SIMULATION AND CONTROL SYSTEM ANALYSIS

Transcription

1 CHAPTER FIVE SIMULATION AND CONTROL SYSTEM ANALYSIS 5.1 Simulation As a mathematical program, MATLAB 7.0 has a high accuracy and also enables user to create a simulation of a desired system. In this final project, a simulation which depicted the response of the Fuzzy based fuel control system was created using SIMULINK. SIMULINK is the tool for modeling, analyzing, and simulating mathematical and physical systems, including those with nonlinear elements and those that make use of continuous and discrete time. The basic concept of this simulation was to keep the N 1 RPM stabilize at around (set point). To describe the system in general, the user defined input, which was in the form N 1 RPM, would enter the Fuzzy Control System. The output of the Fuzzy Control System, which would be in the form of Fuel flow, would enter the simulated plant. The outcome from the simulated plant would be rooted back into the input port and serve as a feedback error signal. See Figure 5.1 for the schematic diagram of the simulation. 42

2 43 Figure 5.1 Fuzzy Control System Simulation Diagram

3 There are three sources of input for this control system. See Figure 5.2 for a better look on the input port. Figure 5.2 Input Port The first input was the Set Point of For this Set Point, a Constant block was used. This is to make sure that this is where the simulation starts. The second input was a random disturbance. This input was added in order to test the control systems response towards disturbance. In order to create this, a Uniform Random Number block was used. The block generated uniformly distributed random numbers over a specifiable interval with a specifiable starting seed. The third and last input was the feedback signal resulting from the plant. This input was added in order to given an error feedback towards the control system. 44

4 These three inputs were then combined using a Sum block. The Sum block performed addition or subtraction on these inputs according to user. In this control system, the sum of the set point and disturbance value was subtracted with the feedback signal and extreme value. The combined result was then delivered to the Fuzzy Control System. A MATLAB Function block was used to generate the Fuzzy Control System. The Fuzzy Control System was generated as a function in M-File and the MATLAB Function block applies the specified MATLAB function to the input. The output of the Fuzzy Control System, which is the fuel flow error, was then delivered as input for the plant. The following shows the M-File used to create the Fuzzy Control System: function flow=model6(errorrpm) a=newfis('model6'); a.input(1).name='errorrpm'; a.input(1).range=[ ]; a.input(1).mf(1).name='negsmall'; a.input(1).mf(1).type='trimf'; a.input(1).mf(1).params=[ ]; a.input(1).mf(2).name='zero'; a.input(1).mf(2).type='trimf'; a.input(1).mf(2).params=[ ] ; a.input(1).mf(3).name='possmall'; a.input(1).mf(3).type='trimf'; a.input(1).mf(3).params=[ ]; a.input(1).mf(4).name='neglarge'; a.input(1).mf(4).type='trapmf'; a.input(1).mf(4).params= [ ]; a.input(1).mf(5).name='poslarge'; a.input(1).mf(5).type='trapmf'; a.input(1).mf(5).params=[ ] ; a.output(1).name='flow'; a.output(1).range=[ ]; a.output(1).mf(1).name='low'; a.output(1).mf(1).type='trimf'; a.output(1).mf(1).params=[ ]; a.output(1).mf(2).name='stabil'; a.output(1).mf(2).type='trimf'; a.output(1).mf(2).params=[ ]; a.output(1).mf(3).name='high'; 45

5 a.output(1).mf(3).type='trimf'; a.output(1).mf(3).params=[ ]; a.output(1).mf(4).name='verylow'; a.output(1).mf(4).type='trapmf'; a.output(1).mf(4).params=[ ]; a.output(1).mf(5).name='veryhigh'; a.output(1).mf(5).type='trapmf'; a.output(1).mf(5).params=[ ]; a.rule(1).antecedent=[2]; a.rule(1).consequent=[2]; a.rule(1).weight=1; a.rule(1).connection=1; a.rule(2).antecedent=[1]; a.rule(2).consequent=[1]; a.rule(2).weight=1; a.rule(2).connection=1; a.rule(3).antecedent=[3]; a.rule(3).consequent=[3]; a.rule(3).weight=1; a.rule(3).connection=2; a.rule(4).antecedent=[4]; a.rule(4).consequent=[5]; a.rule(4).weight=1; a.rule(4).connection=1; a.rule(5).antecedent=[5]; a.rule(5).consequent=[4]; a.rule(5).weight=1; a.rule(5).connection=1; a.rule(6).antecedent=[3]; a.rule(6).consequent=[5]; a.rule(6).weight=1; a.rule(6).connection=2; flow = evalfis([errorrpm],a); Instead of going straight into the Plant, the Fuzzy output was combined with an initial value and a memory block. See Figure 5.3 for a better illustration. The initial value was added to make sure that the control system would start working when the fuel flow value was around 2.0. While the Memory block was added to prevent Algebraic Loop error, and also to add the previous input with the next output from the Fuzzy Control System. The combined result of the Fuzzy Control System output, initial value, and memory block output was then delivered into the Plant. 46

6 Figure 5.3 Fuzzy Control System. The Plant itself was a subsystem block dedicated to simulate the behavior of engine during stabilized condition. Inside this subsystem block was several constant value blocks and mathematical operation blocks which builds the mathematical equation to simulate the plant. See Figure 5.4 and 5.5 for a look of the Plant subsystem and the equation inside it. Figure 5.4 Plant Subsystem. 47

