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FullInformationOutputRegulator
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FullInformationOutputRegulator

✖

gives the full state information output regulator for sys using specification rspec.

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FullInformationOutputRegulator[{sys,{out1,…},{in1,…}},…]

specifies the regulated outputs outi and the controlled inputs inj.

Details and Options

  • FullInformationOutputRegulator returns a regulator that drives the sys outputs to zero and is typically used to suppress or track known inputs to the system.
  • The system sys is taken to have state equations and and outputs , with being the controllable input. The state is not affected by the input and is used to model signals to suppress or track, as indicated by the output function .
  • Typical output functions , which the regulator will drive to zero:
  • suppress the effects of on the states
    cause to track
  • The system sys can be StateSpaceModel, AffineStateSpaceModel, or NonlinearStateSpaceModel.
  • The computed state feedback regulates sys about an operating point using .
  • The state feedback has the form , where , , and is computed following rspec.
  • Possible regulator specifications rspec:
  • {"Poles",{p1,…}}computed with StateFeedbackGains
    {"Weights",{p,…}}computed with LQRegulatorGains
    {"Gains",κ}explicitly given gains
  • With the specification {"method",pars,opts}, the options opts are passed to the gain computation function.
  • The outputs {out1,…} and inputs {in1,…} are part specifications and by default are taken to be All.

Examples

open allclose all

Basic Examples  (1)Summary of the most common use cases

Compute the regulating feedback for a system with a constant disturbance of 0.5:

In[1]:=1
✖
https://wolfram.com/xid/01lg39xalr04hou5q-80xxz0

The regulator is a function of the states and the disturbance state :

In[2]:=2
✖
https://wolfram.com/xid/01lg39xalr04hou5q-znqwvt
Out[2]=2

The closed-loop system:

In[3]:=3
✖
https://wolfram.com/xid/01lg39xalr04hou5q-xcbb2q
Out[3]=3

The output is regulated to zero:

In[4]:=4
✖
https://wolfram.com/xid/01lg39xalr04hou5q-c6w8bj
In[6]:=6
✖
https://wolfram.com/xid/01lg39xalr04hou5q-1dgu03
Out[6]=6

Scope  (8)Survey of the scope of standard use cases

The regulator for a linear system with the exosystem pole at the origin:

In[1]:=1
✖
https://wolfram.com/xid/01lg39xalr04hou5q-xjnz24
Out[1]=1

The closed-loop system:

In[2]:=2
✖
https://wolfram.com/xid/01lg39xalr04hou5q-3k8jbh
Out[2]=2

The exosystem has a pair of complex poles:

In[1]:=1
✖
https://wolfram.com/xid/01lg39xalr04hou5q-8kn0ux
In[2]:=2
✖
https://wolfram.com/xid/01lg39xalr04hou5q-ep043b
Out[2]=2

The closed-loop system:

In[3]:=3
✖
https://wolfram.com/xid/01lg39xalr04hou5q-htwnxn
Out[3]=3

The exosystem's states are part of the regulator:

In[1]:=1
✖
https://wolfram.com/xid/01lg39xalr04hou5q-8xa4ja
In[2]:=2
✖
https://wolfram.com/xid/01lg39xalr04hou5q-hji5ng
Out[2]=2

The closed-loop system:

In[3]:=3
✖
https://wolfram.com/xid/01lg39xalr04hou5q-ly5htl
Out[3]=3

The response:

In[4]:=4
✖
https://wolfram.com/xid/01lg39xalr04hou5q-inbizy
Out[4]=4

The system is regulated if pf is negative:

In[5]:=5
✖
https://wolfram.com/xid/01lg39xalr04hou5q-nu8uni
Out[5]=5

Regulate an AffineStateSpaceModel:

In[1]:=1
✖
https://wolfram.com/xid/01lg39xalr04hou5q-sddj7a
Out[1]=1

Regulate a NonlinearStateSpaceModel:

In[1]:=1
✖
https://wolfram.com/xid/01lg39xalr04hou5q-xiwndc
Out[1]=1

Specify the regulated outputs and feedback inputs:

In[1]:=1
✖
https://wolfram.com/xid/01lg39xalr04hou5q-ptvzc
Out[1]=1

Use LQRegulatorGains to compute the stabilizing gains by specifying the weights:

In[1]:=1
✖
https://wolfram.com/xid/01lg39xalr04hou5q-8o8m6q
Out[1]=1

Specify the gains to use:

In[1]:=1
✖
https://wolfram.com/xid/01lg39xalr04hou5q-p2ysoy
Out[1]=1

Applications  (6)Sample problems that can be solved with this function

Reject a disturbance modeled as :

In[1]:=1
✖
https://wolfram.com/xid/01lg39xalr04hou5q-pqn11a

The full model of the system with disturbance:

