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Description  |
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This invention relates to systems having automatic feedback capabilities
wherein the controller provides controls over inputs (manipulated
variables) to adjust a process or an environment, and wherein outputs
(controlled variables) from that controlled environment or process provide
inputs to the controller.
More specifically this patent provides a description of the controller
features which allow the controller to operate in a predictive manner on a
multiplicity of variables with the ability to perform nonlinear cost
minimization.
BACKGROUND OF THE INVENTION
Fundamental to the performance of any control algorithm, is its
servo-regulatory ability. That is, changes in the set-point should be
tracked quickly and smoothly and the controlled variable should be kept at
or near its set-point despite unmeasured disturbances affecting the
process. In addition the controller should maintain stability and
acceptable control performance in the face of structural and/or parametric
uncertainty. In certain applications the cost of providing effective
control is also a significant factor. While most multivariable control
laws utilize some form of cost minimization, the costs typically reflect
control movement rather than actual costs. The invention described in this
patent teaches a scheme that is based on minimizing costs while still
providing effective control. The nonlinear cost functions used in defining
the control sequence can be stated to reflect either actual operating
costs (dollars) or auxiliary costs (efficiency, quality, etc.) Cost
minimization is predicated on the assumption that there are more
manipulated variables than controlled variables. Thus it is up to the
controller to allocate the correct blend of the manipulated variables such
that both control and cost objectives are met. The control scheme
described herein was designed specifically to address these basic
criteria.
A predictive control law provides the fundamental structure for the new
controller. The adaptive controller utilizes a receding horizon
formulation. The receding horizon formulation can be used for
multivariable control with or without cost minimization. It can also be
used for robust univariate servo-regulatory control. Predictive control in
and of itself is by no means new. Indeed predictive control is the central
theme behind the benchmark works of Cutler and Ramaker in their Dynamic
Matrix Control (DMC) algorithm (Cutler, C. R., and B. L. Ramaker, "Dynamic
Matrix Control--A Computer Control Algorithm," Joint Automatic Controls
Concerence Proceedings, San Francisco (1980)) and Richalet et. al. in
their Model Algorithmic Control (MAC) algorithm (Richalet, J. A., A.
Rault, J. D. Testud, and J. Papon,, "Model Predictive Heuristic Control:
Application to Industrial Processes," Automatica 14, 413 (1978)).
Much of the current control work reported in the literature today is based
in some degree on these approaches. Horizon based prediction and control
has also been described and implemented in the past (Tung, L. S.,
"Sequential Predictive Control of Industrial Processes," Proc. ACC, San
Francisco (1983); Ydstie, B. E., L. S. Kershenbaum, and R. W. H. Sargent,
"Theory and Application of an Extended Horizon Controller," AlChE J., 31,
771 (1985); and Lee, K. S., and W. K. Lee, "Extended Discrete Time
Multivariable Adaptive Control Using Long Term Predictor," Int. J.
Control, 38, 495 (1983)). The unique aspects of the new control law
described herein are that it combines the attractive features of DMC and
horizon control and eliminates the inherent disadvantages of the original
formulations.
In DMC there is no direct mechanism to tune the controller. In addition the
size of the matrix to be inverted at each control update is specified by
the number of input terms used in the prediction. These deficiencies which
cause considerable practical difficulties in implementing a controller
based on such strategies can be eliminated by using a horizon formulation.
Unfortunately, previously known horizon based techniques do not eliminate
the impracticalities since the number of terms that need to be estimated
by the identifier depend on the horizon window. For many uses this can be
computationally too burdensome to be acceptable. In the new formulation, a
horizon based technique is utilized where the prediction is accomplished
using an auto-regressive moving average (ARMA) model in a recursive
fashion. In addition, the controller using the new control law described
herein allows for the direct imposition of constraints on both process and
control outputs at the end of the horizon window.
Use of optimization strategies in plant operation is also not a new
concept. Many optimization techniques are global strategies that determine
appropriate allocation levels among competing resources. Typically the
global approaches do not take into account transient performance at the
regulatory level. In a recent patent (U.S. Pat. No. 4,873,649) Grald and
MacArthur teach an on-line method for control of vapor compression space
conditioning equipment such that COP (coefficient of performance) is
optimized. The optimization technique however does not deal directly with
transient response and hence satisfactory servo-regulatory performance can
not be insured. Morshedi et al (Morshedi, A. M., C. R. Cutler, and T. A.
