State Space ModelThe process by which the state of a system is determined is called state variable analysis. Advantages of State Space Techniques
State Space representation of electrical system:Consider an RLC network, At time t = 0 Current = i_{L}(0) Capacitor Voltage = V_{c}(0) Thus, the state of the network at time t=0 is specified by the inductor current and capacitor voltage. Therefore i_{L}(0) and V_{c}(0) is called the initial state of the network and the pair i_{L}(t), V_{c}(t) is called the state of the network at 't'. The variable iL and vc are called the state variables of the network. Apply KVL Also, From eq.1 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 The general form of state equation is Y = n dimensional output vector U = rdimensional 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 Representation of nth order differential Equation For the nth order differential equation Example 1A system is described by the differential equation Where y is the output and u is the input to the system. Obtain the state space representation of the system. Solution
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