Use Matlab commands and Simulink to perform the following tasks. You must submit
the Matlab commands you used as well as resulting outputs/plots in your report. For
Q10, you should also include a discussion of the results.
Submit the report in PDF format on Canvas by the deadline.
Block Diagram Models
Q1 Use Matlab to find the roots of the following polynomials:
a) p = s6+3s5+2s4+3s3+2s2+3s+5
b) p = 3s2+2s+3
Q2 Use Matlab to find the pole(s) and zero(s) of the following transfer functions:
2 5 2
s s s
Q3 Use Matlab to determine the open loop transfer function of the following system:
Q4 Use Matlab to determine the closed loop transfer function of the following unity feedback
s s 5
s s 3
Q5 Use Matlab to determine the closed loop transfer function of the following feedback system:
Q6 In matlab, use block reduction techniques to determine the closed loop transfer function of
the following system:
System Stability-Routh Hurwitz Criterion
a) Find the closed loop transfer function of the following unity feedback system:
The closed loop transfer function can be found using
1 ( ) ( )
G s H s
where, for this system,
H(s) = 1.
b) Using the characteristic equation from above and the Routh Hurwitz Stability Criterion,
find the range of gain k for system stability.
c) What is the value of k that makes the system oscillate and the frequency of oscillation?
Illustrate your results using Simulink and/or Matlab simulations.
Q8 For the unity feedback system shown below, use the Routh Hurwitz Stability Criterion to find
Q9 A second order position control system is shown in the following diagram:
The output Y(s) gives the position in mm and is subject to the effect of disturbances. A proportional
plus integral controller is used.
a) With K = 0.5, plot the output y(t) for a disturbance input of magnitude 2. What does the plot
b) Let K take the following values: K = 0.5, 1.0, 1.5 and 2.0. Draw a table showing the effect of
the disturbance on the output response.
The process to be controlled is a liquid level process consisting of 2 storage tanks.
The process dynamics are described by the following transfer function:
(𝑇1𝑠 + 1)
where H2 is the level in tank 2 and M is the input to the inflow valve of tank 1.
Choose values for your process parameters using your date of birth:
K = day of birth (in range 1 to 31)
T1 = month of birth (in range 1 to 12)
Open Loop Step Response
a) Simulate the process transfer function with a unit step change in input.
b) Take required measurements from the response in a) for use in the Ziegler-Nichols open
loop PID tuning method.
c) Design a P controller gain (Kc) for the process using your results in b) and Ziegler-Nichols
open loop method. Simulate the closed loop P control response to a unit step input.
A PID block can be used to simulate the controller, shown in the following example diagram.
Transfer function is the process. PID, Multiplexer (MUX) and Sum simulation blocks are used.
Note The PID block implements a parallel form of the controller: 𝐺𝑐
(𝑠) = 𝐾𝑝 +
This should be compared to the standard form: 𝐺𝑐
(𝑠) = 𝐾𝑐(1 +
+ 𝑇𝑑𝑠), to enter the
correct values for the block.
c) Adjust Kc and simulate the response to achieve a percent overshoot (%OS) of between 10 to
General Note: To get a more accurate simulation (more data points, smoother plots), set
the Max. Step Size (Simulation → Simulation Parameters menu on SIMULINK model) from
‘auto’ to a smaller value, e.g. 0.1.
d) Design a PI controller (Kc and Ti) for the process using your results in part b) and ZieglerNichols
open loop method. Simulate the closed loop PI control response to a unit step input.
Compare the response with the previously designed P controller in terms of %OS, settling
time and steady state error.
e) Adjust Kc if required to achieve a percent overshoot (%OS) of between 10 to 20%. With this
value of Kc, choose two other values for Ti to show the effect of changing the integral action
time (Ti) on the controlled response. Include:
i. plots of the step responses (max. 3),
ii. a table comparing the percent overshoot (%OS), settling time and steady state error
for the three values of Ti used.
Routh Hurwitz Stability Criterion
Guide to Performance Criteria
70% and above:
Your work must be of outstanding quality and fully meet the requirements of the coursework
specification and learning outcomes stated. You must show independent thinking and apply this to
your work showing originality and consideration of key issues. There must be evidence of wider
reading on the subject.
Key words which may describe a coursework at this level include: appraises, compares, concludes, contrasts,
criticizes, critiques, defends, discriminates, evaluates, explains, interprets, justifies, relates, supports.
Your work must be of good quality and meet the requirements of the coursework specification and
learning outcomes stated. You must demonstrate some originality in your work and show this by
applying new learning to the key issues of the coursework. There must be evidence of wider reading
on the subject.
