StateResponse

The state response of a single-input system to a unit step:

The initial conditions are assumed to be zero:

Specify as the initial state values:

The state response of a three-input system to inputs {Sin[t], Cos[t], Cos[t]}:

Plot the response:

If the number of input signals is less than the number of the system's inputs, the remaining inputs are assumed to be zero:

If a scalar input signal is specified for a multiple-input system, the signal is applied to each input channel in turn:

StateResponse gives the result in terms of interpolating function objects:

Plot the response:

The state response for a generic continuous-time system:

The response to a unit step input:

The state response of a single-input system to a unit step input:

The state response to a sampled sinusoid:

Plot the response with a zero-order hold:

The state response of a two-input system to two randomly sampled inputs:

If the number of sampled inputs is less than the number of system inputs, the remaining inputs are assumed to be zero:

The second and fourth states are not excited because the second input is zero:

If only a single-input sequence is given to a multi-input system, the sequence is applied to each input in turn:

For this system, the first input excites only the first and fourth states, the second input excites only the second and fifth states, and the third input excites only the third and sixth states:

The response for a generic discrete-time system:

The response to a unit step sequence:

The model of a stabilized inverted pendulum on a moving cart has the cart displacement d and velocity v, together with the pendulum's angular position and velocity as the state variables:

Compute the acceleration a of the cart and the angular acceleration of the pendulum by differentiating the cart's velocity and the pendulum's angular velocity obtained using StateResponse:

Plot the results:

Analyze the response of the states to each control input for a multi-input system:

The state-space model of a production and inventory control system with desired production rate and sales rate as inputs and actual production rate and inventory level as states:

Determine the response for a given production rate and 10% jump in sales from the initial equilibrium condition:

Plot the response for specific initial conditions:

The Clohessy-Wiltshire equations model the relative motion between two satellites orbiting a central body:

Use StateResponse to obtain the closed relative orbits from a particular set of launch conditions:

The results of StateResponse and OutputResponse are the same when the output matrix is identity and the transmission matrix is zero:

The natural response is determined by the poles of the system:

It is invariant under any similarity transformation:

The original states: