

the mathematical strength to check the uncertainty connected with human

thinking or reasoning. Fuzzy logic is suitable for model that is hard to control or

non-linear models. This system also provides over MIMO systems and also

allows decision making with incomplete information. Human reasoning can also

be known as multi valued ‘imprecise’.

In Fuzzy Logic controller design, the first step is to understand and

characterize the system behavior by using knowledge and experience. The

second step is to directly design the control algorithm using fuzzy rules, which

describe the principles of the controller's regulation in terms of the relationship

between its inputs and outputs. The last step is to simulate and debug the design.

The fuzzy logic controller (FLC) can be designed without the exact model of the

system. For FLC, it is sufficient to understand the general behavior of the

system. Such a FLC is designed and implemented for stator side PWM inverter

fed wound rotor induction motor and the PID controller is also designed to

control the PWM inverter connected on the rotor side.

The FLC involves three stages namely Fuzzification, Rule-Base and

Defuzzification. The Mamdani type controller is used in this work. This

controller has the membership function in the output variable which will give

accurate results. Moreover it can be easily implemented. The general structure of

Fuzzy Logic controller is given in Figure 4.1.

71

Figure 4.1 Structure of Fuzzy Logic Controller

4.2.1 Fuzzification

In Fuzzy logic system the linguistic variables are used instead of

numerical variables. The process of converting a numerical variable (real

number or crisp variables) in to a linguistic variable (fuzzy number or fuzzy

variable) is called fuzzification.

The speed is controlled by stator side fuzzy logic controller. The actual

speed ωr and the reference speed ωr* are compared to get speed error e, which is

shown in the equation (4.1). The reference three phase stator currents are utilized

for generating the PWM signals for the stator side inverter. The three phase

reference stator currents are derived from stator reference dq-currents. The stator

d-axis reference current is found from flux (it is known that the flux is estimated

from d-axis actual current). Then the outer loop speed error and the flux are used

for q-axis current calculation. The q-axis current is a combination of motor

speed and flux. Hence the q-axis current is controlled; the motor speed can be

controlled effectively. So the q-axis current is considered for control.

The stator quadrature current iqs is calculated using speed error e and flux

φ then it is normalized, in order to use the same FLC for different reference

speed. The stator quadrature current iqs and the change in quadrature current diqs

are given as inputs to the fuzzy logic controller. At kth sampling the change in

72

current diqs(k) is calculated from the current iqs(k) and pervious current iqs(k-1) as

per the equation (4.2).

rre * (4.1)

)1()()( kikikdi qsqsqs (4.2)

This process stage is called as preprocessing which is shown in Figure

4.1. Then the quadrature current iqs and the change in quadrature current diqs are

fuzzified.

Seven linguistic variables are used for the input variable iqs and diqs. That

are negative big (NB), negative medium (NM), negative small (NS), zero (Z),

positive small (PS), positive medium (PM) and positive big (PB). There are

many types of membership functions, such as triangular-shaped, Gaussian,

sigmoidal, pi-shaped, trapezoidal-shaped, bell-shaped etc. The triangular

membership function is used for simplicity and also to reduce the calculations.

4.2.2 Defuzzification

The reverse process of fuzzification is called defuzzification. The linguistic

variables are converted in to a numerical variable. The centroid method is

considered to be the best well-known defuzzification method, it is utilized in the

present model. The defuzzified output is the reference quadrature current iq*.

This process stage is called as post processing which is also shown in Figure 4.1.

The reference stator current isabc* is calculated from the iq*, id* and theta. This

reference stator current is utilized for generating the PWM signals for the stator

side inverter. The input and output fuzzy membership functions are shown in

Figure 4.2.

73

Figure 4.2 Fuzzy memberships used for simulation

4.2.3 Rule Table and Inference Engine

The control rules that relate the fuzzy outputs to the fuzzy inputs are

derived from general knowledge of the system behavior, also the perception.

However, some of the control rules are developed using “trial and error” method.