Skrovanek, "Optimal Solution of Dynamic Matrix Control with Quadratic
Programming Techniques (QDMC)," Proc. ISA, Part 1, 40 (1985)) describe a
pseudostatic approach for incorporating cost into the control design. In
their formulation the manipulated variables in question are assigned
pseudo set-points which are determined by solving a static linear
optimization subproblem for the final value of the inputs. The nominal
inputs are then treated as controlled variables with their set-points
given by the computed values of the steady state inputs. The conventional
control strategy is then augmented to reflect this additional information.
In the controller described in the instant patent, a technique for coupling
dynamic nonlinear cost minimization with uncompromised servo-regulatory
response is accomplished for the first time. While cost minimization is a
desirable option of the controller, robust servo-regulatory performance is
still the fundamental objective. To this end one simple form of the
controller uses a multivariable feedforward/feedback algorithm.
Feedforward compensation offers the potential for improved control
performance since it allows the controller to react before a measurable
disturbance has a chance to affect the response of the plant. In addition,
as will be described later, it provides the mechanism for coupling the
cost minimization to the desired servo-regulatory response.
To be effective, the controller requires an internal model that relates all
controller outputs and measurable disturbances to all process outputs.
(The process outputs are the outputs of the plant as indicated by sensing
means located proximate thereto.) The parameters of this internal model
are determined on-line by measuring the system response to the controller
outputs over time, and provide the adaptive ability of the controller.
Evaluation of the unknown model coefficients for each process output is
accomplished by a recursive least squares (RLS) estimate. Other standard
techniques may be used to accomplish this model identification and are
well known.
While techniques for model identification are well known, insufficient
excitation or inappropriate sample rate selection will render the
identification inaccurate. The invention described in this patent teaches
a method for automatically determining the correct control and
identification sample rate. In addition, a technique is given for
automatically selecting the horizon window and for adjusting the control
algorithm when excitation is insufficient for accurate model
identification.
SUMMARY OF THE INVENTION
With the advent of controllers having computer resources integrally built
in (or microcomputer-based controllers), more sophisticated control
functionality such as is taught in this patent is possible by utilizing
the memory and processing capability that accompanies the micro-computer
to implement a control program.
The main objective of the present invention is to provide a new and
improved means for efficient robust adaptive control with the ability to
control a plurality of process outputs such that operating efficiency is
maximized or operating costs are minimized.
Equipped with or connected to sensor means, microcomputer means, memory
means, and actuator means, the microcomputer-based controller can measure
the desired process output variables. From these measurements and user
inputs the controller can automatically determine the appropriate
identification and control sample rate as well as the horizon window,
estimate and continuously update a dynamic model of the process being
controlled, predict the future effect of current and past inputs on
process outputs over the horizon window, determine the appropriate
sequence of control moves to insure that all process outputs attain their
user specified set-point by the end of the horizon window, impose user
specified constraints on manipulated and controlled variables, determine
the control moves which result in minimum cost or maximum efficiency
without compromising servo-regulatory control, and output these efficient
control moves as signals to the actuators.
An exemplary use of the controller taught herein would be to employ it in
conjunction with a variable speed vapor compression heat pump to maintain
a comfort level set by the occupants of a building. In this exemplary use,
the occupants (user) would specify the setpoint (comfort level) and the
controller would adjust the compressor speed, blower speed and evaporator
superheat to maintain comfort at the desired set-point while insuring
maximally efficient operation. Since this strategy results in optimal
control, it is apparent that in steady state operation any other choice of
compressor speed, blower speed and evaporator superheat will result in
either increased energy consumption or reduced comfort.
Previous attempts at incorporating optimization into regulatory control
have failed to recognize that static or pseudostatic techniques do not
correctly deal with transient operation due to set-point or load changes.
