Engineering and Construction: The MATLAB Code - Essay Example

 Engineering And Construction: The MATLAB Code 1.3 Solution Description 15 marks The MATLAB Code was used to estimate the critical gain value (Kcr) by looping through a range of K values from 1 to 50,000 in steps of 1. The existence of a pole in either the positive region or 0 made it stop the looping. The K values were generated, which presented the output of poles. The formula below is the procedure used The procedure through which the MATLAB stopped looping when it found a positive pole value is displayed by the MATLAB ‘if’ statement. if max(r) >= 0, % if the maximum number of the poles was greater or equal to one, then the Kc value would poles % equal the current K value in the loop. K=K(n) break end Another procedure was run to calculate the precise value for Kcr. The past computed value of Kcr was utilized by MATLAB by running it through a similar loop but, between Kcr -1 and Kcr + 1. The procedure was undertaken in steps of 0.0005. Below is the value of Kcr found. 1.4 Test Results 10 marks Table 1: Poles and stability for a given gain K (experiment 1) 1.5 Discussion & Conclusions Q1: What did your results show as the region of stability? As found in the outcomes, when K is not exactly its basic worth, (I.e., when K= Kcr - 50), the framework is steady. This is on the grounds that there are no genuine positive poles. It was clarified before that all together for a framework to be in the steady express; all the genuine shafts must be in the negative locale. At the point when K levels with its discriminating quality (I.e., when K = Kcr), the framework was sensibly steady. There were genuine poles on the zero point, and that is the reason the framework was not totally stable. As presented in Figure1.4.3, the frameworks wavered however it stayed reliable and in this way it was steady. At the point when K was more prominent than the frameworks increase discriminating quality Kcr, the framework was unsteady. This is on account of there were genuine poles in the positive area. Q2: Describe the poles and step response for gains less than, equal to, and greater than the critical gain. Relate your observations to definitions for stability. Figure1.4.1 shows that the framework is steady, however with extensive settling time and starting motions yet does get to an unfaltering state and along these lines is steady. A steady framework can be known when every bounded input generates a bounded input – when closed-loop transfer function poles are in the left half-plane. Figure1.4.3 shows that the value of (K) is equivalent to the framework’s critical value, the stride reaction was a consistent swaying. The System was hardly steady as the framework sways however the motions were neither expanding nor diminishing. The framework likewise demonstrated an awesome unfaltering state slip in the stride reaction. The figure1.4.4 shows 2 genuine poles on the zero pivot that demonstrates that the quality of basic increase was ascertained effectively. Figure1.4.5 shows that the framework is flimsy. A framework is temperamental if an aggregate reaction is unbounded; no less than one pole of The closed-loop transfer function is in the right half-plane. The graphical plot of poles exhibited that no less than one genuine value of pole is in the positive/right half plane. It is difficult to see that the post is in the positive half, however as found in the outcomes table, it is demonstrated that the genuine pole is in a positive locale with an estimation of 0.0011. Q3: What does the pole map tell you about the change in pole/zero locations as K increases? Figure 1.4.7 shows that as the value of K increase, the poles draw nearer to zero on the genuine pivot, and the zero areas move far from the genuine hub and get more prominent on the nonexistent hub. The percentage overshoot of the framework is directly related to the increase in the fictional pole. As the zero areas get to be more noteworthy in the fictional direction, they likewise get closer to the zero point of the genuine axis. 1.6. References Image1.1.1: Example of a stable system and an unstable system Source : http://www.bpb-co.com/articles/03rootlocuseasy.php Laboratory Manual No.1 – System response in time domain Designed in line with textbook by N. Nise: Control Systems Engineering, prescribed for the course Norman S.Nise – Control Systems Engineering (sixth edition) Experiment 2 2.2 Solution Description The figure below shows