The open-loop transfer function of a DC-motor is a second order transfer function, e() K P(s)...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
The open-loop transfer function of a DC-motor is a second order transfer function, e() K P(s) - V(o) (Ja+b)(La + R) + K² where the rotational speed è is considered the output, the armature voltage V is considered the input, the physical parameters for the considered DC motor are: 0.02 kg.m² (J) moment of inertia of the rotor (b) motor viscous friction constant 0.2 N.m.s 0.02 V/rad/sec 2 Ohm 1 H (K) static DC gain (R) electric resistance (L) electric inductance An automatic controller is used to control the DC-motor rotational speed, as shown the block diagram. controller C(s) 11 The transfer function for a PID controller is: K₁ C(s) = K₂ + + Kas plant P(s) Kas²+K₂s+Ki For a 1-rad/sec step reference, the design criteria are the following. • Settling time less than 2 seconds • Overshoot less than 5% Steady-state error less than 1% Use MATLAB to create a Simulink block diagram representing the closed-loop system shown in the block diagram. Obtain the response (t) to the unit step input for the following cases: • Use proportional controller with K, 10. (Simulate for 10 sec) • Use proportional controller with K, 100. (Simulate for 10 sec) • Use a PID controller with K, - 75, K-1 and K-1. (Simulate for 300 sec) • Use a PID controller with K, 100, K, • Use a PID controller with K, 100, K, 200 and Ka= 1. (Simulate for 10 sec) 200 and K-10. (Simulate for 10 sec) Z Then discuss the effect of the controller on the system response, taking into consideration the rise time, the overshot, the settling time and the steady state error. The open-loop transfer function of a DC-motor is a second order transfer function, e() K P(s) - V(o) (Ja+b)(La + R) + K² where the rotational speed è is considered the output, the armature voltage V is considered the input, the physical parameters for the considered DC motor are: 0.02 kg.m² (J) moment of inertia of the rotor (b) motor viscous friction constant 0.2 N.m.s 0.02 V/rad/sec 2 Ohm 1 H (K) static DC gain (R) electric resistance (L) electric inductance An automatic controller is used to control the DC-motor rotational speed, as shown the block diagram. controller C(s) 11 The transfer function for a PID controller is: K₁ C(s) = K₂ + + Kas plant P(s) Kas²+K₂s+Ki For a 1-rad/sec step reference, the design criteria are the following. • Settling time less than 2 seconds • Overshoot less than 5% Steady-state error less than 1% Use MATLAB to create a Simulink block diagram representing the closed-loop system shown in the block diagram. Obtain the response (t) to the unit step input for the following cases: • Use proportional controller with K, 10. (Simulate for 10 sec) • Use proportional controller with K, 100. (Simulate for 10 sec) • Use a PID controller with K, - 75, K-1 and K-1. (Simulate for 300 sec) • Use a PID controller with K, 100, K, • Use a PID controller with K, 100, K, 200 and Ka= 1. (Simulate for 10 sec) 200 and K-10. (Simulate for 10 sec) Z Then discuss the effect of the controller on the system response, taking into consideration the rise time, the overshot, the settling time and the steady state error.
Expert Answer:
Answer rating: 100% (QA)
Here are the actual Simulink models and responses for each case 1 Proportional controller with Kp 10 ... View the full answer
Related Book For
Posted Date:
Students also viewed these marketing questions
-
What ethical considerations arise in the context of globalization, particularly regarding issues of cultural appropriation, exploitation, and the responsibility of global actors toward vulnerable...
-
Portions of the financial statements for Alliance Technologies are provided below. ALLIANCE TECHNOLOGIES Income Statement For the Year Ended December 31, 2024 Net sales Expenses: Cost of goods sold...
-
Question 3 (20 marks) a). Let X, be iid, E(X) = and Var(X) = o. Set X = Xi/n. Show that i=1 n (X-X) 0 n i=1 (10 marks) b). Suppose X, x 1 are independent random variables and suppose that X, has...