The general rule can be written as “If iqs is X and diqs is Y, then iq* is Z”,

where X, Y and Z are the fuzzy variable for iqs, diqs and iq* respectively. Here

stator quadrature current iqs is counterpart to speed error. If the iqs is positive

74

(actual speed is lesser than the reference speed), it has to decrease toward zero.

Therefore iq* is set to positive in order to increase the actual speed and to reduce

the speed error to zero. In the fuzzy controller the input side current iqs and

change in current diqs are divided into seven triangular membership functions,

output side iq* is divided into nine triangular membership functions. Out of these

totally 49 rules are formed; the rule table for the designed fuzzy controller is

given in the Table 4.1. The element in the first row and first column means that

“If error is NB, and change in error is NB then output is NVB”.

Table 4.1 Fuzzy Rules

iqs

diqs

NB NM NS Z PS PM PB

NB NVB NVB NVB NB NM NS ZE

NM NVB NVB NB NM NS ZE PS

NS NVB NB NM NS ZE PS PM

Z NB NM NS ZE PS PM PB

PS NM NS ZE PS PM PB PVB

PM NS ZE PS PM PB PVB PVB

PB ZE PS PM PB PVB PVB PVB

75

4.2.4 Fuzzy Logic Controller in MATLAB

The detailed design procedure for the development of Fuzzy Logic

Controller using MATLAB is given in section. As mentioned in the previous

section there are three variables chosen, two for input variables stator quadrature

current iqs and Change in stator quadrature current diqs, the third one is for output

variable reference quadrature current iq*.

Table 4.2 Specifications for the input variable iqs

Linguistic variable for iqs

Linguistic Value Notation Numerical Value

Negative Big NB [-1.333 -1 -0.6665]

Negative Medium NM [-1 -0.6665 -0.3334]

Negative Small NS [-0.6665 -0.3334 0]

Zero Z [-0.3334 0 0.3334]

Positive Small PS [0 0.3334 0.6665]

Positive Medium PM [0.3334 0.6665 1]

Positive Big PB [0.6665 1 1.334]

The general procedure to develop the Fuzzy Logic Controller is

• Identify the inputs and their ranges and name them

• Identify the outputs and their ranges and name them

76

• Create the degree of fuzzy membership function for each input and output

• Construct the rule base that the system will operate under

• Decide how the action will be executed by assigning strengths to the rules

• Combine the rules and defuzzify literature the output

Figure 4.3 Input membership functions for iqs

77

Figure 4.4 Input membership functions for diqs

Table 4.2 shows the membership function names and ranges of input

variable stator quadrature current iqs. Here Seven triangular membership

functions were used and ranges between -1 to +1. The triangular membership

function is simple and easy to implement. Figure 4.3 represents the input

membership function for stator quadrature current iqs. The range of membership

function shows that the maximum possible normalised current is +1 and

78

minimum is -1. This range is possible for controlling the speed of the motor.

From many literature the seven membership function is the suitable choice of

selection.

Similarly for the other input, stator change in quadrature current diqs is

chosen. Table 4.3 shows the membership function names and ranges of input

variable change in stator quadrature current diqs.The membership function range

for change in error is maximum +2 and minimum is -2. Change in current is the

difference between present current and previous current. Figure 4.4 represents

the input membership function for Change in current.

Table 4.3 Specifications for the input variable diqs

Linguistic variable for diqs


Negative Big NB [-2.666 -2 -1.333]

Negative Medium NM [-2 -1.333 -0.6672]


Zero Z [-0.6672 0 0.6668]


Positive Medium PM [0.6668 1.333 2]

Positive Big PB [1.333 2 2.66]

79

Likewise the membership function is chosen for the output variable

reference stator quadrature current iq*. Table 4.4 shows the membership function

names and ranges of output variable reference stator quadrature current iqs*.

Figure 4.5 represents the output membership function for reference stator

quadrature current iq*. The rule viewer and surface viewer of the designed Fuzzy

Logic Controller are shown in Figures 4.6 and 4.7 respectively.

