Note: Descriptions are shown in the official language in which they were submitted.
INTEGRATED QUADRATIC CONTROL OF INDUSTRIAL PROCESSES
TECHNICAL FIELD
[0001] The present disclosure relates to industrial process control
systems and in
particular to control optimization of multivariable industrial process control
systems.
BACKGROUND
[0002] Industrial processes such as manufacturing plants, chemical
plants, refineries
or ore processing plants utilize multiple control systems throughout the
stages of the
processes. The process control systems manage the use of loads within the
process. The
load may be for example motors, generators, valves, pumps, actuators,
conveyors, or
industrial equipment in the production process with each component potentially
having
operational constraints which impact the overall production output. Optimizing
the output
of the industrial process, defined as the profit of the system, can be complex
due to the
multiple operational constraints of each of the loads within the system
comprising the
industrial process. The interaction of the loads within the process impact the
output/profit
of the entire process. Achieve optimal operation of each load to achieve the
optimal output
present significant challenges.
[0003] Various types of industrial controllers such as Model
Predictive Control (MPC)
or Proportional-Integral-Derivative (PID) controllers are used to provide a
method of process
control while satisfying a set of constraints. However, optimization of these
controllers when
used in a multivariable environment presents complexities in determining the
optimal overall
profit for the process while managing the variables of each load within the
process.
[0004] Accordingly, systems and methods integrated quadratic control
of
multivariable industrial process control remains highly desirable.
- 1 -
Date Recue/Date Received 2021-10-08
BRIEF DESCRIPTION OF THE DRAWINGS
[0005]
Further features and advantages of the present disclosure will become
apparent from the following detailed description, taken in combination with
the appended
drawings, in which:
FIG. 1 shows a representation of industrial process utilizing an integrated
quadratic
control system;
FIG. 2 shows a method of instigated quadratic control;
FIG. 3 shows a method determining QP-optimized proportional action gains;
FIG. 4 shows an integrated in closed loop block diagram.
[0006] It will be noted that throughout the appended drawings, like
features are
identified by like reference numerals.
- 2 -
Date Recue/Date Received 2021-10-08
DETAILED DESCRIPTION
[0007] Embodiments are described below, by way of example only, with
reference to
Figs. 1-4.
[0008] A system of one or more computers can be configured to perform
particular
operations or actions by virtue of having software, firmware, hardware, or a
combination of
them installed on the system that in operation causes or cause the system to
perform the
actions. One or more computer programs can be configured to perform particular
operations
or actions by virtue of including instructions that, when executed by data
processing
apparatus, cause the apparatus to perform the actions. One general aspect
includes a
method of operating an industrial process by an integrated quadratic
controller (IQC). The
method also includes determining a target process value (PV) associated with
an output of
the industrial process defining a single-input of a multiple-outputs (SIMO)
process;
determining manipulated-variables (MVS) associated with a plurality of loads
within the
industrial process, where each of the MVS is associated with one of the
plurality of loads
controlling a rate of operation associated with the load impacting the PV of
the industrial
process; determining quadratic programming (QP) optimized proportional action
gains for
the determined MVS given an updated control variable PV; integrating QP gain-
modified
proportional action into a control system of the industrial process; and
applying modified
control system to update my output state map defining multiple outputs to
control
respective loads in the industrial control process for achieving the target
PV. Other
embodiments of this aspect include corresponding computer systems, apparatus,
and
computer programs recorded on one or more computer storage devices, each
configured to
perform the actions of the methods.
[0009] Implementations may include one or more of the following
features. The
method where applying the modified control system to update my output state
map further
may include: sending the determined my control values to the respective load
controllers,
and determining the my result on PV of the industrial process from the
application of the my
control values. The method may include for each of the MVS, determining a
maximum value
and a minimum value range associated with the respective MV. The method may
include
sending the determined MV control values to respective load controllers. The
method may
- 3 -
Date Recue/Date Received 2021-10-08
include for each respective my of the MVS if the respective my has reached a
maximum value
and removing the respective my from the QP optimized proportional action. The
method may
include: modifying MV values within the range of the determined maximum value
and
minimum value range, and determining QP allocation of proportional gain
weights for MVS.
The load is associated with an industrial component having an associated
control interface.
The industrial component is one of a motor, a generator, a valve, a pump, an
actuator, or a
conveyor. Implementations of the described techniques may include hardware, a
method or
process, or computer software on a computer-accessible medium.
