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CHAPTER 5 SIMULATION RESULTS

Department of Electrical & Electronics Engineering 40 | P a g e VJIT-HYD

5 Simulation Results:

5.1 Introduction :

A proportional-integral controller (PI controller) is a generic control loop feedback

mechanism widely used in industrial control systems. A PI controller attempts to correct the

error between a measured process variable and a desired set point by calculating and then

outputting a corrective action that can adjust the process accordingly.

The PI controller calculation involves two parameters; the Proportional, the Integral

values. The Proportional value determines the reaction to the current error, the Integral

determines the reaction based on the sum of recent errors and the Derivative determines thereaction to the rate at which the error has been changing. The weighted sum of these three

actions is used to adjust the process via a control element such as the position of a control valve

or the power supply of a heating element. By "tuning" the three constants in the PI requirements.

The response of the controller can be described in terms of the controller algorithm the PI can

provide control action designed for specific process responsiveness of the controller to an error,

the degree to which the controller overshoots the set point and the degree of system oscillation.

5.2 PI controllers:

5.2.1 Proportional term:

The proportional term makes a change to the output that is proportional to the current

error value. The proportional response can be adjusted by multiplying the error by a constant Kp,

called the proportional gain.

The proportional term is given by :

P out = K p e(t) ( 4.1)

Where

Pout : Proportional output

Kp : Proportional Gain, a tuning parameter

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e : Error = SP PV

t : Time or instantaneous time (the present)

A high proportional gain results in a large change in the output for a given change in the

error. If the proportional gain is too high, the system can become unstable (See the section on

Loop Tuning) In contrast, a small gain results in a small output response to a large input error,

and a less responsive (or sensitive) controller. If the proportional gain is too low, the control

action may be too small when responding to system disturbances.

In the absence of disturbances pure proportional control will not settle at its target value,

but will retain a steady state error that is a function of the proportional gain and the process gain.

Despite the steady-state offset, both tuning theory and industrial practice indicate that it is the

proportional term that should contribute the bulk of the output change.

5.2.2 Integral term:

The contribution from the integral term is proportional to both the magnitude of the error

and the duration of the error. Summing the instantaneous error over time (integrating the error)

gives the accumulated offset that should have been corrected previously. The accumulated error

is then multiplied by the integral gain and added to the controller output. The magnitude of the

contribution of the integral term to the overall control action is determined by the integral gain,

K i.

The integral term is given by:

I out =K

Where

Iout : Integral outputK i : Integral Gain, a tuning parametere : Error = SP PV : Time in the past contributing to the integral response

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The integral term (when added to the proportional term) accelerates the movement of the

process towards set point and eliminates the residual steady-state error that occurs with a

proportional only controller. However, since the integral term is responding to accumulated

errors from the past, it can cause the present value to overshoot the set point value (cross over the

set point and then create a deviation in the other direction). For further notes regarding integral

gain tuning and controller stability, see the section on Loop Tuning .

The output from the three terms, the proportional, and the integral terms are summed to

calculate the output of the PI controller.

Fig:5.2.1 Discrete PI controller

First estimation is the equivalent of the proportional action of a PI controller. The integral

action of a PI controller can be thought of as gradually adjusting the output when it is almost

right. Derivative action can be thought of as making smaller and smaller changes as one gets

close to the right level and stopping when it is just right, rather than going too far. Making a

change that is too large when the error is small is equivalent to a high gain controller and will

lead to overshoot. If the controller were to repeatedly make changes.

Those were too large and repeatedly overshoot the target, this control loop would be

termed unstable and the output would oscillate around the set point in either a constant, a

growing or a decaying sinusoid. A human would not do this because we are adaptive controllers,

learning from the process history, but PI controllers do not have the ability to learn and must be

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set up correctly. Selecting the correct gains for effective control is known as tuning the

controller.

If a controller starts from a stable state at zero error (PV = SP), then further changes by the

controller will be in response to changes in other measured or unmeasured inputs to the process

that impact on the process, and hence on the PV. Variables that impact on the process other than

the MV are known as disturbances and generally controllers are used to reject disturbances

and/or implement set point changes.

In theory, a controller can be used to control any process which has a measurable output

(PV), a known ideal value for that output (SP) and an input to the process (MV) that will affect

the relevant PV. Controllers are used in industry to regulate temperature, pressure, flow rate,

chemical composition, level in a tank containing fluid, speed and practically every other variable

for which a measurement exists. Automobile cruise control is an example of a process outside of industry which utilizes automated control. K p: Proportional Gain - Larger K p typically means

faster response since the larger the error, the larger the feedback to compensate. An excessively

large proportional gain will lead to process instability. K i: Integral Gain Larger K i implies steady

state errors are eliminated quicker. The trade-off is larger overshoot: any negative error

integrated during transient response must be integrated away by positive error before we reach

steady state. K d: Derivative Gain - Larger K d decreases overshoot, but slows down transient

response and may lead to instability

5.2.3 Loop tuning:

If the PI controller parameters (the gains of the proportional, integral terms) are chosen

incorrectly, the controlled process input can be unstable, i.e. its output diverges, with or without

oscillation, and is limited only by saturation or mechanical breakage. Tuning a control loop is the

adjustment of its control parameters (gain/proportional band, integral gain/reset) to the optimum

values for the desired control response.