Table 4.4 Specifications for the output variable iq*

Linguistic variable for iq*


Negative Very Big NVB [-1.25 -1 -0.75]

Negative Big NB [-1 -0.75 -0.5]

Negative Medium NM [-0.75 -0.5 -0.2498]


Zero ZE [-0.2498 0 0.2504]


Positive Medium PM [0.2504 0.5 0.7504]

Positive Big PB [0.5 0.7504 1]

Positive Very Big PVB [0.7504 1 1.25]

80

Figure 4.5 Output membership function for iq

*

Figure 4.6 Rule viewer of FLC

81

Figure 4.7 Surface viewer of FLC

4.3 SIMULATION OF THE SYSTEM WITH STATOR SIDE FLC

AND ROTOR SIDE PID CONTROLLER

The complete simulation model of the wound rotor induction motor

with Fuzzy Logic Controller on stator side and PID controller on rotor side is

given in Figure 4.8. The fuzzy logic controller block from fuzzy logic toolbox is

used to test and evaluate the Fuzzy Logic Controller. At every sampling interval,

the reference speed and actual speed are used to calculate the error signals. This

error is converted into iqs and diqs act as the inputs to the Fuzzy Logic Controller.

82

Figure 4.8 Simulink Model of WRIM with FLC on stator side and

PID controller on rotor side

The closed loop simulation using fuzzy logic controller on stator side

and PID controller on rotor side is carried out using MATLAB/Simulink

software. The fuzzy set parameters instruction and function blocks available in

MATLAB are used to update the new switching frequency of the pulse

generators. The entire system is simulated with a switching frequency of 100

kHz. The stator side Fuzzy controller changes the Modulation Index according to

the actual speed and reference speed which is given to the PWM unit. The PWM

generates and produces the three phase pulses which are given to the stator side

inverter switches, there by the stator side inverter varies the stator supply

voltage.

83

The rotor side PID controller changes the modulation index of the rotor

side inverter according to actual speed and reference speed. Furthermore the

rotor side inverter varies the rotor voltage.

The Structure of the stator side fuzzy logic controller using

MATLAB/Simulink is shown in Figure 4.9. The sequencing control action of

fuzzy logic controller on stator side of WRIM is shown in Figure 4.10 as flow

diagram.

Figure 4.9 Structure of FLC with MATLAB for stator side inverter

The reference quadrature current id* is calculated from mutual

inductance Lm, rotor flux r and the reference flux ref*. It can be expressed as

given in equation (4.3) and (4.4).

m

rd L

i*

* (4.3)

Where,

Lm=69.31 mH

rrefr **

84

Figure 4.10 Fuzzy Controller Flow Diagram

85

Here the rotor flux can be calculated from direct axis current and motor

specifications,

)1( sT

iLr

dmr

(4.4)

where, r

rr R

LT

Lr = Li’r + Lm

Lr = 0.8+69.31

and Rr = 0.816 ohms, the simulink blocks for calculation of id* are shown in

Figure 4.11.

Figure 4.11 Simulink blocks for current id*calculation

4.3.1 Results and Discussions for Speed Change with Constant Load

The designed Fuzzy Logic controller for stator side inverter and

conventional PID controller for rotor side inverter are tested to run with load.

The speed response, deflecting torque, three phase stator currents, stator line

86

voltage, stator d-q currents, three phase rotor currents and rotor d-q currents are

the parameters taken for analysis. The results are shown for the closed loop

stator side FLC and rotor side PID based controller. The specification of WRIM

motor used for simulation is given in Table 2.4 in section 2.5. It is observed that

the stator side FLC and rotor side PID based control of WRIM gives the speed

response with quick settling time compared to both side PID controller and one

side (either stator or rotor side) PID with other side open loop (no controller)

control system.