[0010] One general aspect includes a system of operating an industrial
process. The
system of operating also includes a plurality of loads forming part of the
industrial process,
each load having an associated process controller for manipulating a
respective manipulated-
variable (MV) associated with the load controller for controlling a rate of
operation of the
respective load; and an process controller coupled to the controllers of the
plurality of loads
through a network, the process controller may include: a processor; and a
memory coupled
to the processor, the memory containing instructions to determining a target
process value
(PV) associated with an output of the industrial process defined by a single-
input multiple-
output (SIMO) system, determining quadratic programming (QP) optimized
proportional
action gains for the determined MVS given an update control variable PV, the
QP gain-
modified proportional action is integrated into a control system executed by
the IQC, which
is applied to modified control system to update MV output state map defining
the multiple
outputs to control respective load controllers in the industrial control
process for achieving
the single input defined by the target PV. Other embodiments of this aspect
include
corresponding computer systems, apparatus, and computer programs recorded on
one or
more computer storage devices, each configured to perform the actions of the
methods.
[0011] Implementations may include one or more of the following features.
The
system where the my control values from the MV output state map is sent to the
respective
load controllers for application by the respective load. For each of the MVS,
a maximum value
and a minimum value range associated with the respective my are defined for
the respective
load controllers. The process controller, for each respective my of the MVS if
the respective
my has reached a maximum value and removing the respective my from the QP
optimized
- 4 -
Date Recue/Date Received 2021-10-08
proportional action. The my values are modified within the range of the
determined
maximum value and minimum value range and are QP allocated by proportional
gain weights
for MVS. The load is associated with an industrial component having an
associated control
interface for interfacing with the respective load controller. The industrial
component is one
of a motor, a generator, a valve, a pump, an actuator, or a conveyor. The
process controller
is incorporated in a proportional-integral-derivative (PID) controller. Each
of the load
controllers are an industrial control system (ICS). Implementations of the
described
techniques may include hardware, a method or process, or computer software on
a
computer-accessible medium.
[0012] The disclosed integrated quadratic controller (IQC) provides an
elegant way to
negotiate maximum feed-rate across multiple manipulated variables (MVs). With
a single
manipulated variable the IQC (i.e. at the limit) when applied to proportional-
integral-
derivative (PID) controller behaves exactly the same as the traditional PID.
For multiple MVs
a quadratic programming (QP)-optimized control is applied with respect to
proportional
.. action that ends up maximizing profit according to the QP form at the
execution (scan-to-
scan) level. QP is the process of solving mathematical optimization problems
involving
quadratic functions by seeking to optimize (minimize or maximize) a
multivariate quadratic
function subject to linear constraints on the variable. Final convergence
(linear programming
(LP) vertex or QP optimal, etc.), depends if velocity form is used (is like
derivative with respect
to x of QP = LP) or not and whether profits are dynamically modified. The
function described
can be integrated in existing control methods and can provide multivariable
control of a
single constraint with multiple outputs, mid-ranging control and single
variable traditional
controllers control for enhanced saturation recovery.
[0013] A single constraint variable may be controlled using multiple
outputs. Each
load can be tuned like a traditional controller, such as a PID controller, and
the profit
designation along with the maximum constraint dictates how each load optimizes
their
output to maximize total profit. For mid-ranging control, duty is allocated by
the IQC
according to the relative differences between the profits and the optimizer
will not attempt
to optimize profit on its own.
- 5 -
Date Recue/Date Received 2021-10-08
[0014] In industrial processes multiple steps of the process 140 can
have multiple
stages each having a respective load as shown in Figure 1. Each operation
stage of the
process 140 is controlled by a respective controller 130, 132, 134, 136
controlling respective
loads such as for example motor 142, valve 144, pump 146 and motor 148. The
load at each
of the stages need to be controlled for efficient operation of the overall
process. The output
of the process 140 can be defined as a the profit of the process. The profit
may be adjust
based upon the variables of each step. The load controllers 130, 132, 134 and
136 can be
controlled, via a network 120, by an integrated quadratic controller (IQC)
100. Various
control algorithms in industrial control systems (ICS) may be utilized by each
controller based
upon the type of load and the respective parameters, such for example a
programmable logic
controllers (PLCs), distributed control systems (DCS) and supervisory control
and data
acquisition (SCADA) controller.