Key words which may describe a coursework at this level include: categorizes, combine
Divine force of War is truly founded on Greek folklore and concentrated on hero Kratos. It frames some portion of an adventure which is the arrangement of God of War with the retaliation as a focal topic. In this diversion, Kratos ought to confine the God of War from pulverizing the Athens by finding the mythical Pandora's Box. In March 2005, God of War is discharged for the PlayStation 2 comfort by Sony Computer Entertainment's. Lord of War is a Third-Person Camera diversion. In that the player controls the character Kratos in battle mix, astound amusement components and plat shaping. The player needs to explore Kratos through a long arrangement of tests, labyrinths and preliminaries to achieve objectives. Kratos he traversed Greece trying to slaughter the Ares. In PC and Video amusements, Third Person is a graphical viewpoint see from a settled separation which is marginally above and behind the player character. Through this perspective players are permitted to see all the more emphatically portrayed symbol. It is most generally found in real life experience and activity amusements. General Discussion: Divine force of War is again one of such diversions which made its entrance. It is certainly something beyond a great plat previous. It is a standout amongst the most rough, aggravating and darkest diversions. The substance and importance of the amusement altogether surpasses the impeccably created interactivity. History of Greece: Fundamentally, the Greece history is isolated into six periods. 1. Promotion of Peisistratus at Athens and Croesus in Lydia was from 776 BC to 660 BC 2. Peifflstratus Accession and Croesus to the repel of Xerxes from Greece 3. Repel of Xerxes to the end of the Peloponnesian war and topple of Athens 4. Close of the Peloponnesian war to the skirmish of Leuctra 5. Skirmish of Leuctra to that of Chaeroneia 6. Skirmish of Chaeroneia as far as possible of Alexander age From Peisistratus to the demise of Alexander and his age, the five time frames displays the authentic dramatization which was fit for perspicuous progression. Undertakings of Sicilian and Italian Greeks were joined. At times, Introduced notification of Grecian political constitutions, verse, speech and rationality. The Greece political activities had turned out to be debased, after the age of Alexander. Fundamentally the insurgencies of Agis and Eleomenes at Sparta are informative and influencing. From that point forward the estimation of Greeks had a place with them as individual preceptors, logicians, stargazers, mathematicians, abstract men and pundits, therapeutic practioners, and so on. In antiquated occasions of Greece, wars were exceptionally normal. Greeks used to live in a little urban communities which has around100, 000 individuals in every city. Athens, Corinth, Sparta, Thebes used to battle with one another at their outskirts. Greece used to safeguard its urban communities from the trespassers. At times the urban areas inside Greece used to battle together and some of the time they battle alone. Indeed, even Greece attacked different nations and assumed control them. The four principle wars that happened in antiquated occasions were Trojan War (around 1250 BC), the Persian Wars (490-480 BC), the Peloponnesian War (441-404 BC) and the crusades of Alexander the Great (331-323 BC). Afterward, as indicated by Polybius, Romans assumed control Greece. Story of God of War Game: Kratos who is known for his mercilessness was once Spartan armed forces general. Just the powerful Barbarians at long last vanquished the Spartans. After a long battle Kratos was altogether vanquished and his troopers were severely slaughtered and were around his inclined body before the Barbarian King. Kratos yelled to the sky, when the Barbarian swung his sledge and promised his life to Ares. Consequently he motivated capacity to overcome his adversaries. Around then Kratos turned into Ares' hireling and with the intensity of Blades of Chaos he vanquished the Barbarian King utilizing these new weapons. Be that as it may, these forces included some major disadvantages for Kratos. Being Ares' hireling he driven his armed force to different triumphs. By following the Ares indiscriminately he copied and plundered a town. He killed everybody inside the neighborhood sanctuary of Athena. In his frenzy, he executed his significant other and little girl unconsciously. At the point when the Kratos understood his missteps, he promised retaliation on Ares. Ares clarified Kratos how he organized this transpire, with the goal that he will wind up serving him. Amid the collections of his better half and little girl were scorched, Kratos was reviled by the village's. Later the consumed fiery debris of his better half appended to his skin and made him pale. From that point forward he was named as Ghost of Spartans . Kratos helped Athena to crush Ares in the God of War. At long last divine beings evacuated his agony and bad dreams. Kratos was told about Pandora's Box by Athena which is an antiquated relic that will help Kratos to crush a God. In the wake of going into the Temple of Pandora, he had run over numerous difficulties. He was slaughtered by Ares subsequent to getting away from Hades. At last, Kratos found the Pandora's Box and obtained its capacity which enabled him to execute his previous ace. Later even