A state-of-the-art configuration of the control system according to the
present invention provides a process control means having a microcomputer
with a real-time clock, memory and floating point processing. It will have
a data input means through which the user can specify desired set-points
and constraints, overriding the horizon determined by the tuner and
selecting perturbation step(s) for initial identification if desired, and
mode selection (auto, manual, tune). The system will likely have multiple
sensors for measuring all parameters necessary for control purposes
although in some instances only one sensor will be needed. There should be
at least as many sensor outputs as controlled variables. The system also
needs to be able to provide manipulated variable (also called control
output) signals to an actuator or actuators. In the preferred embodiment,
the adaptive receding horizon control program is in the controller's
memory; however, it is possible to implement the scheme in hardware. The
controller provides fundamental robust servo-regulatory control based on
multiple sensory data. The controller calculates the control and
identification sample rate and to synthesize a dynamic process model, and
predicts future effects of control moves on process outputs. The
controller also employs optimization to minimize operating cost without
compromising servo-regulatory behavior.
The above and other objects, features and advantages of the invention will
become more apparent from the ensuing detailed description taken in
conjunction with the accompanying drawings and appended claims.
In some situations, the Receding Horizon Control (RHC) may suggest control
moves which are greater than the actuator can perform. In such situations,
it is useful to use other manipulated variables to control other actuators
to assist in accomplishing the desired result or achieving set point. The
ability to switch to other control actuators can be accomplished with some
additional features described herein. These additional features also
accommodate situations wherein one wishes to not only avoid only the
unacceptable control instructions but also to enhance the cost control
function by assigning a primary status to control moves of the less costly
function(s) and secondary status to control moves of more costly control
function(s). These additional features include having a separate RHC for
each of the manipulated variables and setting each RHC for a new feedback
data path and adding a constraint handling logic selector which both
selects which RHC output to use, and may also provide feedback to one or
more RHC units.
The concept is taught with reference to a two-actuator system having cubic
feet per minute (CFM) and compressor revolution per minute (RPM) actuators
(a fan and a compressor motor), as would be typical in a heating or
cooling air system. A CFM move is considered less costly, in general, than
an RPM control move.
In the event the CFM control move that is required to satisfy the criteria
for the controller is out of range for the CFM fan to accomplish, the
system will accommodate this by making an RPM control move. In the cost
function case, where the size of the CFM control move required for
achieving set point is not near the least cost curve, and where the same
or better result can be achieved with an RPM control move, the RPM control
move is made. The cost function in this example is called the Coefficient
of Performance, or COP, by those of ordinary skill in this industry.
In this invention this is done by the constraint handler determining that
at least some portion of the CFM-Primary sequence of control moves are for
out-of-range (or out of proper cost) conditions. Where that is the case,
feedback is supplied to the RPM optimizing RHC indicating that CFM is
constrained. The RPM optimizing RHC then uses these constrained values and
computes the control moves for RPM required to achieve setpoint within m
control moves and maintain stability for m and L control moves with the
constrained CFM.
The end result of this process is a CFM and RPM control value supplied to
the process (55 of FIG. 15). A multiplicity of RHC units may be configured
into a larger system having a multiplicity of control outputs (n in FIG.
16).
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a block diagram of the preferred embodiment of the control system
showing interactive channels between elements.
FIG. 2 is a graph used to show the concept used by the tuner to evaluate
critical process response parameters for use in determining sample rate
and horizon window.
FIG. 3 is a graph of the performance of the tuner with 50% full scale
noise.
FIGS. 4a and 4b are graphs of a response variable and a manipulated
variable, respectively, illustrating the hueristics used for control
adaptation during process upsets.
FIG. 5 is a graph of two response trajectories, illustrating the horizon
concept for a SISO process for use in deriving the fundamental control
law.
FIGS. 6a and 6b are graphs of the response variable and the manipulated
variable, respectively, showing typical receding horizon performance for a
highly underdamped SISO (Single Input, Single Output) process.
FIG. 7 is a graph of a steady state cost surface for a particular process.
FIGS. 8a and 8b are graphs of the response and manipulated output
variables, respectively, showing the servo-performance of the controller
for set point response without cost minimization.
FIGS. 9a and 9b are graphs of the same variables used in FIGS. 8a and 8b,
respectively, and show the servo-performance of the controller for set
point response with cost minimization taught by this patent.
FIGS. 10a and 10b are graphs of the response and manipulated output
variables, respectively, showing the servo-performance of the controller
for set point response with steady state cost minimization.
FIGS. 11a and 11b are graphs showing cost performance of the controller
corresponding to the servo-performance illustrated in FIGS. 8a through
10b.