Some processes must not allow an overshoot of the process variable beyond the set point

if, for example, this would be unsafe. Other processes must minimize the energy expended in

reaching a new set point. Generally, stability of response (the reverse of instability) is required

and the process must not oscillate for any combination of process conditions and set points.

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If the system must remain online, one tuning method is to first set the I value to zero.

Increase the P until the output of the loop oscillates, and then the P should be left set to be

approximately half of that value for a "quarter amplitude decay" type response. Then increase I

until any offset is correct in sufficient time for the process. However too much I will cause

instability. Finally, increase D, if required, until the loop is acceptably quick to reach its

reference after a load disturbance. However too much D will cause excessive response and

overshoot. A fast PI loop tuning usually overshoots slightly to reach the set point more quickly;

however, some systems cannot accept overshoot, in which case a "critically damped" tune is

required, which will require a P setting significantly less than half that of the P setting causing

oscillation.

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5.2.4 Limitations of PI control

While PI controllers are applicable to many control problems, they can perform poorly

in some applications. PI controllers, when used alone, can give poor performance when the PI

loop gains must be reduced so that the control system does not overshoot, oscillate or "hunt"

about the control set point value. The control system performance can be improved by

combining the PI controller functionality with that of a Feed-Forward control output as described

in Control Theory. Any information or intelligence derived from the system state can be "fed

forward" or combined with the PI output to improve the overall system performance. The Feed-

Forward value alone can often provide a major portion of the controller output. The PI controller

can then be used to respond to whatever difference or "error" that remains between the controllerset point and the feedback value. Since the Feed-Forward output is not a function of the process

feedback, it can never cause the control system to oscillate, thus improving the system response

and stability.

Another problem faced with PI controllers is that they are linear. Thus, performance of PI

controllers in non-linear systems (such as HVAC systems) is variable. Often PI controllers are

enhanced through methods such as gain scheduling or fuzzy logic. Further practical application

issues can arise from instrumentation connected to the controller. A high enough sampling rate

and measurement precision and measurement accuracy (more relevant to FF and MPC).

A problem with the differential term is that small amounts of measurement or process

noise can cause large amounts of change in the output. Sometimes it is helpful to filter the

measurements, with a running average, also known as a low-pass filter. However, low-pass

filtering and derivative control cancel each other out, so reducing noise by instrumentation

means is a much better choice. Alternatively, the differential band can be turned off in most

systems with little loss of control. This is equivalent to using the PI controller as a PIDcontroller.

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5.3 Simulation:

5.3.1(a) Simulation Model of a Double Frequency Buck Converter.

Fig 5.3.1(a) simulation model of a double frequency buck converter

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5.3.1(b) simulation model of a high frequency buck converter:

Fig5.3.1 (b) simulation model of a high frequency buck converter

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5.3.1(C) simulation model of a low frequency buck converter:

Fig 5.3.1(c) simulation model of a low frequency buck converter

\

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5.3.1(D) Simulation model of a double frequency buck converter fed with dc motor

Fig 5.3.1(d) simulation model of a double frequency buck converter fed with dc motor

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5.3.1(e) Simulation result for double frequency buck converter fedwith dc motor

Fig : 5.3.1(e) Double frequency buck converter fed with dc motor outputarmature current ,eletromagentic torque ,speed wave forms

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5.3.2 Simulation result :

5.3.2(a) steady state response :

Fig 5.3.2.(b) output voltage steady state response comparison of the double frequency, single

high and low frequency buck converter .

Ripple voltage in double frequency buck converter = 5x vRipple voltage in single high frequency buck converter = 1x vRipple voltage in single low frequency buck converter = 1x v

The output voltage waveforms of various buck converters are shown in Fig. 7.in the above large

magnitudes denote that the low frequency buck converter output voltage in steady state. It can be

seen that the steady state performance of DF buck and that of single high-frequency buck

converter are almost the same.

DF

HF

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5.3.2(b) transient response when load is step up:

Fig 5.3.2.(b)output voltage transient response comparison on of the double frequency, single

high and low frequency buck converter when load is step up

Output voltage Transient response comparison of the double frequency, high frequency and low

frequency buck converter when load is increased from R to 2R as shown in above fig

4.3.2(b).transient response of the double frequency buck converter is same as the transient

response of the single high frequency buck converter.