the emptying of liquid steel into a mold of the nonstop caster. As presented in the diagram, the desired height of the steel or the set point of the molten steel is the input, whereas, the yield is the real tallness of the liquid steel. At that point is the plant capacity and the plant increase Ks and, in addition, the PID Controller, which can all be consolidated to one transfer function as demonstrated in the figure below. In the figure, the gain Kv is given by τ=, when we make Kv the subject by reorganizing the formula, we get Kv=. Figure 2.1: The block diagram for the controlling of the pouring of molten steel into a mold. The chart beneath shows the nonstop caster framework with corresponding control (Ki=0, Kd=0) and proportional gain Kp. Figure 2.2: The Block diagram for the continuous caster system Figure 2.3: Simplified block diagram of caster system Subsequently this is the easiest type of box graph for this inquiry. By setting the Kp, Kv values, we can get our exchange capacity. 2.3 Test Results Characteristics (a) CCVL Simulation, small Kp (b) Matlab Simulation, small Kp (c) CCVL Simulation, Kp=1 (d) Matlab Simulation, Kp=1 (e) CCVL Simulation, large Kp (f) Matlab Simulation, large Kp Prop. Gain Kp Kp = 0.1 Kp = 0.1 Kp = 1 Kp = 1 Kp = 200 Kp = 200 Steady-state value -///// 1 3.48V 1 7.479 1 Δ steady-state value - 1 1V 1 1V 1 Steady-state error - 0 4.02V 0 0.021 0 Stable? - Yes Yes Yes Yes Yes Time-constant  - 35.5 3.56sec 3.57 0.39 Sec 0.028 Closed-loop Poles -0.0281 -0.2812 -56.2430 Table 2.1: Characteristics for given K values / Figure 2.4: CCVL screen when Kp=1 The above is a print screen of the CCVL program that contains the inputs given and the Kp value, which is 1. It appears that there is a lot of unfaltering state slip as the slant is smooth, and it requires investment for the deliberate stature (top line) to get up to speed to the coveted tallness (main concern). It is noticed that the Kp value, 1, is entirely low. Based on the figure, a causal slope is represented. / Figure 2.5: CCVL screen when Kp=10 In the above figure 2.6, there is a noteworthy abatement in the measure of the constant state error. The Kp value of 10 was used to run the program. As a result, the figures 2.5 and 2.6 show a significant change in the chart which decreases the constant state error altogether. / Figure 2.6: CCVL screen when Kp=100 Figure 2.7 show a huge decline in the measure of steady state error as compared to the amount in the previous figure. The Kp value of 100 was utilized to run the program. Accordingly, when the value of Kp was enlarged by a scale of 1000%, the steady state error was still significantly small as compared to the amount in the previous figure 2.6. / Figure 2.7: CCVL screen when Kp=200 Figure 2.8 shows a very little contrast in the error from figure 2.8 contrasted with figure 2.7. It is observable when looking in the base right corner where the qualities are given, and the blunder in this figure is 0.021V and the mistake in figure 2.7 is 0.042V which is still little. Figure 2.8: CCVL screen when Kp=0.5 The Figure 2.9 above represents a print screen of the CCVL program that contains both the inputs and the Kp value, which is 0.5. The above photo of the liquid steel shows that there is an issue or the like and that the machine is broken. The reason is that is that the values of K are just too low. This examination indicates exactly how critical the right settings are for the machine or debacle can happen. / Figure 2.9: CCVL screen when Kp=0.1 The Figure 2.10 above represents a print screen of the CCVL program that contains both the inputs and the Kp value, which is 0.1. In any case as the past graph in figure 2.9, the Kp worth is just too low and the machine will break down bringing about a flood or some likeness thereof. 2.4 Discussion & Conclusions Q1: Is the response stable? Figure 2.5 shows that the framework is steady. Despite the fact that there is a smooth incline it in the end draws near to the wanted reaction and stays at a flat zero slant; along these lines making the framework stable. Q2: Is the shape of the closed-loop response consistent with a first order system? Yes, the first order system shown below is consistent with the closed loop response shown in figure 2.2. / Figure 10: First order system Q3 : (a) How does the change in molten height compare to the change in height of the setpoint? Figures 2.5 to 2.8 shows that the stature of the molten height contrasts from the setpoint height