Paired FIGS. 12a and 12b, and 13a and 13b are graphs of the response and
manipulated output variables, respectively, in each pair, showing
controller performance for various set point and load disturbances.
FIGS. 14a and 14b are graphs showing cost performance of the controller
corresponding to the servo-regulatory performance illustrated in FIGS. 12a
through 13b.
FIG. 15 is a block diagram illustrating a preferred embodiment having
additional features to enhance cost control and resolve actuation
constraints.
FIG. 16 is a heuristic block diagram of extensions to the basic two-RHC
design, having more than two RHC's.
FIG. 17 is a flow chart.
FIG. 18 is a paired set of line charts, showing the effect on m and n on
control performance where l=3.
FIG. 19 is a line chart showing the effect of l on control performance
(augmented prediction, m=6, n=0).
DESCRIPTION OF THE PREFERRED EMBODIMENT
A preferred embodiment of the control system of the invention will now be
described with reference to FIG. 1. As shown in FIG. 1, the controller is
composed of several interacting components. The overall block diagram of
the dynamic system 10 comprises both the controller (which has components
23, 24, 25, 26, and 28 and works with the inputs from interface unit
(sometimes called a sequencer 27)) and the environment (identified as
plant 20) for which the controller is responsible. The plant 20 may be
exposed to unmeasured disturbances represented here by disturbance 21,
which may affect the plant 20 but which is only measurable by its
influence on the plant output(s) 22. At least one and probably a
multiplicity of sensors are provided that measure and report on the plant
20 (but are not shown). These sensors monitor and report on the output(s)
22 from plant 20. For example, to reference the heat pump mentioned in the
Summary of the Invention, the sensors may measure the humidity,
temperature, et cetera. As illustrated in FIG. 1, the outputs of these
sensors are shown as line 22. These output(s) provide input to and affect
the tuner 23, the identifier 24, the predictor 25, the control law 26 and
indirectly the optimizer 28.
Analog to Digital (A/D) and Digital to Analog (D/A) conversion boxes are
shown at locations 1 and 2 to indicate appropriate placement. However, if
the entire controller, or parts thereof are implemented in analog
components whether different placement or removal would be indicated, as
will be apparent to one of ordinary skill in this art.
Data input means are provided for establishing a link between the user and
interface unit 27. User input data is accomplished via user manipulation
of this interface 27. The user may change the horizon window, define cost
functions or, to cite a simplistic single variable example, change the
set-point. Various forms of interface devices may be used without
deviation from this invention.
Components 23, 24, 25, 26, and 28 provide the fundamental features of the
controller. These elements can be configured in either software or
firmware as desired by the builder of the controller. A brief description
of the functionality of each component follows.
Outputs from the sensing elements at plant 20 and outputs from the
interface unit 27 are either converted to, or already are in digital form.
These signals are supplied to a microcomputer device in the controller
which may be a single processor performing variety of the component
functions over time, as directed by programming control, as will be
understood by one of ordinary skill.
Tuner 23 is responsive to said sensing element output(s) and interface 27
output as well as to the outputs of control law calculator 26 and
identifier calculator 24. The tuner is activated upon start-up, i.e., when
the controller is commissioned. In the manual mode (a mode in which the
manipulated variables are held fixed as set directly by the user), the
tuner forces a step change to each of the controller outputs 29. Said
tuner monitors the process response and based on the time history of the
process response, selects the appropriate control and identification
sample rate as well as the horizon window, and makes these parameters
available as outputs.
After the appropriate sample rate and horizon have been determined, the
tuner invokes identifier calculator 24 which is responsive to sensor
outputs 22 and the outputs of the control law calculator and said tuner
calculator. The invocation is done in the preferred embodiment by having
the tuner repeatedly send data as it is developed by the tuner. Data
recorded by tuner calculator during the open loop step is then used to
drive said identifier. The output of said identifier calculator is the
dynamic process model. As discussed in the Summary of the Invention, any
number of modeling techniques could be employed. Once identification is
complete, the model is then made available to predictor calculator 25 and
said control calculator 26.
The manual mode is then terminated and automatic control commences. At this
point, the identifier remains active continually monitoring the process
response. Said tuner is also used to monitor the process in normal
automatic (also called closed loop) operation. If the control performance
degrades, said tuner will adjust the control parameters in a heuristic
fashion based on frequency response data. If control performance is
unacceptable, said tuner will recommission itself as described above.
