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Linear Systems Control
创建日期：2024-03-29 11:38:50
所属分类：物理Physical
标签： 7CCSMRTS
Linear Systems Control

6CCS3RSC/7CCSMRTS

Assignment: Linear Systems Control

16th March 2021

For this assignment, you will need the template code assignment.m. Download this from the module’s

KEATS page and save it to your computer. When you are ready to submit your assignment, you will need

to upload this file so bear this in mind while completing the assignment (further instructions on how to

submit your assignment are given below). Open the file using Matlab, and complete the following exercises.-L-C circuit.

A series resistor-inductor-capacitor circuit (see Figure 1) can be described as a linear system, in whichthe

current across the components follows the equation

d

where I is the current, R the resistance, L the inductance, C the capacitance and dV /dt the rate of change

of the voltage at the power source.

1. Write (1) in state space formulation, as a continuous time, linear time invariant system. You may

assume that the rate of change of the voltage is the control input (i.e., u = dV /dt) and the system

state is the current and its first time derivative1

(i.e., x = (I, dI/dt)

>). Using the template code

implement the matrices A and B assuming that L = 20 H, C = 0.1 F, R = 4 ?.

[5 marks]

2. Derive the equations for the system in discrete time, such that you can compute xt+1 as a function

of xt and ut

. Using the template file, implement a simulation of the system, such that you can

compute the current for 0 ≤ t ≤ 20 s if the voltage increases at a constant rate of 1 V /s. Assume

that the current is zero and constant at t = 0 s and use sampling rate δt = 2 ms.

[10 marks]

1Throughout the assignment, treat the state and its derivatives as a column vector.

3. Consider the case that the circuit is equipped with a multimeter that enables measurement of current

at the same sampling rate. Using the template file, implement the observer matrix C and the

observability matrix H using your answer to Question 2. Derive the transfer function for this system

and solve for the poles to four decimal places. Implement a vector z in the template file that contains

the poles.


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关键词一 关键词二 关键词三 关键词四 关键词五 和法规和的发更好的风格和 ECON 615 FINC 612 CSC148 COMP 639 ACCT 203 ACCT 211 PSYC 101 MTH2009 COMP52315 PSYCO 432 statistics MATH4063 11 xxx 1 MA1MSP MAST30028 MATH3888 CS341 EEE30002 ES2F5 MCD4160 CC0933 ECON 1101 MCHM3001 CHEM3118 COMMGMT 2511 COMP41280 STAT 631 24T1 IRE379 SENG365 ECON433 FIT3139 MATH4602 LING5621M FINS5516 ECON3208 MN2177 L2 SM EEET1415 Finance DS4023 COMP3004 7CCSMRTS K1S5B6 Stat230 CSCI4211 CSI2132 ECON30130 MAS6100 ENVS222 COM2107 INFO1112 STAT 4004 FIT2100 comp2022 COMP4691 Physics 307 Econ 659 probability CSCI316 fir29 CSCI203 COMP3160 COMP6714 INFO1113 Physics 7B Physics Photonics S203031 STAT2005 COMP90015 CSCI 2110 CSCC46 Information CSC477 COMP4650 Statistical COMP 346 COMP1017 ELEC340 MATH1007 Programming function STAT 244 CS 134 Java cse13s Math 108A FW20 ECON3389 CSE 130 Science 331 COMP9020 engineering COSC 445 CSE 5523 GAME2012 visualization MATH 235 Math 370 CSC343 COGS 108 EE524 COMP10200 STAT 416 3FK4 MSCI 311 ECON6113 ACC40700 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