[0015] The IQC 100 comprises one or more processors 110, coupled to a
memory 112
which contain instructions that are executed by the processor 110 to control
the process. A
non-volatile storage 116 can contain the instructions, processing data,
control parameters
and codes for executing functions of the IQC 100. An input/output interface
114 couples the
memory to the network 120 and other computer interfaces to enable access and
control of
the IQC 100. The IQC 100 integrates a quadratically optimized proportional
feedback
response into the controller that may include other control elements such as
integral action,
derivative action, and feed-forward to name a few.
[0016] In the IQC 100, the optimized proportional feedback response
acts
proportionally to the change in the process value (PV) or the controller error
(set-point minus
PV) is shaped by a quadratic program. While the IQC 100 may be applied to
single input (single
control variable) ¨ single output (single manipulated variable) processes, IQC
100 is an
exceptional multivariable controller for single-input multiple-output (SIMO)
systems. As a
SIMO controller, the integrated quadratic proportional feedback response
optimizes the
entire set of manipulated variable outputs such that an optimal, maximum
profit, system
state is achieved. IQC 100 can be implemented as a velocity-form controller (a
controller that
acts on the change of the controller PV or error between controller
executions) that
quadratically allocates the incremental (velocity) proportional feedback
response to the
- 6 -
Date Recue/Date Received 2021-10-08
current state of the constrained set of outputs. Internally, as a velocity
form controller the
objective function flips between solving a quadratic program that maximizes
profits and one
that minimizes costs depending if the change in PV tends away from a
constraint limits or
towards it, respectively.
[0017] IQC 100, as a velocity form controller, effectively converges to the
vertex of a
linear optimal solution that first maximizes the most profitable control
outputs subject to
their constraints and may converge to a quadratic or higher order optimal
solution when the
profits are dynamically set. A velocity form controller is more desirable than
a position form
controller (a controller that acts directly on the PV or error) as it provides
more flexibility as
the profits may be dynamically set without sudden transitions to the
manipulated outputs
and the outputs can start off at any state and converge to an optimal solution
at a tunable
response speed.
[0018] The IQC 100 can adopt other control elements such as integral
feedback and
derivative feedback for example. In application, IQC 100 is capable of
optimizing SIMO
problems using the relative profit values of each control output and can be
readily deployed
as an advanced multivariable controller with minimal complexity as relative
profit is the only
additional tuning parameter on top of proportional gain. In comparison, IQC
100 is superior
to model predictive control (MPC) for SIMO problems where the disturbances are
poorly
measured (if at all) owing to the superior feedback mechanism afforded by the
quadratically
optimized proportional feedback response, and IQC 100 is superior to using
multiple
proportional-integral-derivative (PID) controllers in parallel that control to
the same PV and
are only pseudo-optimized using different set-points applied to the integral
feedback of the
controllers or are pseudo-optimized using exceptionally complex nonlinear
tuning between
each controller to act as communication bridges.
[0019] FIG. 2 shows a method 200 of instigated quadratic control. The
process
variable (PV) target is determined (202). The manipulated variables (MVs)
available for
control (204) for respective loads, and controllers, are determined. The MVs
are dependent
on the type of load, for example the speed, torque, feed rate, pressure,
power, etc. For each
of the MV values a maximum and minimum is also be determined (205) for
optimizing the
- 7 -
Date Recue/Date Received 2021-10-08
profit of the respect load. The values may be based upon pre-defined
parameters associated
with the respective load equipment or provided as operator input.
[0020] The QP gain-modified proportional action is integrated into
chosen control
algorithm (208). QP-optimized proportional action gains available for given
MV's given an
updated control variable PV are determined (206).
[0021] The QP form applied to P action is min(x): xAx
Subject to: x < H and x> L
where x is the manipulated variable output vector. A is the cost vector
(inverted costs i.e.
profits). H is the high limit vector. L is the low limit vector.
Also written as:
min(x): ai*x12 a2*x22 an*xn2
subject to: xi < Hi; x2 < H2;..; xn < He;
Xi > Li; X2 > L2; ; Xn > Ln;
xi=load(1)...xn=load(n)
[0022] Each load parameter is normalized. The modified control algorithm is
then
applied to MV output state map (210) to control the functions of the
respective loads.
[0023] FIG. 3 shows a method 300 for determining QP-optimized
proportional action
gains. The determined MV control variables are sent to the respective load
controllers (302)
based upon the updated MV output state map. The MV result on the PV is then
determined
(304). If the PV is optimized (YES at 306), that is the determined PV is at
the target PV or
within a defined margin, the process continues operation until there is a
change in the PV
value (314) to a non-optimal value. If the PV is not at the optimal value (NO
at 306), for each
MV, it is determined if the particular MV is at the maximum value threshold.