The optimizer calculation means 28 is responsive to said control and
predictor calculation means. Said optimizer 28 continuously searches for
alternate control sequences that result in a lower cost of operation.
Within each time step said optimizer uses both 25 and 26 to determine the
control moves that result in minimum cost yet offer uncompromised
servo-regulatory control performance.
The control sequence is determined by said control law calculator 26 based
on said predictor calculator 25. Said predictor 25 is responsive to the
tuner, the control calculator, and uses the discrete time model obtained
from the identifier to determine the nominal output trajectory that would
occur if no future changes are made to the input. The output of the
predictor calculator is the nominal output trajectory which is based on
current and past recorded data. The control calculator is responsive to;
interface 27, prediction calculator, tuner, identifier calculator, and
optimizer calculator for affecting the calculation of the values for each
of the manipulated variables. The control variable command signals may be
converted to analog outputs by a D/A converter where the equipment
requires analog input.
In the discussion below, a more detailed description of the tuner, the the
control law calculator, the predictor calculator, and the optimizer will
be given.
THE TUNER
As described previously, the primary function of the tuner is to select the
appropriate control and identification sample rate and the horizon window.
These parameters can be directly determined from the open-loop response
characteristics of the process. The selection is based on settling time
for overdamped open-loop processes and on rise time and period of
oscillation for underdamped open-loop processes. For overdamped systems
the sample rate is determined by recording the settling time and dividing
this number by five times the minimum number of terms in the predictive
model. For underdamped systems the sample rate is determined by recording
the time to reach the second inflection point and dividing this number by
five times the minimum number of terms in the predictive model. For
open-loop-unstable processes, the sample rate is determined by recording
the time taken to exceed a predefined range limit (set by the user). This
number is then divided by twice the minimum number of terms in the
predictive model to determine the sample rate. The default horizon is set
to fifteen times the sample rate. While other numbers could be used,
experience shows these to be most reliable.
The following is a detailed description of the method used for determining
an appropriate horizon overdamped systems. The basic concept is to apply a
step in the process input and observe the process output in order to
determine the maximum slope, the time at which it occurs, the magnitude of
the output at that time, and ultimately the settling time of the response.
Establishing reliable time/slope data with no a priori process knowledge
in spite of noise-corrupted data is the primary contribution of the tuner.
Although for overdamped systems the settling time is itself sufficient to
determine the window and sample rates for the preferred implementation,
the approach can also be used to fit a second order model with delay to
the observed data. Numerical techniques relating the transport delay, gain
and time constants to the time/slope information are well known and will
not be discused here.
FIG. 2 illustrates graphically the concept used by the tuner. The tuner
assumes the value of the output will start at zero and makes sure the
output value changes in the positive direction when the step in the input
occurs. Based on the direction of the control input step and the direction
of control (reverse- or direct-acting), the expected direction of movement
of the output is determined. If a negative change is expected, the output
is multiplied by -1. This output value, which starts at zero and changes
in the positive direction, is what is referred to as "the output" in the
remaining of the description of the tuner.
To reduce the effect of noise, the output is averaged over a number of
samples. The number of samples used depends on the response of the system
and is determined differently in various stages of the analysis. A running
sum of the output is kept, and when established criteria (described in the
following paragraphs) are met, this sum is divided by the number of
samples included in the summation to yield the average output value for
that time period. The goal is to average over as many steps as possible to
allow the algorithm to function accurately in the presence of large noise
levels, without letting the average continue right through the significant
changes in the output. The averaged output value is referred to as "y",
and the slope of y with respect time as "dy". The time, referred to as
"t", associated with each y value is the time at the middle of the range
of samples averaged. The slope associated with a given y and t is
calculated as the average of the slopes from y to the previous y and from
y to the next y.
The tuner begins by looking for the point at which the slope begins to
decrease (the inflection point). When the inflection point is found, a
parabola of dy as a function of t is fit to the first point at which the
slope decreases and the two which precede it. The slope and time of the
inflection point are determined by finding the maximum dy of the parabola
and the associated time. The y value at the inflection point is obtained
by interpolation. These values are saved as t1, y1, and dy1. In the
presence of noise, false inflection points may be found (when the slope in
the noise decreases), but these are detected and handled in the later
phases of the analysis.
