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A human brachial artery system prototype controller calibration (static model).

1 INTRODUCTION

Cardiovascular disease (CVD) involves heart and/or blood vessels. This is typically caused by impeded supply of blood to brain, heart or leg muscles [1]. Ischemic heart disease, congestive heart failure, stroke and acute myocardial infarction are typical examples of cardiovascular disease. This is the leading cause of morbidity and mortality in many developed and developing countries of the world [1]. Studies have proved that cardiovascular disease causes a heavy burden on society in terms of disability, illness and financial cost. In Australia, one in six people suffers from cardiovascular disease that costs $14.2 billion dollars to the economy a year [2]. In 2008, CVD caused 34% of all deaths in Australia while approximately 800,000 people with CVD experienced disability [3]. In United Stated of America, approximately 70 million people suffer from this disease costing billions of dollars to the economy every year [4]. By the time cardiovascular disease is detected using existing technologies such as magnetic resonance imaging, angiography, ultrasound, X-ray computed tomography and pulse wave velocity measurement, the underlying cause (atherosclerosis) is usually in a complicated stage [5]. Major constraints such as excessive cost, inaccuracy and necessity of large equipments also exist for available detection technologies. Thus, a large portion of cardiovascular patients is currently undiagnosed, misdiagnosed or mistreated [5]. Approximately 80% of CVD deaths occur in low and middle income countries in the world [6]. Despite of all the efforts, approximately 92% of Australian adults possess at least one CVD risk factor and nearly 40% possess three or more CVD risk factors [7]. Thus a local biomedical engineering company has recently developed an inexpensive, precise and user-friendly device to detect arterial stiffness. Quality, consistency and performance are the three most significant features of this device. This developed device differs from currently available innovations as it focuses on the complete engineering process in an innovative manner. To verify the legitimacy of the formulated detection process, a significance of fabrication of human brachial artery system prototype is the paramount.

Section II of this paper presents information of designed prototype [8]. Section III presents details of utilized controller design and tuning technologies with verification strategies with respect to a static model. The conclusion fragment summarizes key findings with suggestion of future work.

2 DESIGN OF PROTOTYPE

After performing comprehensive theoretical research, numerical modeling and experimentations, prototype model illustrated in Fig. 1 was devised in this paper.

[FIGURE 1 OMITTED]

In the designed prototype, a pump was incorporated to lift fluid from the reservoir. The pump also supplied the required base pressure. The flow rate and performance characteristics of the pump were directed by voltage variations. Afterwards, a closed tank was integrated to store fluid before directing to the tested brachial artery. The tank removed fluctuations generated by the pump. Subsequently, a shaker provided the obligatory fluctuations on the peak of the base pressure. The characteristics of the shaker were also regulated by voltage variations. The pressure sensor was incorporated in the network to monitor accessible pressure level. The information was sent to multiple controllers built in LabVIEW Software where the difference between the required pressure and the available pressure was analyzed [9-13]. Then based upon the analysis results, feedback signals were directed to the pump and the shaker via data acquisition cards and electronic amplifiers [14-19]. The design was finalized after extensive experiments as this was relatively uncomplicated, consistent and reasonably priced with precise components.

3 FINE TUNING OF CONTROLLER PARAMETERS

The procedure of selecting the controller parameters to analyze and control any physical process is known as controller tuning [20-21]. A properly tuned controller offers the followings: (i) Minimized energy cost, (ii) Reduced process variability, (iii) Maximized efficiency and (iv) Increased production rate. In this paper, the following requirements were specified for the prototype controller: (i) Minimum overshoot, (ii) Minimum settling time and (iii) Zero steady state error. P, I and D values for the PID (Proportional-Integral-Derivative) controllers were identified for a static system. Thus, the investigation was performed in a state where the relative positions of subsystems were considered non-variant over time or where components and structures were considered at rest under the action of external forces of equilibrium [22-24]. Since a linear system was constructed, two prime mechanisms (pump and shaker) were considered autonomously for the determinism of P, I and D values. At the concluding stage, the controller values were united to identify the overall performance of the complete system [25-28]. Thus, the following configurations were analyzed:

(3.1) System with Pump and without Shaker

(3.2) System with Shaker and without Pump

(3.3) Complete System with Pump and Shaker

3.1 System with Pump and without Shaker

A closed loop Simulink block diagram was constructed in this section as shown in Fig. 2. In the designed Simulink diagram, "Analog Filter" signified the low pass filter for pump. Afterwards, "PID Controller" block showed the controller used to control the characteristics of the pump. Then "TF for motor" represented the transfer function of the motor section of the pump. Subsequently, "Gain for pump" signified the relationship that was used to represent the rest of the pump. This gain transferred the output speed from motor to the pressure output from pump. Next, "Gain for Tank" corresponded to the tank that solved oscillation problem created by the pump. The block named "Gain for BA" characterized the tested brachial artery. Finally, "Gain for sensor" symbolized the pressure sensor that was used to measure the achieved pressure level in the system.