Df

Lf

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5.3.2(c) transient response when load is step down:

Fig 5.3.2.(c): output voltage transient response comparison of the double frequency, single high

and low frequency buck converter when load is step down

Output voltage Transient response comparison of the double frequency, high frequency and

low frequency buck converter when load is decreased from 2R to R as shown in above fig

4.3.2(c). Transient response of the double frequency buck converter is same as the transient

response of the single high frequency buck converter. In single low frequency transient response

is increased.

Lf

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5.3.2(d) step change waveforms

Fig 5.3.2(c) step change waveforms of the double frequency buck converter, single high

frequency, and low frequency buck converter.

The above figure shows step change wave forms of the double frequency buck converter, single

high frequency, and low frequency buck converter. Load current is changes when load resistance

is reduced from 4 to 2 . Then the load current will increase from 0.5 IR to IR. (2.5 to 5A).as

shown in above figure.

.

Df

Hf

Lf

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5.3.2(e) switching states of the switches(S, S d, S a)

Fig 5.3.2(e) switching states of the high frequency buck cell switches(S, S d),and low frequency

switch S a of the double frequency buck converter.

The above figure shows the switching states of the high frequency buck cell switches (S,

Sd), and low frequency switch S a of the double frequency buck converter. That shows high

frequency is 10 times of the low frequency. Where S a is the low frequency switch and its

switching frequency is 10khz, and S, S d are the high frequency switch and its switchingfrequency is 100khz.

Sd

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Fig 5.3.2(a): Switch current waveforms .

The current waveforms are shown in Fig. 4.3.2(a). The waveform with large magnitude

denotes the current flowing through the low-frequency switch i sa, and the small magnitude is the

current of the high-frequency switch i s. The load is changed from 4 to 2 at the 12-ms time

instant. A major portion of the increased load current (shown in Fig. 4.3.2) is diverted to the low-

frequency buck cell, while the current through the high-frequency switch remains the same. The

current diversion enables the reduction of switching loss in high-frequency buck cell and

improves the efficiency .

5.4 Efficiency Analysis:

In order to analyze the efficiency improvement of the proposed Double Frequency

buck converter, the efficiency expression is analyzed in the section. The analysis is also appliedto the single high frequency buck and low-frequency buck converters.

A simple loss model is adopted here in that we just want to show the efficiency relationship

between the DF buck and single high-frequency buck, not to develop a new loss model

In the analysis, we have the following assumptions;

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1. The conduction losses of active switch and diode are estimated, respectively,

according to their conduction voltages U on and U F.

2. The switching transient processes are assumed to satisfy the linear current and

voltage waveforms. Moreover, the turn-on time ton is the same for all switches and

diodes, so is the turn-off time t off .

3. Since the switching loss usually dominates the total loss, losses of the output

capacitor and output inductor are not calculated here.

In a single-frequency buck converter, the total loss P SF comes from four parts, the

conduction loss P scon and switching loss P ss of the active switch S , and the conduction loss P dcon

and switching loss P sd of the diode. When the input voltage is U in, duty ratio is D, the inductor

average current is I L, and the switching frequency is fs, the losses can be estimated according to

the following equations.

4.4.1(a)

4.4.1(b)

4.4.1(c)

4.4.1(b)

For single-frequency buck converter, the conduction losses are the same; the difference ison the switching frequencies f h and f l . For DF buck, the losses consist of two portions: highfrequency cell losses and low-frequency cell losses. The current chopped by the high-frequencycell is the difference between high-frequency inductor current i L and low-frequency inductorcurrent i La . This difference is roughly equal to 0.5 I Lapk , where I Lapk is the peak peak low-

frequency inductor current ripple, because the inductor current ripple of the high-frequency cellis small compared with that of the low-frequency cell. Moreover, the average current in low-frequency inductor is I L 0.5 I Lapk with the peak current control. The loss break down can beexpressed as follows:

The losses in the high-frequency cell are,

4.4.2(a)

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D t t f El t i l & El t i E i i 59 | P

4.4.2(b)

4.4.2(c) 4.4.2(d)

The losses in the low-frequency cell include,

4.4.3(a) 4.4.3(b)

( ) 4.4.3(c) 4.4.3(d)

Then, from (24) (26), the total conduction loss P conDF in the DF buck is approximately the

same as that in the single frequency buck converter,

4.4.4

In the case the low-frequency inductor current is small with reference to the inductor average

current, the total switching loss P sDF can be approximated as,

4.4.5

It follows from (4.4.2) (4.4.5) that the total conduction loss of DF buck converter is the

same as the single-frequency buck conductor. This result also can be reasoned from the fact that

the total currents owing through the DF buck switches and diodes are the same as that through a

single-frequency buck. On the other hand, the total switching loss is nearly the same as the single

low-frequency buck, and is much smaller than that of the single high-frequency buck. Hence, the

DF buck converter improves the efficiency by current diversion to the low-frequency cell.Although assumptions and approximations are made in the aforementioned analysis, it reveals

the efficiency mechanism of the DF buck converter.

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