-
Water is an essential resource. For that reason moral considerations exert considerable pressure to assure that everyone has access to at least enough water to survive. Yet it appears that equity and...
-
The famous comedian Groucho Marx once quipped that "I would never join a club that would have me as a member." Modified to apply to market settings, the quote might be rewritten, "I would never buy...
-
At the beginning of the fiscal year, Andy Company purchased for $2,060,000 a patent that applies to the manufacture of a unique tamper-proof lid for medicine bottles. Andy incurred legal costs of...
-
Linda Chidister is planning to send her son, Edward, to college. While he is in college, Linda intends to give him $3,000 at the end of each year. Required: How much must Linda invest today so she...
-
On May 3, 2012, Eisler Company consigned 80 freezers, costing $500 each, to Remmers Company. The cost of shipping the freezers amounted to $840 and was paid by Eisler Company. On December 30, 2012, a...
-
At the beginning of 2020, Co. X acquired a 90% interest in Co. Y when Co. Y's book values of identifiable net assets equaled their fair values. On December 26, 2020, Co. Y declared dividends of...
-
Norm and Sheila consume only meat pies and beer. Meat pies used to cost $2 each and beer was $1 per can. Their gross income used to be $60 per week, but they had to pay an income tax of $10. Use red...
-
This is a partial adjusted trial balance of Wildhorse Company. WILDHORSE COMPANY Adjusted Trial Balance (partial) January 31, 2022 Debit Credit Supplies $770 Prepaid Insurance 1,698 Salaries and...
-
Explore the evolutionary processes that lead to enzyme diversification and adaptation. What role do gene duplication and convergent evolution play in the evolution of enzyme functions ?
-
What is the wavelength of an x - ray photon with energy 1 0 keV ( 1 0 , 0 0 0 eV ) ? What is its frequency?
-
The stock of Sedly Inc. is expected to pay the following dividends. Year 1 2 3 4 Dividend $2.30 $3.50 $1.75 $2.20 At the end of the fourth year its value is expected to be $37.70. What should...
-
A sound wave has a speed of 3 8 0 meter / second in some gas. There is a source of waves with a frequency of 6 7 0 hertz, the source is not moving. There is an observer moving towards the source, the...
-
The price of a stock is $59, and a six-month call with a strike price of $57 sells for $7. Round your answers to the nearest dollar. What is the option's intrinsic value? What is the option's time...
-
Mass Balance company is manufacturing a new digital scale for use by a large chemical company. The order is 40 units. The first scale took 60 hours of Direct Labor.Learning rate is 80%. What is the...
-
Design an experiment to demonstrate that RNA transcripts are synthesized in the nucleus of eukaryotes and are subsequently transported to the cytoplasm.
-
For the circuit of Figure P2.39, determine the transform of the output voltage V0(s). Assume that the circuit is in steady state when t Figure P2.39 Model of an electronic circuit. IF 2 H Ion 2 4
-
A cassette tape storage device has been designed for mass-storage [1]. It is necessary to control the velocity of the tape accurately. The speed control of the tape drive is represented by the system...
-
Determine the transfer function X2(s)/F(s) for the system shown in Figure E2.26. Both masses slide on a frictionless surface, and k = 1 N/m. m2 1 kg l kg Two connected masses on a frictionless FIGURE...
-
Correctly apply the rules for the order of operations to accurately compute \(\left(\frac{3}{16}+\frac{7}{16} ight)^{2}+\frac{1}{5} \div \frac{3}{10}\).
-
Danny, a nutritionist, is designing a diet for her client, Callum. Danny determines that Callum's diet should be \(30 \%\) protein. If Callum consumes 2,400 calories per day, how many calories of...
-
Calculate \(45.63 \div 17.13\) using a calculator. Round to three decimal places, if necessary.
Study smarter with the SolutionInn App