In[2]:=2
✖
https://wolfram.com/xid/01lg39xalr04hou5q-77gtvb
In[3]:=3
✖
https://wolfram.com/xid/01lg39xalr04hou5q-8cr9mb
Out[3]=3

The regulator:

In[4]:=4
✖
https://wolfram.com/xid/01lg39xalr04hou5q-8pn45c
Out[4]=4

The closed-loop system:

In[5]:=5
✖
https://wolfram.com/xid/01lg39xalr04hou5q-tkuy5g
Out[5]=5

The output is regulated in the presence of the disturbance:

In[6]:=6
✖
https://wolfram.com/xid/01lg39xalr04hou5q-2bpvmz
In[7]:=7
✖
https://wolfram.com/xid/01lg39xalr04hou5q-wmw4u1
Out[7]=7

Track an input modeled as :

In[1]:=1
✖
https://wolfram.com/xid/01lg39xalr04hou5q-5a8gm9

The full model of the system and input model:

In[2]:=2
✖
https://wolfram.com/xid/01lg39xalr04hou5q-cdl42x
In[3]:=3
✖
https://wolfram.com/xid/01lg39xalr04hou5q-ibddnl
Out[3]=3

The regulator:

In[4]:=4
✖
https://wolfram.com/xid/01lg39xalr04hou5q-jvlb1j
Out[4]=4

The closed-loop system:

In[5]:=5
✖
https://wolfram.com/xid/01lg39xalr04hou5q-ooq5wa
Out[5]=5

The output tracks the input:

In[6]:=6
✖
https://wolfram.com/xid/01lg39xalr04hou5q-vyyqfu
Out[6]=6

Simultaneously track a step input and reject a sinusoidal disturbance:

In[1]:=1
✖
https://wolfram.com/xid/01lg39xalr04hou5q-doy3xr
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/01lg39xalr04hou5q-klc2k1
Out[2]=2

The complete system:

In[3]:=3
✖
https://wolfram.com/xid/01lg39xalr04hou5q-zl4v3q
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/01lg39xalr04hou5q-odqckk
Out[4]=4

Obtain the regulator:

In[5]:=5
✖
https://wolfram.com/xid/01lg39xalr04hou5q-w97svn
Out[5]=5

The closed-loop system:

In[6]:=6
✖
https://wolfram.com/xid/01lg39xalr04hou5q-ktwtto
Out[6]=6

The simulation shows the output tracking a step signal:

In[7]:=7
✖
https://wolfram.com/xid/01lg39xalr04hou5q-0g88yk
Out[7]=7

Regulate an aircraft's longitudinal dynamics in the presence of disturbances:»

In[1]:=1
✖
https://wolfram.com/xid/01lg39xalr04hou5q-y3lb4i

The disturbances consist of two frequency components:

In[2]:=2
✖
https://wolfram.com/xid/01lg39xalr04hou5q-14b6v0

The complete system:

In[3]:=3
✖
https://wolfram.com/xid/01lg39xalr04hou5q-j95gbs
Out[3]=3

A control law that regulates the output (speed) in the presence of the disturbances:

In[4]:=4
✖
https://wolfram.com/xid/01lg39xalr04hou5q-tix8me
Out[4]=4

The closed-loop system:

In[5]:=5
✖
https://wolfram.com/xid/01lg39xalr04hou5q-1e0b5w
Out[5]=5

Simulation showing regulation being achieved:

In[6]:=6
✖
https://wolfram.com/xid/01lg39xalr04hou5q-kl30xb
Out[6]=6

The control effort:

In[7]:=7
✖
https://wolfram.com/xid/01lg39xalr04hou5q-log4o3
Out[7]=7

Regulate a Rössler prototype-4 system:»

In[1]:=1
✖
https://wolfram.com/xid/01lg39xalr04hou5q-qnma0x

Its chaotic behavior:

In[2]:=2
✖
https://wolfram.com/xid/01lg39xalr04hou5q-8nzejx
Out[2]=2

The complete model such that the state is regulated and kept constant:

In[3]:=3
✖
https://wolfram.com/xid/01lg39xalr04hou5q-vsgmni
Out[3]=3

A feedback law:

In[4]:=4
✖
https://wolfram.com/xid/01lg39xalr04hou5q-9jwmp1
Out[4]=4

The closed-loop system:

In[5]:=5
✖
https://wolfram.com/xid/01lg39xalr04hou5q-qhihbq
Out[5]=5

Simulations show that is regulated and the system has no chaotic behavior with feedback:

In[6]:=6
✖
https://wolfram.com/xid/01lg39xalr04hou5q-8blu31
Out[6]=6

Regulate the voltage in a Chua circuit to follow a sinusoid while rejecting a disturbance that is the output of another Chua circuit:»

The affine model of the Chua circuit where the nonlinearity is a cubic polynomial:

In[1]:=1
✖
https://wolfram.com/xid/01lg39xalr04hou5q-owf96l
In[2]:=2
✖
https://wolfram.com/xid/01lg39xalr04hou5q-y49ytn