[FIGURE 2 OMITTED]

3.1.1 Ziegler - Nichols first tuning method

The Ziegler - Nichols tuning methods are heuristic techniques for tuning PID controllers [29]. The first tuning method is an open loop technique, which means we needed to define an open loop transfer function (OLTF) of the system in the following form:

OLTF = 141.1/0.00016[s.sup.3] + 0.01168[s.sup.2] + 0.1058s + 0.0501

The open loop system was tested using a step input and the following response was achieved:

[FIGURE 3 OMITTED]

As depicted in the above figure, a tangent line was drawn at the inflection point of the nearly "S-shaped" curve known as the reaction curve. Afterwards, a delay time L, as well as a time constant T, were determined from the graph as: L = 0.6sec, T = 4.1sec. This was noted that the open loop method or Ziegler - Nichols first tuning method depended on determination of the L and T constants in a manual manner from the open loop transfer function graph of the designed system. Thus there were always some risks of a human error which could alter the accurateness of the determined values. Table 1 shows Ziegler-Nichols first tuning rule:

Afterwards controller values were calculated and placed in the table below:

The response demonstrated in Fig. 4 was obtained for P controller.

[FIGURE 4 OMITTED]

The response demonstrated in Fig. 5 was obtained for PI controller.

[FIGURE 5 OMITTED]

The response demonstrated in Fig. 6 was obtained for PID controller.

[FIGURE 6 OMITTED]

So, this was concluded from simulation results that satisfactory performance of the system could not be reached using calculated controller values. This was also noted that the first tuning method was only suitable for simple systems without any integrator or dominant complex conjugate poles in open loop transfer function [29]. Therefore, the cause of unsatisfactory behaviour became evident.

3.1.2 Ziegler-Nichols second tuning method

Ziegler-Nichols second tuning method is based on the closed loop response of the system [29]. Because this technique allows fluctuations in the process variable as long as each successive peak is not more than the size of one-fourth of its predecessor, additional tweaking of parameters may be required. The closed loop system depicted in Fig.7 was designed incorporating open loop transfer function (OLTF) obtained from previous section.

[FIGURE 7 OMITTED]

According to this method, only P controller had to be used while setting derivative time constant ([T.sub.d]) as zero and integral time constant ([T.sub.i]) as infinity. The gain ([K.sub.u]) that caused sustained oscillation, as well as the period of oscillation ([P.sub.u]), had to be recorded and used for calculating controller's parameters [29]. Table 3 shows Ziegler-Nichols second tuning rule using [K.sub.u] and [P.sub.u] values and Table 4 denotes the determined values:

Due to proportional controller, response shown in Fig. 8 was obtained.

[FIGURE 8 OMITTED]

This was evident from the response graph that there was always error present in the system because the proportional controller could not completely remove the steady state error. However, there was no overshoot in the system and the output settled down within a reasonable period of time as well.

The following response was obtained for PI controller:

[FIGURE 9 OMITTED]

It was concluded from obtained simulation graph that the steady state error was cancelled by the integral component of the controller. However, integral component added oscillation in the system which increased the overshoot. So, the output took longer to settle down.

The satisfactory response demonstrated in Fig. 10 was obtained for PID controller. Thus, this was selected as the controller for pump.

[FIGURE 10 OMITTED]

3.2 System with Shaker and without Pump

For shaker, the following Simulink block diagram was developed:

[FIGURE 11 OMITTED]

In the above block diagram, "Analog Filter" symbolized the analogue high pass filter for the shaker. "PID Controller" represented the controller that was used to control the fluctuations produced by the shaker. Afterwards, "Gain for shaker" signified the physical structure of the shaker itself. Subsequently, "Gain for BA" symbolized the tested brachial artery and "Gain for sensor" represented the pressure sensor. For this system, the open loop transfer function (OLTF) was calculated as:

OLTF = 1492s/0.16s + 1

The following block diagram was designed for simulation incorporating the open loop transfer function:

[FIGURE 12 OMITTED]

Subsequently, the designed closed loop system was tested using various controller parameters as stated underneath:

(i) Proportional gain constant, [K.sub.P] = 1

(ii) Integral gain constant, [K.sub.i] = 1

(iii) Derivative gain constant, [K.sub.d] =0

For the above controller parameters, the subsequent response was obtained:

[FIGURE 13 OMITTED]

(i) Proportional gain constant, [K.sub.P] = 5

(ii) Integral gain constant, [K.sub.i] = 5

(iii) Derivative gain constant, [K.sub.d] = 0

For the stated controller parameters, the subsequent response was obtained:

[FIGURE 14 OMITTED]

(i) Proportional gain constant, [K.sub.P] = 0.5

(ii) Integral gain constant, [K.sub.i] = 1

(iii) Derivative gain constant, [K.sub.d] = 1

For the above controller parameters, the subsequent response was obtained:

[FIGURE 15 OMITTED]

Thus, it became evident from simulation analysis that the system would never become unstable or would never provide the required "S" shape. Therefore, it was not possible to utilize any of the Zeigler-Nichols methods, because it was impossible to achieve critical gain, delay time and other necessary parameters for defining P, I and D controllers. For this reason, a pole placement method was utilized to place the closed loop poles in pre-determined locations in s-plane. In the designed linear system, poles influenced system response, band width, transient response and stability [29].