For example if
a motor is working at maximum torque or a valve is at a fully open setting.
When the PV
moves towards the constraint limit, the most profitable loads have diminished
control action.
If the MV is at the maximum threshold (YES at 308) it therefore can not be
changed further
and is removed from the optimization (316) in evaluating the QP. The MV values
can then
- 8 -
Date Recue/Date Received 2021-10-08
be modified (310) within the maximum and minimum limits and in respect to the
particular
algorithm being utilized and at a defined rate of allowable change. The
optimal proportional
action multiplier is calculated to apply to each MV to achieve a maximum
optimal output
with a normalized weighted average providing a combined value of 1. The
quadratic
programming (QP) allocation of proportional gain weights for the remaining MVs
(312) are
allocated to optimized the PV.
[0024] With reference to Figure 4, an integrated in closed loop is
demonstrated with
two MVs of a of a single-input multiple-output (SIMO) system. The following
terms are used
with reference to Figure 4 and the example below. :
SP Set-point;
PV Process Value;
Proportional action modifier;
Kp Proportional action gain;
KlIntegral action gain;
KD Derivative action gain;
P quadratic cost matrix;
q linear cost vector;
s Laplace variable.
The QP optimization form applied:
minimize: 1 õ,
¨2x'Px+qTx+ r
subject to: rx --- h
gT x ..._ I
ex= b
- 9 -
Date Recue/Date Received 2021-10-08
where bold upper-case denotes a matrix, and bold lower case denotes a vector.
Here, P is
the quadratic cost matrix and is typically symmetric and positive definite in
IQC; q is the linear
cost vector; h is the high constraint limit vector; 1 is the low constraint
limit vector; a is the
equality constraint weight vector; f, g are the inequality constraint vectors;
b is the equality
constraint scalar; r is a scalar constant. The quadratic program can be solved
numerically
using Newton's Method and the method illustrated in Fig 3. The solutions to x
constitute the
QP-optimized proportional action weights, depicted with
[0025] Example: Integration of quadratically optimized proportional
action into a
standard PID form for two manipulated variables
The standard form for a PID controller is:
IC/ KDs
OUT(s) = [Kp + + KDs + 1e(s) + F(s)
s
and the IQC form having QP-optimized proportional action gain is:
KDS
KDs + 1
OUT(s) =RKp + + _______________________________ e(s) + F(s)
s
where is the QP optimized proportional action modifier; Kp is the proportional
action gain;
K1 is the integral action gain; KD is the derivative action gain; s is the
Laplace variable; e is
the control error (SP ¨ PV); F is the feed-forward contribution.
In this example, we apply QP optimization to the standard velocity form PID.
The QP
optimization form, chosen for this demonstration example is:
minimize: (1N + qT
subject to: 1.7'
= 1
and we'll set P =[ 20.5 0'5] as a symmetric profit matrix, and q = [0'51.
Expressed explicitly
1 1.0
this is:
minimize: 2 + + 12 + +
- 10 -
Date Recue/Date Received 2021-10-08
subject to: 0, 0
1 + = 1
We solve with Newton's Method and find = [0.3751. In other words, the QP-
optimized
0.625
proportional action for this example is:
OUT1(s) = [0.375Kp1]e1(s)
OUT2(s) = [0.625Kp2]e2(s)
[0026] As would be understood a person of skill in the art, the
example described
above can be extended to a multiple output system defining multiple loads.
[0027] Each element in the embodiments of the present disclosure may
be
implemented as hardware, software/program, or any combination thereof.
Software codes,
either in its entirety or a part thereof, may be stored in a computer readable
medium or
memory (e.g., as a ROM, for example a non-volatile memory such as flash
memory, CD ROM,
DVD ROM, Blu-rayTM, a semiconductor ROM, USB, or a magnetic recording medium,
for
example a hard disk). The program may be in the form of source code, object
code, a code
intermediate source and object code such as partially compiled form, or in any
other form.
[0028] It would be appreciated by one of ordinary skill in the art
that the system and
components shown in Figures 1-4 may include components not shown in the
drawings. For
simplicity and clarity of the illustration, elements in the figures are not
necessarily to scale,
are only schematic and are non-limiting of the elements structures. It will be
apparent to
persons skilled in the art that a number of variations and modifications can
be made without
departing from the scope of the invention as defined in the claims.
- 11 -
Date Recue/Date Received 2021-10-08