The exosystem, where ω is the frequency of the sinusoid to be tracked:

In[3]:=3
✖
https://wolfram.com/xid/01lg39xalr04hou5q-v4mr7n
In[4]:=4
✖
https://wolfram.com/xid/01lg39xalr04hou5q-n9ipd2

The complete system:

In[5]:=5
✖
https://wolfram.com/xid/01lg39xalr04hou5q-6gbhuu
Out[5]=5

The poles of the disturbance model:

In[6]:=6
✖
https://wolfram.com/xid/01lg39xalr04hou5q-gwt7o3
Out[6]=6

The system poles consist of the three new poles and the stabilizable poles:

In[7]:=7
✖
https://wolfram.com/xid/01lg39xalr04hou5q-4pvrjo
Out[7]=7

The regulator:

In[8]:=8
✖
https://wolfram.com/xid/01lg39xalr04hou5q-xrmdal
Out[8]=8

The closed-loop system:

In[9]:=9
✖
https://wolfram.com/xid/01lg39xalr04hou5q-s5myjw
Out[9]=9

The simulation shows that the regulation is achieved:

In[10]:=10
✖
https://wolfram.com/xid/01lg39xalr04hou5q-kcesg6
Out[10]=10

Properties & Relations  (4)Properties of the function, and connections to other functions

StateFeedbackGains is a special case:

In[1]:=1
✖
https://wolfram.com/xid/01lg39xalr04hou5q-q2qlf6
In[3]:=3
✖
https://wolfram.com/xid/01lg39xalr04hou5q-leqj70
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/01lg39xalr04hou5q-5tt0ls
Out[4]=4

LQRegulatorGains is a special case:

In[1]:=1
✖
https://wolfram.com/xid/01lg39xalr04hou5q-29bv7p
In[2]:=2
✖
https://wolfram.com/xid/01lg39xalr04hou5q-unjs0m
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/01lg39xalr04hou5q-wrdtg7
Out[3]=3

Obtain the closed-loop system using SystemsModelStateFeedbackConnect:

In[1]:=1
✖
https://wolfram.com/xid/01lg39xalr04hou5q-3iqdmg
In[2]:=2
✖
https://wolfram.com/xid/01lg39xalr04hou5q-1qtz0r
Out[2]=2

Output regulation is achieved:

In[1]:=1
✖
https://wolfram.com/xid/01lg39xalr04hou5q-lrkd8o
In[2]:=2
✖
https://wolfram.com/xid/01lg39xalr04hou5q-dxgwfp
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/01lg39xalr04hou5q-ywbfrc
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/01lg39xalr04hou5q-5u7rsj
Out[4]=4
Wolfram Research (2014), FullInformationOutputRegulator, Wolfram Language function, https://reference.wolfram.com/language/ref/FullInformationOutputRegulator.html.
✖
Wolfram Research (2014), FullInformationOutputRegulator, Wolfram Language function, https://reference.wolfram.com/language/ref/FullInformationOutputRegulator.html.

Text

Wolfram Research (2014), FullInformationOutputRegulator, Wolfram Language function, https://reference.wolfram.com/language/ref/FullInformationOutputRegulator.html.

✖
Wolfram Research (2014), FullInformationOutputRegulator, Wolfram Language function, https://reference.wolfram.com/language/ref/FullInformationOutputRegulator.html.

CMS

Wolfram Language. 2014. "FullInformationOutputRegulator." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/FullInformationOutputRegulator.html.

✖
Wolfram Language. 2014. "FullInformationOutputRegulator." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/FullInformationOutputRegulator.html.

APA

Wolfram Language. (2014). FullInformationOutputRegulator. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FullInformationOutputRegulator.html

✖
Wolfram Language. (2014). FullInformationOutputRegulator. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FullInformationOutputRegulator.html

BibTeX

@misc{reference.wolfram_2025_fullinformationoutputregulator, author="Wolfram Research", title="{FullInformationOutputRegulator}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/FullInformationOutputRegulator.html}", note=[Accessed: 30-March-2025 ]}

✖
@misc{reference.wolfram_2025_fullinformationoutputregulator, author="Wolfram Research", title="{FullInformationOutputRegulator}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/FullInformationOutputRegulator.html}", note=[Accessed: 30-March-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_fullinformationoutputregulator, organization={Wolfram Research}, title={FullInformationOutputRegulator}, year={2014}, url={https://reference.wolfram.com/language/ref/FullInformationOutputRegulator.html}, note=[Accessed: 30-March-2025 ]}

✖
@online{reference.wolfram_2025_fullinformationoutputregulator, organization={Wolfram Research}, title={FullInformationOutputRegulator}, year={2014}, url={https://reference.wolfram.com/language/ref/FullInformationOutputRegulator.html}, note=[Accessed: 30-March-2025 ]}