by the unfaltering state error. The consistent state error for the capacity proceeds at the same rate and does not accelerate or decelerate. (b) Increase Kp to 10, then larger values such as 100 and 200. Observe the response and note how response characteristics change. Tabulate characteristics for K=200 in table 2 column (e). The steady state error for Kp value of 10 is shown in Figure 2.6. The steady state error for the Kp value of 100 is shown in Figure 2.7. The steady state error for the Kp value of 200 is shown in figure 2.8. Q4: As K increases, describe the effect on: (i) response shape The reaction curve is more straightforward and has less slope as contrasted with the lower k values as K increases. Figures 2.5-2.8 above shows that the as the k values increase, the response curve become sharper. In the steady state error, K values above 100 have no significant influence. It is clearly when taking a gander at the genuine qualities from the outline yet not exceptionally evident when taking a gander at the chart alone. (ii) Stability As the molten height becomes more and more close the desired height, the K value increases and so is the stability of the function. Figures 2.5 -2.8 shows that the stability is indicated by the time taken to change the value and settle. As a result, the system’s stability increases with the values of K. (iii) Steady-State error As the molten height becomes more and more close the desired height, the K value increases but, the steady state error for the function decreases. Figures 2.5 -2.8 shows that as Kp expands the two voltage qualities turn out to be much closer in this way diminishing the steady state error. (iv) response characteristics The graphs show that the response curves become steeper when Kp increases. In addition, the curve becomes sharper indicating an increase in response with an increase in Kp. Q5: Decrease Kp to very small values such as 0.1, 0.5. Observe the response and note how response characteristics change. Figures 2.9 and 2.10 demonstrate that when the K value is too little, the program’s functionality will experience a glitch creating huge harm to the framework. In the upper right-hand corner of both the pictures there is it is a flood of liquid steel. At the point when the Kp is too little or too expansive, this is precisely what happens. This demonstrates to us precisely that it is so imperative to be right on the money with programming as a mistake in the code could cost a huge number of dollars in harms and millions in time delays. Q6: As Kp decreases, explain what happens to the system. As said above, when the Kp expands the steady state error turns out to be less, the curve becomes sharper, and the capacity turns out to be more steady. Hence if the Kp diminishes the incline will turn out to be all the more smooth, the error will get to be more prominent, and the framework will turn out to be less steady, and if the Kp is too low the framework will get to be shaky as demonstrated in figure 2.9 and 2.10 above. In conclusion, as showed by the analysis, the estimation of Kp for this framework specifically couldn't be more essential. Modifying the K worth changes the entire framework. At the point when expanding the Kp it is clear that the framework turns out to be considerably more responsive which diminishes the relentless state slip. Likewise by expanding the Kp the framework turns out to be a great deal more steady as the mistake diminishes the soundness increments. Likewise by expanding the Kp fundamentally more than 1000 will likewise make the framework temperamental which was tried through Matlab. In this way, when the value of Kp is diminished, there will be inverse impacts. The consistent state lapse will build, the security will diminish and if the Kp quality is too low, the framework will get to be precarious and will wreck the ceaseless caster machine. This would be an exceptionally costly result and would be to each individual's advantage included to be maintained a strategic distance from. Table 2.1 unmistakably demonstrates that some Matlab qualities are inconsistent with the CCVL program. This is on account that Matlab won't consider any true experience. Matlab just operates as it is programmed to, no more. 2.5. References Laboratory Manual No.1 – System response in time domain Designed in line with textbook by N. Nise: Control Systems Engineering, prescribed for the course Norman S.Nise – Control Systems Engineering (sixth edition) Read More