The length of time over which to average for this initial stage of the
analysis is limited by two criteria. When one average is calculated, a y
limit and a t limit are set and when either one of these limits is
exceeded, the next average is calculated. The time limit is set to the
twice the previous time limit, with an initial time limit of one time
step. The y limit is set to 1.4 times the largest non-averaged y value
occurring since the beginning of the run. The y limit is the most
important because it is the one which determines the appropriate spacing
of the averages through the significant changes in the output. By the time
the output reacts to the step input, the t limit can grow to be large
enough to miss the entire change in the output, but the y limit (which
gets set to 1.4 times the noise) forces the averaging to occur frequently
enough to provide several data points through the area of the inflection
point. If, instead of 1.4, a smaller value were used the allowable noise
to signal ratio of the system would be reduced, since the averages would
be calculated more frequently and the effect of the noise would be reduced
less. If a much larger value were used, the y limit would be set above the
line-out value of the output before the inflection point was found meaning
it would be missed completely.
In the next phase of the analysis, the tuner will determine whether it has
found a false inflection point. It will look for the point where the slope
decreases to less than 80% of the slope at the inflection point. If,
during this phase, the slope either increases twice in a row or becomes
greater than the slope at the inflection point, the inflection point is
considered to be false and the tuner reverts back to the initial phase and
looks for another decrease in slope. In this phase and in later phases,
the y limit is abandoned and a time limit equal to the total time spanned
by the three averages around the inflection point is used. When a slope
less than 80% is found, the t, y, and dy values are saved as t2, y2, and
dy2. (The 80% figure has yielded good results, but a similar number could
be employed.)
In the third phase of the analysis, the tuner is just looking to make sure
it was not just an artifact of the noise that created an apparent
inflection point. The time limit for the averages is set equal to t2 minus
t1 (the time to get from maximum slope to 80% slope). If the slope
increases or goes negative in either of the next two averages, the
inflection point is considered false and again the tuner reverts back to
the initial phase and looks for another decrease in slope. Beyond this
phase there are no more checks for false inflection points, but one could
include more if desired.
In the final phase of the analysis, the tuner determines the settling time.
The time limit used is the same as in the previous phase. There are three
criteria, any one of which is considered to constitute line-out (also
known as reaching approximate steady state): (1) if the absolute value of
the slope is less than 5% of dy1 (the slope at the inflection point) three
times in a row; (2) if the value of y decreases and remains lower than its
largest value for three averages in a row; or (3) after ten averages are
calculated in this phase.
FIG. 3 shows a process reaction curve contaminated with noise. The actual
process has a transport delay of 200 seconds, a unity gain and two time
constants of 150 and 160 seconds. The tuner was able to determine settling
time, and the maximum slope and the time at which it occurred with
sufficient accuracy to identify the process time constants, gain and
transport delay with a maximum error of 10%.
The tuner also acts as a heuristic supervisor which monitors the controller
output (manipulated variable, also line 29 of FIG. 1) and the measured
process output (process variable, also line 22 of FIG. 1) for symptoms of
system instability during automatic control mode. Upon detection of
unacceptable system stability, the tuner, acting as heuristic supervisor,
applies a set of recovery rules to stabilize the system.
The heuristic supervisor's corrective actions may include changing the
identified process model or altering the horizon window to recover from
the observed instability. In the preferred embodiment the heuristic
supervisor is limited to one model change per system upset (set-point
change or system disturbance) but can alter the horizon window any number
of times. If a model change has been necessary to stabilize the system,
the heuristic supervisor switches the controller into manual control mode
and forces a complete system re-tune as described previously.
The heuristic supervisor monitors the process variable at all times during
automatic control mode whereas the manipulated variable is monitored only
after a window is computed directly from observed system dynamics. The
formulation of this manipulated variable observation window is discussed
below.
The process variable parameters identified by the heuristic supervisor
during a system upset are shown in FIGS. 4a and 4b. These are the peak
amplitudes, a.sub.1 a.sub.2, the dimensionless amplitude decay ratio, d,
the period of oscillation, p, and the closed loop settling time, T.sub.s.
The amp | | |