Figure 4.12 Speed response for the step change in speed from

100 rad/s to 200 rad/s with 50% of full load

Figure 4.12 shows the speed response of wound rotor induction motor

with 50% of full load for the step change in speed from 100 rad/s to 200 rad/s at

87

0.3 s. The action of fuzzy logic controller on stator side reduces the speed

overshoot more effectively. The simultaneous action of FLC and PID controllers

on stator side and rotor side respectively improves both transient and steady state

performances. The transient and steady state performances with respect to speed

response for 50% load torque are given in Table 4.5 for step change in speed.

Figure 4.13 Deflecting Torque response for the step change in speed

from 100 rad/s to 200 rad/s with 50% load torque

The deflecting torque variations corresponding to step change in speed

is shown in Figure 4.13. The stator side FLC and rotor side PID controller

induces small distortion in deflecting torque during step change in speed.

88

Table 4.5 Transient and steady state Performances

with respect to speed response

Parameter Transition from

0 to 100 rad/s

Transition from

100 to 200 rad/s

Rise time 0.10 s 0.10 s

Settling time 0.18 s 0.20 s

Peak over shoot NIL NIL

Steady state Error 2.85% 2.80%

Figure 4.14 Three phase stator current with respect to time response for step change in speed with 50% of full load

The variations of three phase stator current of WRIM for 50% load are

shown in Figure 4.14. It is seen that the stator current is pure sinusoidal form

89

without any harmonics. This reduces the motor iron loss. The frequency of

current for higher speed is more than that of lower speed. The peak over shoot

occurs at the instant of speed change. This fuzzy logic controller on stator side

and PID controller on rotor side of wound rotor induction motor reduce the

settling time.

Figure 4.15 Stator d-q current with respect to time response for

step change in speed with 50% of full load

The Stator d-q current response of stator side fuzzy logic and rotor side

PID controlled WRIM with respect to time is shown in Figure 4.15 for 50%

load. It can be seen from the figure that the steady state d-q current response is

smooth for double side controller. Figure 4.16 shows the stator voltage for the

set speed of 100 rad/s with 50% load and the stator d-q voltage wave forms are

shown in Figure 4.17.

90

Figure 4.16 Stator voltage with respect to time response for 50% load

Figure 4.17 Stator d-q voltage with respect to time response for step change in speed with 50% load

91

Figure 4.18 Three phase rotor current with respect to time response

for step change in speed with 50% of full load

Figure 4.18 shows the variations of three phase rotor current for the

step change in speed from 100 rad/s to 200 rad/s at 0.3 s with 50% of full load.

The double side controller gives good steady state and transient performances.

Figures 4.19 and 4.20 present the d-q rotor current and voltage response for step

change in speed with stator side FLC and rotor side PID controller for 50% load.

It can be seen from the rotor current and voltage wave forms that they also have

minimum overshoot at the time of speed change.

92

Figure 4.19 Rotor d-q current with respect to time response for

step change in speed with 50% load

Figure 4.20 Rotor d-q voltage with respect to time response for


93

The Fuzzy logic and PID controller on stator and rotor side gives superior

transient behavior of speed response than the other combination of controllers. It

is found that the speed control with Fuzzy logic controller on stator sides and

PID controller on rotor side gives better response even as the set speed is

changed. It can be seen that the speed responses are good accuracy. It is showing

a good tracking performance of the controller.

4.3.2 Results and Discussions for Load change with constant speed

Figure 4.21 Speed response for step change in load from

50% to 75% of full load at 0.3 s

94


with the reference speed of 100 rad/s for the step change in load from 50% to

75% of full load at 0.3 s. The action of fuzzy logic controller on stator side

reduces the speed overshoot more effectively. The simultaneous action of FLC

and PID controllers on stator side and rotor side respectively improves both

transient and steady state performances. In the steady state operation, when the

load is raised from 50% to 75% at 0.3 s the speed drops 8% and it resumes its

actual set speed after 0.2 s. The corresponding deflecting torque, stator voltage,

three phase stator current, stator d-q current, stator d-q voltage, three phase rotor

current, rotor d-q current and d-q voltage wave forms are shown in Figures 4.22

to 4.29.

