Figure 1 shown a DC motor including free body diagrams of its electric circuit of the...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Figure 1 shown a DC motor including free body diagrams of its electric circuit of the amature and the rotor. The imput is the amature voltage V in Volts (driven by a voltage source). Measured variables are the angular velocity of the shaft w in radians per second, and the shaft angle e in radians. R L. T. V, = Ko Figure 1 The rotor and the shaft are assumed to be rigid, and the values for the physical parameters are listed in Table 1 below. Table 1 moment of inertia of the rotor damping (friction) of the mechanical system (back-Jelectromotive force constant J =0.01 kg m b =0.1 Nms K =0.01 Nm/A R =1N L = 0.5 H electric resistance electric inductance (a) Develop the mathematical model of the system intem of ODE, Transfer Function, and State-Space Forms. (15 marks) (b) Simulate and plot the responses of the system based on intial, step and impulse inputs using Matlab, respectively, where tspan=[0 5] and all initial conditions zero. (20 marks) (c) By referring to the response results on (b), give your comments relating to stability and performance parameters (rise time, over shoot, settling time, etc). (15 marks) Figure 1 shown a DC motor including free body diagrams of its electric circuit of the amature and the rotor. The imput is the amature voltage V in Volts (driven by a voltage source). Measured variables are the angular velocity of the shaft w in radians per second, and the shaft angle e in radians. R L. T. V, = Ko Figure 1 The rotor and the shaft are assumed to be rigid, and the values for the physical parameters are listed in Table 1 below. Table 1 moment of inertia of the rotor damping (friction) of the mechanical system (back-Jelectromotive force constant J =0.01 kg m b =0.1 Nms K =0.01 Nm/A R =1N L = 0.5 H electric resistance electric inductance (a) Develop the mathematical model of the system intem of ODE, Transfer Function, and State-Space Forms. (15 marks) (b) Simulate and plot the responses of the system based on intial, step and impulse inputs using Matlab, respectively, where tspan=[0 5] and all initial conditions zero. (20 marks) (c) By referring to the response results on (b), give your comments relating to stability and performance parameters (rise time, over shoot, settling time, etc). (15 marks)
Expert Answer:
Related Book For
Posted Date:
Students also viewed these electrical engineering questions
-
The Q of a dielectric medium is defined as the ratio of displacement current density to conduction current density . For monochromatic wave propagation we find that Q = w /g. Determine Q for quartz...
-
How can you forecast of funds needed for staffing, equipment, materials, and supplies and approve expenditures and implement budgetary adjustments necessary?
-
Kansas City Castings (KCC) is attempting to obtain the maximum loan possible using accounts receivable as collateral. The firm extends net-30-day credit. The amounts that are owed KCC by its 12...
-
Big bang Pty (Ltd) is a company which is involved in sale of manufacturing goods. The company had the following income and expenses for the year of assessment: R15 000 for the collection of debts...
-
* Find i0 (t) for t > 0 in the circuit of Fig. 16.50. 2 1 1 F 0.5v
-
A survey found that 68% of adults ages 18 to 25 think that their generation is unique and distinct. Twelve adults ages 18 to 25 are randomly selected. The random variable represents the number of...
-
The variance process in the Heston model satisfy a CIR process: \[d V_{t}=\kappa\left(\bar{V}-V_{t} ight)+\sigma \sqrt{V_{t}} d W_{t}\] Use Ito to calculate the dynamics of the volatility process...
-
Assume that all assumptions of the single-index model hold, except that the covariance between residuals is a constant K instead of zero. Derive the covariance between the two securities and the...
-
Performance Development Plan State the intention of moving to Customer Value Management department.
-
At Vision Club Company, office workers are employed for a 40-hour workweek on either an annual or a monthly salary basis. Given on the form below are the current annual and monthly salary rates for...
-
How many operations (multiplications, divisions, additions, and subtractions) are re- quired for one iteration of the Jacobi method in solving a system of n equations and n variables? How many...
-
People with very good pitch discrimination can very quickly determine what note they are listening to. The note on the musical scale called \(\mathrm{C}_{6}\) (two octaves above middle \(\mathrm{C}\)...
-
Police radar guns work by measuring the change in frequency of a reflected pulse of electromagnetic waves. A gun reads correctly only if a car is moving directly toward or away from the person making...
-
Prove that if \[\operatorname{Pr}\left(y_{i}=1 \mid \mathbf{x}_{i} ight)=\Phi\left(\beta_{0}+\mathbf{x}^{\top} \boldsymbol{\beta} ight), \quad \operatorname{Pr}\left(y_{i}=0 \mid \mathbf{x}_{i}...
-
A standard gold bar stored at Fort Knox, Kentucky, is 7.00 inches long, 3.63 inches wide, and 1.75 inches tall. Gold has a density of \(19,300 \mathrm{~kg} / \mathrm{m}^{3}\). What is the mass of...
-
Research vessels at sea can create images of their surroundings by sending out sound waves and measuring the time until they detect echoes. This image of a shipwreck on the ocean bottom was made from...
-
Describe a cognitive bias that may skew an entrepreneur's perception of the opportunity to open a new hip - hop dance studio near Ryerson's campus. Why is an entrepreneur more prone to this bias...
-
The Taylor's series expansion for cosx about x = 0 is given by: where x is in radians. Write a user-defined function that determines cosx using Taylor's series expansion. For function name and...
-
A parallel-plate capacitor has plate area 200 cm2 and plate separation 3 mm. The charge density is 1C/m2 with air as dielectric. Find (a) The capacitance of the capacitor (b) The voltage between the...
-
The magnetic field intensity is H = 1200 A/m in a material when B = 2 Wb/m2. When H is reduced to 400 A/m, B = 1.4 Wb/m2. Calculate the change in the magnetization M.
-
A 30-cm by 40-cm rectangular loop rotates at 130rad/s in a magnetic field 0.06 Wb/m2 normal to the axis of rotation. If the loop has 50 turns, determine the induced voltage in the loop.
-
Suppose there are only 3 rating categories: A, B, D. Their one-year transition probabilities are given by the following matrix. Construct the transition probability matrix for two years. Ending...
-
Let \(q(t)\) be the survival probability and let \(q^{-1}\) be its inverse function. Also, let \(U\) be a uniform random variable on \([0,1]\). For each realization \(u\), let \(\tau\) be chosen such...
-
Let \(p(t)\) be the probability of survival from 0 to \(t\). The probability of surviving to \(s\) given survival to \(t\) is then \[p(s \mid t)=\frac{p(s)}{p(t)}\] Let...
Study smarter with the SolutionInn App