help_imc.hlp

内模控制器（IMC）工具箱。包括参数整定、PID控制器参数转换等

EDIT SPECIAL

Use this option to enter a process/model/controller in case its
LaPlace form cannot be entered in the standard form of

	    Polynomial1
Process =  ------------- * exp(-T*s)
	    Polynomial2

with independently varying uncertain parameters.
Example:

          K*(1+exp(-T*s))
P1 = -------------------------------
      (Tau1*s+1)*(Tau2^2*s^2+Tau2*s+1)


would be entered as

P1 = x(1)*(1+exp(-x(2)*s))/(x(3)*s+1)/((x(4)*s)^2+x(4)*s+1)


Enter the model in similar fashion 

M1 = 10*(1+exp(-5*s))/(3*s+1)/(s^2+s+1)

or, for example with an uncertain gain for optimality calculation

M1 = y(1)*(1+exp(-5*s))/(3*s+1)/(s^2+s+1)


and a full IMC controller, e.g.

Q1 = (3*s+1)*(s^2+.5*s+1)/10/(e*s+1)^3   with "e" as the filter
                                         time constant.

or, for example with an uncertain gain for optimality calculation

Q1 = (3*s+1)*(s^2+.5*s+1)/y(1)/(e*s+1)^3


!!! Watch the syntax !!! Any syntax error will result in stopping
all routines (with a beep) when they encounter the error. If 
an error is detected, check the entries. It is up to the user to
enter the correct number of uncertain parameters and their bounds.
The error checking routines which work with the normal edit 
windows do not work with the edit special window. Also, the IMC
Time Response window does not work when the process is entered
through the edit special window. The PID controller calculation
does not work when the model or the controller is entered through
the edit special window.

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		VIEW functions
		**************


PROCESS

Allows the user to view entered process, model, controller and
a disturbance lag time constant with associated time constant 
Alpha for the qd portion of 2-degree-of-freedom controller

      Alpha*s+1
qd = -----------
        e*s+1


Also, the ranges for all uncertain process and model parameters 
are displayed.

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DEFAULT VARIABLES

Displays current values of all parameters and control variables.

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		COMPUTE functions
		*****************


ONE-DEGREE-OF-FREEDOM CONTROLLER TUNING

Automatically finds a filter time constant for an IMC controller
such that both the Maximum peak and Noise amplification criteria
are satisfied for the complementary sensitivity function. Shows 
intermediate results in the command window (press the space bar 
to follow the computations). The command window also shows the
results of the computations and provides the filter time constant,
the frequency and value of the maximum peak and process parameters 
associated with the maximum peak.

Minimal inputs:
- an uncertain process
- a model 
- a part of the model to invert
- uncertainty limits on all process parameters

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TWO-DEGREE-OF-FREEDOM CONTROLLER TUNING

Automatically finds a vector of two filter time constants for 
a 2-degree-of-freedom IMC controller such that both the Maximum 
peak and Noise amplification criteria are satisfied for both 
sensitivity and complementary sensitivity functions. Finds 
a minimal Maximum peak of sensitivity functions if the 
pre-specified Maximum peak is not achievable.)* Shows intermediate 
results in the command window (press the space bar to see it) 
as well as final results of the computations such as the filter 
time constant, the frequency and the value of the maximum peak 
and the process parameters associated with the maximum peak.

Minimal inputs:
- an uncertain process (with uncertain disturbance lag)
- a model (with a disturbance lag)
- a part of the model to invert
- uncertainty limits on all process parameters

)* Finds only a minimal Maximum peak of sensitivity functions
   in this version of the program.

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FIND OPTIMAL MODEL

Finds an optimal model from given range of models. The optimality 
criterion is to speed up the slowest response of all possible
closed loop responses of all possible plants. Works only for
1-degree-of-freedom SISO control systems in this version of 
the program.

Minimal inputs:
- an uncertain process
- a model with some its parameters allowed to vary (equivalent
  to "uncertain" parameters)
- a part of the model to invert; some parameters may also vary
  !!! if a gain of a model varies, gain of the invertible part must
  also vary !!!
- uncertainty limits on all process parameters
- model range limits and a nominal model (a starting point in the
  optimal model calculations that is also used as a fixed model
  in all other calculations)
- in default variables: a 1-degree-of-freedom SISO IMC control structure
  must be defined

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FIND UNCERTAINTY BOUNDS

An inverse procedure to tuning. Given a control system it finds
allowed percentage of uncertainty for which a performance criterion
will be satisfied. Works only for 1-degree-of-freedom SISO control 
systems in this version of the program.

