State-Feedback Controller
Discrete-time state-feedback controller with integral action
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Simscape / Electrical / Control / General Control
Description
The State-Feedback Controller block implements a discrete-time state-feedback controller with integral action. Use this block to control linear systems with single or multiple inputs and single or multiple outputs. The integral action serves to eliminate steady-state error in the controlled outputs. You can define the controller using a precomputed optimal gain or use the state-space model of your system to generate this gain using pole placement.
Equations
The integral of the tracking error, xi, is an additional state that ensures zero steady-state error for the closed-loop system. The extended state vector is
Where:
x is the state vector.
xi is the integral of the tracking error.
xe is the extended state vector.
Therefore, the control action is
Where:
K is the feedback matrix, that is, the pole placement.
u is the controller output.
Assumptions
System state measurement and estimation occur outside the controller.
Ports
Input
r — Plant reference
scalar
Plant system reference signal.
Data Types: single | double
x — State vector
vector
Measured or estimated system state vector.
Data Types: single | double
Reset — Integrator reset
scalar
External reset signal (rising edge) for the integrator.
Data Types: Boolean
y — Plant output
scalar
Plant system output signal.
Data Types: single | double
Output
u — Controller output
scalar
Control system output signal.
Data Types: single | double
Parameters
State-feedback design — Controller generation
State-feedback gain (default) | Desired eigenvalues
Select the strategy for parameterizing controller gain:
State-feedback gain— Specify the controller gain directlyDesired eigenvalues— Specify the plant model and desired eigenvalues from which to generate the controller gain
State-feedback parameterization — State-feedback parameterization
Discrete-time (default) | Continuous-time
Select the strategy for parameterizing the state-space matrices and desired poles for the controller. The block implementation is discrete regardless of this parameterization.
Dependencies
To enable this parameter, set State-feedback
design to Desired
eigenvalues.
Controller matrix — Controller matrix
[1 1] (default) | matrix
Controller feedback matrix. To determine the controller matrix, if you
have a license for Control System Toolbox™, use the lqr or lqi
function.
Dependencies
To enable this parameter, set State-feedback
design to State-feedback
gain.
Discrete-time A matrix — A matrix in discrete time
1 (default) | real scalar or matrix
State matrix of the discrete-time state-space model. The A matrix must be square, with the number of rows and columns equal to the order of the system.
Dependencies
To enable this parameter, set State-feedback
parameterization to
Discrete-time.
Discrete-time B matrix — B matrix in discrete time
1 (default) | real scalar or matrix
Input matrix of the discrete-time state-space model. The B matrix must have the number of rows equal to the order of the system, and the number of columns equal to the number of system inputs.
Dependencies
To enable this parameter, set State-feedback
parameterization to
Discrete-time.
Discrete-time C matrix — C matrix in discrete time
1 (default) | real scalar or matrix
Output matrix of the discrete-time state-space model. The C matrix must have the number of rows equal the number of outputs of the system, and the number of columns equal to the order of the system.
Dependencies
To enable this parameter, set State-feedback
parameterization to
Discrete-time.
Discrete-time D matrix — D matrix in discrete time
1 (default) | real scalar or matrix
Feedthrough matrix of the discrete-time state-space model. The D matrix must have the number of rows equal to the number of system outputs, and the number of columns equal to the number of system inputs.
Dependencies
To enable this parameter, set State-feedback
parameterization to
Discrete-time.
Continuous-time A matrix — A matrix in continuous time
1 (default) | real scalar or matrix
State matrix of the continuous-time state-space model. The A matrix must be square, with the number of rows and columns equal to the order of the system.
Dependencies
To enable this parameter, set State-feedback
parameterization to
Continuous-time.
Continuous-time B matrix — B matrix in continuous time
1 (default) | real scalar or matrix
Input matrix of the continuous-time state-space model. The B matrix must have the number of rows equal to the order of the system, and the number of columns equal to the number of system inputs.
Dependencies
To enable this parameter, set State-feedback
parameterization to
Continuous-time.
Continuous-time C matrix — C matrix in continuous time
1 (default) | real scalar or matrix
Output matrix of the continuous-time state-space model. The C matrix must have the number of rows equal the number of outputs of the system, and the number of columns equal to the order of the system.
Dependencies
To enable this parameter, set State-feedback
parameterization to
Continuous-time.
Continuous-time D matrix — D matrix in continuous time
1 (default) | real scalar or matrix
Feedthrough matrix of the continuous-time state-space model. The D matrix must have the number of rows equal to the number of system outputs, and the number of columns equal to the number of system inputs.
Dependencies
To enable this parameter, set State-feedback
parameterization to
Continuous-time.
Discretization sample time — Discretization sample time
0.1 (default) | positive real number
Value used to discretize the state space matrices and also approximate the discrete-time eigenvalues.
Dependencies
To enable this parameter, set State-feedback
parameterization to
Continuous-time and Sample time
(-1 for inherited) to -1.
Desired eigenvalues (discrete) — Observer eigenvalues
0 (default) | real vector
Specify the location of the eigenvalues to lie within the unit circle. The controller gain is then calculated based on these eigenvalues. The size of the vector must be equal to the system order plus the number of outputs.
Control action upper limit — umax
5 (default) | scalar greater than the value of the Control action lower
limit parameter
Upper limit for the control output signal.
Control action lower limit — umin
0 (default) | scalar
Lower limit for the control output signal.
Sample time (-1 for inherited) — Sampling interval
-1 (default) | default value or a positive number
Time interval between samples. If the block is
inside a triggered subsystem, inherit the sample time by setting this
parameter to -1. If this block is in a continuous
variable-step model, specify the sample time explicitly. For more
information, see What Is Sample Time? and
Specify Sample Time.
