TheDeveloperBlog.com

Home | Contact Us

C-Sharp | Java | Python | Swift | GO | WPF | Ruby | Scala | F# | JavaScript | SQL | PHP | Angular | HTML

Control System State Space Model

Control System State Space Model with tutorial, introduction, classification, mathematical modelling and representation of physical system, transfer function, signal flow graphs, p, pi and pid controller etc.

<< Back to CONTROL

State Space Model

The process by which the state of a system is determined is called state variable analysis.

Advantages of State Space Techniques

  1. This technique can be used for linear or nonlinear, time-variant or time-invariant systems.
  2. It is easier to apply where Laplace transform cannot be applied.
  3. The nth order differential equation can be expressed as 'n' equation of first order.
  4. It is a time domain method.
  5. As this is time domain method, therefore this method is suitable for digital computer computation.
  6. On the basis of the given performance index, this system can be designed for an optimal condition.

State Space representation of electrical system:

Consider an RLC network,

At time t = 0
Current = iL(0)
Capacitor Voltage = Vc(0) 

Thus, the state of the network at time t=0 is specified by the inductor current and capacitor voltage.

Therefore iL(0) and Vc(0) is called the initial state of the network and the pair iL(t), Vc(t) is called the state of the network at 't'. The variable iL and vc are called the state variables of the network.

State Space Model

Apply KVL


State Space Model

Also,


State Space Model

From eq.1


State Space Model

This type of equation is called State equation. And the variables present in this equation are called state variables.

Eq. 3 and Eq. 4 can be written in matrix form as


State Space Model

The general form of state equation is

x ̇(t)=Ax(t)+Bu(t)  ........Eq.6
y(t)=C x(t)+D u(t)      ........Eq.7

Y = n- dimensional output vector

U = r-dimensional control vector or input vector

A = n � n system matrix

B = n � r control matrix

C = n � n output matrix

When there is no direct connection between input and output in that case D u(t) is not taken.

State Space Model

State Space Representation of nth order differential Equation

For the nth order differential equation

Example 1

A system is described by the differential equation

State Space Model

Where y is the output and u is the input to the system. Obtain the state space representation of the system.

Solution

State Space Model
Next Topic#




Related Links:


Related Links

Adjectives Ado Ai Android Angular Antonyms Apache Articles Asp Autocad Automata Aws Azure Basic Binary Bitcoin Blockchain C Cassandra Change Coa Computer Control Cpp Create Creating C-Sharp Cyber Daa Data Dbms Deletion Devops Difference Discrete Es6 Ethical Examples Features Firebase Flutter Fs Git Go Hbase History Hive Hiveql How Html Idioms Insertion Installing Ios Java Joomla Js Kafka Kali Laravel Logical Machine Matlab Matrix Mongodb Mysql One Opencv Oracle Ordering Os Pandas Php Pig Pl Postgresql Powershell Prepositions Program Python React Ruby Scala Selecting Selenium Sentence Seo Sharepoint Software Spellings Spotting Spring Sql Sqlite Sqoop Svn Swift Synonyms Talend Testng Types Uml Unity Vbnet Verbal Webdriver What Wpf