7 Figure 5.5 Equation Blocks Inside Plant Subsystem. The output of the plant will show how the system stabilized. Before entering the Sum block as a feedback signal, it passed through a memory block in order to eliminate Algebraic Loop error. Along the control system, some scope and display blocks were added in various places to show the outcome graphic and keeping track of the simulation. 5.2 Result And Analysis Simulation With No Disturbance Figure 5.6 (a) and 5.6(b) shows the result of the fuzzy control system for an ideal condition (no disturbance). With a set point of N 1 RPM, the system would stabilize at N 1 RPM on t= 640s. With a difference less then 1%, it can be said that the fuzzy control system worked well. During this condition, the fuel flow would also stabilize at 1.9 on t= 550s. However, the graph may seem to have some anomalies, since 48

8 it shows no rising time (the system reached stability right after t<0). This was caused because on this simulation, only the equation for the third plant was used. Since the third plant simulated the engine during stabilized condition, it was already expected that the system would reached stability right after it started working. Figure 5.6(a). Fuel Flow Figure 5.6(b) N 1 RPM 49

9 5.2.2 Periodic Disturbances. In this session, the disturbance was given periodically. The sample time in use was 1000s. Figure shows the control system s response if it was given disturbance of N 1 RPM with a sample time of N 1 RPM will stabilize around at t= 560 s. The fuel flow also showed similar response. It stabilized on approximately 1.95 at t= 527 s. The control system was able to maintain its stability and only showed very small oscillation in a short brief period every time the disturbance occurs. See figure 5.7 (a) and 5.7(b) to see the responses. Figure 5.7(a). Fuel Flow 50

10 Figure 5.7(b) N 1 RPM The system was able to maintain stability around these points if the disturbances were raised up to When given disturbance up to , the system was still able to stabilize, even though the oscillation appeared more often with bigger amplitude. During t=2000 s to t= 4500 s, oscillations occur at around RPM before finally stabilizing again at N 1 RPM. The fuel flow showed similar behavior before stabilizing at approximately See Figure 5.8(a) and 5.8(b) to see the systems response of given disturbance up to

11 Figure 5.8(a) Fuel Flow Figure 5.8(b) N 1 RPM The stable time for each disturbance stayed at around 400s<t<500s. But as the disturbances grew larger, the oscillation grew increasingly larger. The occurrence of these oscillations also became more often and lasted longer, but the system always 52

12 managed to stabilize afterwards. See Figure 5.9 for the chart of fuel flow using 1000s as sample time and increasing disturbance. Stable Time(s) Fuel Flow With Sample Time=1000s Disturbance(RPM) Figure 5.9 Fuel Flow With Sample Time =1000s Besides increasing the disturbance, an increased sample time was also applied to the system. A fix amount of disturbance of -200 to 200 was used in this test. Figure 5.10 shows the resulted chart. Figure 5.10 Result for Increased Sample Time 53

13 As it can be seen from the chart above, the system would reach its stability faster if the sample time was increased. Based on these results, it can be said that the control system worked well since it was able to handle large disturbances that comes periodically. Since large disturbance would most likely to occur periodically, it may be predicted that this system is stable enough to be applied in actual condition Continuous Disturbance. In the previous session, the disturbance was given periodically. In this session, the disturbance was given continuously, and we increase the disturbance size to test the system. On Figure 5.11(a) and 5.11(b), the system was given disturbance in the range of N 1 RPM with a continuous sample time. Figure 5.11(a). Fuel Flow 54

14 5.11(b). N 1 RPM It can be seen from the graphs that the control system was able to handle the disturbance. The N 1 RPM stabilized at approximately t= 560s and then oscillated around , before finally settling at near the end of the simulation. During this condition, the fuel flow also stabilized at approximately t =550s and continue to oscillate around The control system still showed a good result when the disturbance was increased to -50 to 50 RPM. Figure 5.12(a) and 5.12(b) showed the result of the control system. 55

15 Figure 5.12(a). Fuel Flow Figure 5.12(b) N 1 RPM The N 1 RPM still stabilized at around t=560s, and continue to oscillate around Meanwhile, the fuel flow also stabilized at approximately t= 550s, and continue to oscillate around The control system will maintain its stability around these points until the disturbance reached around -125 to 125 RPM. During this condition, the oscillation was increasingly 56

16 larger and the control system was starting to have difficulties maintaining stability. The N 1 RPM would seem to stabilize at t= 500s, but as the simulation goes on, it will suffer further disturbance starting since t=800s. The amplitude of the oscillation varied around RPM. The fuel flow also had the same behavior. See Figure 5.13(a) and 5.13(b) for the systems response. Figure.5.13(a) Fuel Flow Figure 5.13(b) N 1 RPM 57

17 Similar condition with an increasingly larger oscillation occurs when the disturbance was raised up to -150 to 150. At disturbance -175 to 175, the control system seems to no longer able to maintain its stability. Figure 5.12 shows the fuel flow stable time condition respectively to disturbance. As it can be seen from the chart, the stable time when the disturbances were at the range of -25 to 25 and -75 to 75 remained stable around t=550s. When the disturbances were raised up to -125 to 125, the stable time dropped to t= 510s. But even though the stable time became faster, the oscillation that occurs grew increasingly large. Stable Time(s) Fuel Flow With Continuous Disturbance Disturbance(RPM) Figure 5.14 Fuel Flow With Continuous Disturbance 58