connects the states of the systems model sys to the controller con and the outputs of con to the inputs of sys in feedback.


connects state si of sys to the i^(th) input of con and the j^(th) output of con to input inj of sys with feedback type ftypej



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Basic Examples  (3)

Determine the closed-loop model of a state-feedback system:

Compute the feedback gains to place the poles at z1 and z2 for a discrete-time system:

Determine the closed-loop model:

Verify the pole locations:

Determine the closed-loop model with a set of optimal state feedback gains:

Scope  (15)

Basic Uses  (10)

The closed-loop model of a system with state feedback:

With positive state feedback:

The state feedback gains specified as a transfer-function model:

The gains specified as a state-space model:

A affine state-space model with feedback specified in a vector:

A nonlinear state-space model with feedback specified in a vector:

Positive state feedback:

Only feedback to the first input:

Only feedback to the second input:

Connect the second state to the first input through a feedback system:

The closed-loop model of a multiple-input system:

System Types  (5)

Connect two StateSpaceModel systems:

With delays:

Using descriptor state-space models:

Input linear AffineStateSpaceModel systems:

General nonlinear NonlinearStateSpaceModel systems:

Connecting a standard linear system and an input linear system will give an affine model:

Connecting standard linear or affine system with a nonlinear system gives a nonlinear model:

Applications  (3)

The linearized inverted pendulum model is unstable:

Calculate a gain matrix to place the closed-loop poles in the left half-plane:

Find the closed-loop system:

The closed-loop response is stable:

Calculate a gain matrix to optimize a quadratic cost function of the input and the states:

Find the closed-loop system:

Calculate a gain matrix to optimize a quadratic cost function of the input and the outputs:

Find the closed-loop system:

Properties & Relations  (1)

A model where the output matrix is identity and the direct transmission matrix is zero:

SystemsModelStateFeedbackConnect and SystemsModelFeedbackConnect are equivalent:

Introduced in 2010
Updated in 2014