Figure 4.22 Deflecting Torque response for step change in load

from 50% to 75% of full load at 0.3 s

95

Figure 4.23 Stator voltage with respect to time response

Figure 4.24 Three phase stator current with respect to time response

for step change in load from 50% to 75% of full load at 0.3 s

96


step change in load from 50% to 75% of full load at 0.3 s

Figure 4.26 Stator d-q voltages with respect to time response for


97





98

Figure 4.29 Rotor Voltage with respect to time response for


4.4 SIMULATION OF THE SYSTEM WITH STATOR SIDE PID

CONTROLLER AND ROTOR SIDE FLC

The complete simulation model of the wound rotor induction motor

with Fuzzy Logic Controller on rotor side and PID controller on stator side is

given in Figure 4.30.

99

Figure 4.30 Simulink Model of WRIM with FLC on rotor side and

PID controller on stator side

The designed Fuzzy Logic controller for rotor side inverter and

conventional PID controller for stator side inverter are tested to run with load.

The speed response, deflecting torque, three phase stator currents, stator line

voltage, stator d-q currents, three phase rotor currents and rotor d-q currents are

the parameters taken for analysis. The results are shown for the closed loop rator

side FLC and stator side PID based controller. The specification of WRIM motor

used for simulation is given in Table 2.4 in section 2.5.

100

4.4.1 Results and Discussions for Speed Change with Constant Load


with 50% of full load for the step change in speed from 100 rad/s to 200 rad/s at

0.5 s. The action of fuzzy logic controller on stator side reduces the speed

overshoot more effectively. The simultaneous action of FLC and PID controllers

on rotor side and stator side respectively improves both transient and steady state

performances. The transient and steady state performances with respect to speed

response for 50% load torque are given in Table 4.6 for step change in speed.

Figure 4.31 Speed response for the step change in speed from

100 rad/s to 200 rad/s with 50% of full load

The deflecting torque variations corresponding to step change in speed

is shown in Figure 4.32. The stator side FLC and rotor side PID controller

induces small distortion in deflecting torque during step change in speed. Figure

4.33 shows the stator voltage for the set change in speed with 50% load and the

expanded view of stator voltage wave form during speed change is shown in

Figure 4.34.

101

Table 4.6 Transient and steady state Performances with respect to speed response

Parameter Transition from

0 to 100 rad/s Transition from 100 to 200 rad/s

Rise time 0.11 s 0.11 s

Settling time 0.28 s 0.22 s

Peak over shoot NIL NIL

Steady state Error 3.00 % 4.00 %

Figure 4.32 Deflecting Torque response for the step change in speed from 100 rad/s to 200 rad/s with 50% load torque

102

Figure 4.33 Stator voltage with respect to time response for


Figure 4.34 Expanded view Stator voltage with respect to time

response during speed changes

103

Figure 4.35 Three phase stator current with respect to time response for step change in speed with 50% of full load

The variations of three phase stator current of WRIM for 50% load are

shown in Figure 4.35. It is seen that the stator current is pure sinusoidal form

without any harmonics. This reduces the motor iron loss. The frequency of

current for higher speed is more than that of lower speed. The peak over shoot

occurs at the instant of speed change. This fuzzy logic controller on rotor side

and PID controller on stator side of wound rotor induction motor increase the

steady state error.

The Stator d-q current response of rotor side fuzzy logic and stator

side PID controlled WRIM with respect to time is shown in Figure 4.36 for 50%

load. It can be seen from the figure that the steady state d-q current response is

smooth for double side controller. Figure 4.37 shows the stator d-q voltage wave

form.

104





105

Figure 4.38 Three phase rotor current with respect to time response for step

change in speed with 50% of full load

Figure 4.38 shows the variations of three phase rotor current for the

step change in speed from 100 rad/s to 200 rad/s at 0.5 s with 50% of full load.

The double side controller gives good steady state and transient performances.