3.2.1 Pole placement method

According to Fig. 12, two transfer functions were utilized to find the overall transfer function of the system. Thus, transfer function for the PID controller was defined as:

PID Controller = [K.sub.d][s.sup.2] + [K.sub.p]s + [K.sub.i]/s

So, after rearranging, the closed loop transfer function (CLTF) of the overall system was defined as:

CLTF = 1492 ([K.sub.d][s.sup.2] + [K.sub.P]s + [K.sub.i])/1492[K.sub.d][s.sup.2] + (1492[K.sub.P] + 0.16)s + (1492[K.sub.i] + 1)

The characteristic equation of the system was defined:

1492[K.sub.d][s.sup.2] + (1492[K.sub.p] + 0.16)s + (1492[K.sub.i] + 1) = 0 (1)

The major intention of determining the P, I and D values was to accomplish the fastest non-oscillatory response with a zero steady state error. To achieve this goal, it was required to have double real poles, because this would provide the fastest non-oscillatory response. From the open loop transfer function (OLTF) of the designed system, poles were calculated using MATLAB Software as following:
num = [14 92, 0];
den = [0.16, 1];
roots (den)
ans = -6.2500


Therefore, based upon the results, the desired characteristic equation of the system was defined:

(s + 6.25)(s + 6.25) = 0 [much greater than] s2 + 12.5s + 39.06 = 0 (2)

By comparing (1) and (2), the controller's parameters were determined as stated below:

(1) Proportional gain constant, [K.sub.p] = 0.0083

(2) Integral gain constant, [K.sub.i] = 0.0255

(3) Derivative gain constant, [K.sub.d] = 0.00067

Note: As Kdvalue was very close to zero, this value was neglected in the controller as it had a relatively insignificant influence. Therefore, only PI controller was used for the shaker. By using these calculated parameters, the response depicted in Fig. 16 was obtained from simulation analysis due to unit step input.

[FIGURE 16 OMITTED]

Therefore, it was clear from the response graph that the PI controller offered the best response in terms of overshoot, settling time and steady state error for designed system.

3.3 Complete System with Pump and Shaker

At the concluding stage, the combined system demonstrated in Fig. 17 was fabricated for simulation purposes.

[FIGURE 17 OMITTED]

The following P, I and D controller values obtained from previous sections were used for pump and shaker respectively in analysis:

The responses demonstrated in Fig. 18, 19 and 20 were obtained for unit step, ramp and sine functions respectively.

[FIGURE 18 OMITTED]

[FIGURE 19 OMITTED]

[FIGURE 20 OMITTED]

So, the simulation graphs proved the appropriateness of the calculated controller parameter values.

4 CONCLUSION

The proper artistic response to the recently developed arterial stiffness detection technology is to embrace it as a new window of opportunity and to apply it with passion, wisdom, fearlessness and delight. A prototype has been designed to verify the authenticity of the formulated technology. This paper presents detailed information about design and tuning methods with validation tactics that have been utilized for prototype controller in consideration of a static model. It has been concluded from obtained simulation results that the determined controller parameter values are more than satisfactory for typical test inputs. A further work will take place with respect to a dynamic model in future.

ACKNOWLEDGMENT

The authors would like to acknowledge Professor Adnan Al Anbuky, Engineer Shajib Khadem and Dr. Tek Tjing Lie for their help and contribution in developing this research paper.

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Shahariar Kabir, Nenad Popovich

School of Electrical, Electronic and Computer Engineering, University of Western Australia, School of Engineering, Auckland University of Technology,

mohkab29@smail.com, nenad.popovich@aut.ac.nz
Table 1. Table of Ziegler-Nichols
first tuning rule [29]

Controller    [K.sub.P]     [T.sub.i]     [T.sub.d]

P             T/L           [infinity]    0
PI            0.9 T/L       L/0.3         0
PID           1.2 T/L       2L            0.5L

Table 2. Table of calculated controller values

Controller    [K.sub.P]     [T.sub.i]     [T.sub.d]

P             6.833         [infinity]    0
PI            6.15          2             0
PID           8.2           1.2           0.3

Table 3. Table of Ziegler-Nichols
second tuning rule [29]

Controller    [K.sub.p]       [T.sub.i]         [T.sub.d]

P             [0.5K.sub.u]    [infinity]        0
PI            [0.45K.sub.u]   1/1.2 [P.sub.u]   0
PID           [0.6K.sub.u]    0.5Pu             0.125[P.sub.u]

Table 4. Table of calculated controller values

Controller  [K.sub.P]  [T.sub.i]   [T.sub.d]

P           0.005      [infinity]  0
PI          0.0045     0.833       0
PID         0.006      0.5         0.125

Table 5. Table of calculated controller values for pump

Controller   Value

P            0.006
I            0.003
D            0.00075

Table 6. Table of calculated values for shaker

Controller   Value

P            0.0083
I            0.0255
D            0
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Author:Kabir, Shahariar; Popovich, Nenad
Publication:International Journal of Emerging Sciences
Article Type:Report
Geographic Code:8AUST
Date:Dec 1, 2011
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