EstimatorRegulator
EstimatorRegulator[ssm,{l,κ}]
constructs the feedback regulator for the StateSpaceModel ssm with estimator and feedback gain matrices l and κ, respectively.
EstimatorRegulator[{ssm,sensors},{l,κ}]
uses only sensors as the measured outputs of ssm.
EstimatorRegulator[{ssm,sensors,finputs},{l,κ}]
specifies finputs as the feedback inputs of ssm.
EstimatorRegulator[{ssm,sensors,finputs,einputs},{l,κ}]
specifies einputs as the exogenous deterministic inputs.
Details and Options


- The standard state-space model ssm can be given as StateSpaceModel[{a,b,c,d}], where a, b, c, and d represent the state, input, output, and transmission matrices in either a continuous-time or a discrete-time system:
-
continuous-time system discrete-time system - The descriptor state-space model ssm can be given as StateSpaceModel[{a,b,c,d,e}] in either continuous time or discrete time:
-
continuous-time system discrete-time system - EstimatorRegulator also accepts nonlinear systems specified by AffineStateSpaceModel and NonlinearStateSpaceModel.
- For nonlinear systems, the operating values of state and input variables are taken into consideration when constructing the EstimatorRegulator.
- The input
can include stochastic inputs
, feedback inputs
, and exogenous deterministic inputs
.
- The arguments finputs and einputs are lists of integers specifying the positions of
and
in
.
- The output
consists of the noisy measurements
as well as other outputs.
- The argument sensors is a list of integers specifying the positions of
in
.
- EstimatorRegulator[ssm,{…}] is equivalent to EstimatorRegulator[{ssm,All,All,None},{…}].
- The estimator gains l can be computed using EstimatorGains, LQEstimatorGains, or DiscreteLQEstimatorGains.
- The feedback gains κ can be computed using StateFeedbackGains, LQRegulatorGains, or DiscreteLQRegulatorGains.
- Block diagram of the system with its regulator:

Examples
open allclose allBasic Examples (1)
Scope (5)
The regulator for a SISO system with estimator gain L and regulator gain K:
The regulator for a descriptor state-space model has the same descriptor matrix:
A state-feedback regulator for a system with two sensor outputs, one feedback input, one exogenous deterministic input, and one stochastic input:
An observer-based optimal regulator for a deterministic continuous-time system:
The transfer function of the estimator-regulator:
Compute the estimator-regulator for a NonlinearStateSpaceModel:
Applications (3)
Properties & Relations (2)
The closed-loop poles are the poles of the state-feedback and estimator subsystems:
The poles of the closed-loop system with state feedback matrix k:
The poles of the estimator with gain matrix l:
These make up the closed-loop poles for the system with the estimator-regulator:
Construct an LQG regulator using optimal estimator gains and state-feedback gains:
LQGRegulator gives the same result:
Text
Wolfram Research (2010), EstimatorRegulator, Wolfram Language function, https://reference.wolfram.com/language/ref/EstimatorRegulator.html (updated 2014).
BibTeX
BibLaTeX
CMS
Wolfram Language. 2010. "EstimatorRegulator." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014. https://reference.wolfram.com/language/ref/EstimatorRegulator.html.
APA
Wolfram Language. (2010). EstimatorRegulator. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/EstimatorRegulator.html