Figures 4.39 and 4.40 present the d-q rotor current and voltage response for step

change in speed with rotor side FLC and stator side PID controller for 50%

load. It can be seen from the rotor current and voltage wave forms that they also

have minimum overshoot at the time of speed change.

106



Figure 4.40 Stator d-q voltage with respect to time response for


107

4.4.2 Results and Discussions for Load Change with Constant Speed


with the reference speed of 100 rad/s for the step change in load from 50% to

75% of full load at 0.5 s. The action of fuzzy logic controller on rotor side

reduces the speed overshoot more effectively. The simultaneous action of FLC

and PID controllers on rotor side and stator side respectively improves both

transient and steady state performances. In the steady state operation, when the

load is raised from 50% to 75% at 0.5 s the speed drops 8% and it resumes its

actual set speed after 0.2 s. The corresponding deflecting torque, stator voltage,

three phase stator current, stator d-q current, stator d-q voltage, three phase rotor

current, rotor d-q current and d-q voltage wave forms are shown in Figures 4.42

to 4.49.

Figure 4.41 Speed response for step change in load from

50% to 75% of full load at 0.5 s

108

Figure 4.42 Deflecting Torque response for step change in load

from 50% to 75% of full load at 0.5 s

Figure 4.43 Three phase stator current with respect to time response


109



Figure 4.45 Stator voltage with respect to time response

110





111



Figure 4.49 Rotor Voltage with respect to time response for


112

The performance of closed loop controller response for WRIM have

been estimated and provided in Table 4.7. It is seen that the Fuzzy based closed

loop controller provides better settling time. This ensures that the system can be

controlled effectively with feedback. The steady state error using Fuzzy logic

and PID controller combinations lies between 2.85% - 3.00%.

Table 4.7 Comparative analysis of speed response to various combinations

of controllers for speed change at constant load operation

Controller Rise

time (s) Settling time (s)

% Over shoot

Steady state error (%) Stator side Rotor side

PID No

controller 0.09 0.22 3.00 3.02

No

controller PID 0.06 0.315 11.00 2.95

PID PID 0.07 0.17 NIL 5.00

Fuzzy PID 0.10 0.18 NIL 2.85

PID Fuzzy 0.11 0.28 NIL 3.00

It is clear that the Fuzzy logic is eliminating the overshoot, and rise

time. It is found that the PID controller is ineffective in eliminating the

overshoot and reducing the rise time, settling time and steady state error. The

transient and steady state performance of the WRIM with PID controller, PID –

PID, Fuzzy – PID, PID – Fuzzy controller combinations are given in Table 4.7

113

and Table 4.8. It is seen that the settling time is very low when fuzzy logic

controller is used. Similarly the steady state error and rise time reduced with

FLC and PID controller combinations.

Table 4.8 Comparative analysis of speed response to various combinations

of controllers for load change at constant speed operation

Controller

Speed

drop (%)

Speed Recovery time (s)

Steady state error (%)

Stator side Rotor side Before Load

change

After Load change

PID No

controller 16 0.38 3.02 3.70

No

controller PID 15 0.40 2.95 3.85

PID PID 12 0.25 5.00 5.20

Fuzzy PID 8 0.2 2.85 3.00

PID Fuzzy 8 0.2 3.00 3.15

It is also clear that the PID controller on rotor side, PID - PID, PID –

Fuzzy are ineffective in eliminating the overshoot, rise time, settling and steady

state error. This may be due to the integrator which increases the system type

number, thus minimizing the steady state error. The additional phase delay

introduced by the integrator tends to slow down the response.

114

4.5 CONCLUSION

The performance of the Wound Rotor Induction Motor with closed

loop operation has been investigated. The detailed operation of various

controllers such as fuzzy logic controller was studied and analyzed. The transient

and steady state performance of WRIM was presented with FLC - PID

combination of controllers on stator and rotor sides. It has been concluded that

the PID controller was ineffective in eliminating the overshoot, rise time, settling

time and steady state error compared with Fuzzy logic controller.

chapter 4 performance estimation of wrim with...

Documents