Minimal inputs:
- an uncertain process
- a model 
- a part of the model to invert
- a nominal plant around which the uncertainty limits will be calculated
  (in the process uncertainty limits window)
- in default variables: a 1-degree-of-freedom SISO IMC control structure
  must be defined

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TUNING FOR SATURATION

A filter time constant is found that satisfies a performance criterion
of a model state feedback implementation of an IMC controller in
the presence of saturation.

Minimal inputs:
- an "uncertain process" consisting only of an uncertai gain
  (numerator = u ; denominator = 1) that substitutes for the
  saturation block
- a model 
- a part of the model to invert
- uncertainty limits (lower bound =0; upper bound =1) on the
  "uncertain process gain"
- in default variables: an "imc1msf" control structure
  must be defined

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1 and 2-DEGREE-OF-FREEDOM PID CONTROLLER

Finds PID equivalent for given IMC controller.

The results are shown in the command window. Also, they
can be viewed using the PID controller Results option.
Shows setpoint and disturbance step responses of all stable 
realizable PID controllers and an IMC controller as shown 
in the title of the graphs. Click the Change button to change
the final time and step size. Click any spot in the graph 
to see its coordinates. Press space to see transfer functions
of PID controllers

Minimal inputs:
- a model (optionally with a disturbance lag)
- a part of the model to invert
- a filter time constant (a vector of two filter time constants
  for a 2-degree-of-freedom PID controller)

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UPPER BOUND

Computes an Upper bound of the frequency responses over the range 
of frequencies specified in the Default Variables Edit window for 
all possible processes. Shows the graph. Press the space bar to 
follow the computations.

Click the Add button to add a frequency response of any plant.
Enter the plant parameters inside the rectangular box of the Edit
window. Click the OK button. Click any spot in the graph to see
its coordinates.

Minimal inputs:
- an uncertain process
- a model 
- a part of the model to invert
- uncertainty limits on all process parameters
- in default variables: a SISO control structure must be defined
  (also the filter time constant, frequency range and number of 
  points per dacade are relevant parameters here)

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LOWER BOUND

Computes a Lower bound of the frequency responses over the range 
of frequencies specified in the Default Variables Edit window for 
all possible processes. Shows the graph. Press the space bar to 
follow the computations.

Click the Add button to add a frequency response of any plant.
Enter the plant parameters inside the rectangular box of the Edit
window. Click the OK button. Click any spot in the graph to see
its coordinates.

Minimal inputs:
- an uncertain process
- a model 
- a part of the model to invert
- uncertainty limits on all process parameters
- in default variables: a SISO control structure must be defined
  (also the filter time constant, frequency range and number of 
  points per dacade are relevant parameters here)

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BOTH UPPER AND LOWER BOUND

Computes both Upper and Lower bound of the frequency responses 
over the range of frequencies specified in the Default Variables 
Edit window for all possible processes. Shows the graph. Press 
the space bar to follow the computations.

Click the Add button to add a frequency response of any plant.
Enter the plant parameters inside the rectangular box of the Edit
window. Click the OK button. Click any spot in the graph to see
its coordinates.

Minimal inputs:
- an uncertain process
- a model 
- a part of the model to invert
- uncertainty limits on all process parameters
- in default variables: a SISO control structure must be defined
  (also the filter time constant, frequency range and number of 
  points per dacade are relevant parameters here)

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		RESULTS functions
		*****************


IMC CONTROLLER

Displays the transfer function of an IMC controller as well as
current filter time constant.

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PID CONTROLLER

Displays the ideal and realizable PID equivalents of the IMC 
controller.

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WORST CASE PARAMETERS

Displays the values of uncertain parameters, frequency and filter
time constant for which the Maximum peak was achieved.

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FREQUENCY RESPONSES

Shows previously computed bounds of closed loop frequency 
responses. Closed loop frequency responses can then be added
for any plant.

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IMC TIME RESPONSES

Calculates and shows closed loop responses (for a particular plant
at a time) to setpoint/disturbance step changes. 

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