the divine forces of Olympus were defenseless to delete Kratos recollections from his brain as his wrongdoings were so awful. Regardless of the Ares passing, he kept on getting bad dreams. He even attempted to murder himself however Athena spared and offered him a situation in Olympus. Later he furnished with Athena s Blades in substitution of Blades of Chaos, which was lost when Ares had passed on. Later he controlled as another God of War. Afterward, he slid to assist his armed force with attacking city of Rhodes. A captivated falcon revived the Colossus of Rhodes, and attempted to take Kratos' capacity. It was Athena as per Kratos conviction as he was early taught not to oblige Sparta. After various endeavors he depleted his forces into sword and crushed Colossus as prompted by Zeus. Zeus is the fundamental guilty party who was veiled as hawk with the end goal to execute and send him to Hades. Gaia of Titan raised him again and proposed him to modify the sword to execute the divine beings. Afterward, he ventured out to the Island of Fates where he runs over numerous difficulties. At long last, he killed the Sisters of Fate which enabled him to return in time when he was killed by Zeus. Later Kratos will come to realize that Zeus is his dad. They figured out how to get once Athena kicked the bucket, yet Kratos came back to Olympus with Titans close by to slaughter the Gods. Amusement play: Kratos' principle weapons are Blades of Chaos and auxiliary weapon is Blade of Artemis. Four distinct assaults like Zeus' Fury, Medusa's Gaze, Army of Hades and Poseidon's Rage are accessible. Likewise, the relic Poseidon's is acquired. This enables the Kratos to breathe notwithstanding when submerged. Amid the last battle with Ares, Kratos utilizes the Blade of Gods incidentally. Anger of the Gods is a unique capacity which expands assault harm and incidentally gives insusceptibility. At the point when the adversaries are executed, it will be revived. In the amusement, Gorgon Eyes and Phoenix Feathers are Health and Magic overhauls separately. Circles are the other sort of chests found in the amusement which are set apart with a relating shading (green, blue, and red). Green speaks to wellbeing, blue speaks to enchantment and red speaks to involvement in handling. By executing adversaries and decimating couple of lifeless things, red spheres can be gathered. It likewise has a brisk time highlight that starts when the player has turned out to be powerless. In like manner the player presses the relative directions that show up on screen. On minor adversaries, get man over is accessible which yields red spheres. The introduction of Greece, profundity of the difficulties, basic battling style, and the horrendous completing assaults will give you the best perspective of the activity. The controls enable players to feel ground-breaking, squares, performing amazing strikes, catches and hops. The sound and situations make the ideal setting for this amusement. Over the fun factor, God of War is likewise a superb treat for the faculties with its creative form of antiquated Greece. On occasion each one amusement goes along that pushes the limitations, that goes for broke and develops without losing the characteristics that make so agreeable God of War is one of those diversions. Kratos: In Greek folklore Kratos shows up quickly to establish connection towards them. He is certifiably not a decent person. He is sibling of Nike (Greek goddess of triumph), Zeus (Greek lord of contention) and Bia (Greek goddess of power). Four of them were first among Zeus. In spite of the fact that Kratos was lord of solidarity, in present day times his name is likely most natural as the fundamental character in computer game arrangement God of War. Obviously the title "Divine force of War" alludes not to the character Kratos but rather to the Greek lord of war Ares, who assumes a job in the plot. Ares: Ares is God of War, child of Hera and Zeus and furthermore the most incredible among Olympus divine beings. He was likewise a foe of Athena. His Roman partner was Mars. Ares lay attack to her city Athens, out of his articulate contempt and envy for her. A great many Athenians were butchered by the beasts that he arose from Underworld. Zeus: ZEUS was the ruler of the divine beings, the lord of sky and climate, law, request and destiny. Individuals thought of him as living over a mountain (Mount Olympus), and when he is furious he tosses lightning jolts out of the sky at individuals. Zeus most likely was not loved in Greece before the Indo-European Greeks landed there in the Middle Bronze Age. He is an Indo-European god, and he is essentially equivalent to other Indo-European sky divine beings like Jupiter (this is extremely even a similar word: Ju= Zeus and piter implies father) or Odin. He's identified with Indra, a Hindu sky god, the child of Dyeus Pita. (Zeus), the best of the Olympian divine beings, and the dad of divine beings and men, was a child of Cronos and Rhea, a sibling of Poseidon, Hades (Pluto), Hestia, Demeter, Hera, and in the meantime wedded to his sister Hera. Weapons: Kratos Weapon: Kratos primary weapons in God of War are Blades of Athena. They are a similar like Blades of Chaos which Kratos first got. They have similar capacities like Blades of Chaos toward the finish of God of War. Notwithstanding, in God of War: Betrayal and God of War II their forces of attackin>GET ANSWER