MXPA97008318A

MXPA97008318A - Feedback method for controlling non-linear processes

Info

Publication number: MXPA97008318A
Application number: MXPA/A/1997/008318A
Authority: MX
Inventors: Donald Bartusiak Raymond; William Fontaine Robert
Original assignee: Exxon Chemical Patents Inc
Priority date: 1995-04-28
Filing date: 1997-10-28
Publication date: 1998-02-01

Abstract

A system controls a plant process (12) which includes manipulated variables (e.g. input states) and control variables (e.g. output states). The system includes sensor circuitry for providing measures of the control variables and a memory for storing a correction time constant and upper and lower limits for at least one control variable. The upper and lower limits are separated by a band of values within which the one control variable is considered to be acceptable. A processor includes data describing a process model (16) which relates costs of manipulated variables to control variables and, upon solution, further provides predicted values for the one control variable. Logic within the processor is responsive to a measured value function of the one control variable being outside the band of values, to determine minimum cost manipulated variables which result in areturn of the predicted value of the one control variable to within the acceptable band of values. Control instrumentalitie s within the plant are operative to alter the manipulated variables (and input states) in accordance with signals from the processor.

Description

METHOD OF FEEDBACK TO CONTROL NON-LINEAR PROCESSES Field of the Invention This invention relates to process control systems and, more specifically, to a model-based feedback control system, where there are non-linear relationships between variables manipulated in the plant and plant control variables. Technical Background U.S. Patent No. 4,349,869, issued to Pratt et al., Entitled "Dynamic Matrix Control Method", describes a method and apparatus for controlling and optimizing the operation of a series of interdependent processes in a plant environment. To achieve control actions, the input variables to the plant are subjected to measured perturbations and the dynamic effects on the outputs are annotated to allow the prediction of the future response of the processes during online operation. To implement the control method, Pratt and collaborators built a table of values that are derived during the initial testing phase. The various inputs and the resulting outputs are incorporated into the table, whthen serves as the main point of reference during subsequent operations of the plant.

The procedure of Pratt et al. Is particularly adapted to control linear operations of the system or operations that can be simulated as linear. However, when a non-linear plant operation is found, the procedure of Prett et al. Does not work properly, especially when there is a multiplicity of control and manipulated variables. A control variable is a plant output that is affected by changes in one or more manipulated variables, for example inputs to the plant. An application of the dynamic matrix control method to a polymerization process is described by Peterson et al. In "A Non-Linear DMC Algorithm and its Application to a Semibatch Polymerization Reactor", Chem. Eng. Science, vol. 47, No. 4, pp. 737-753 (1992). Although Peterson et al. Employ a non-linear controller and a numerical algorithm to derive solutions, their procedure does not attempt to minimize input-state costs when arriving at a control solution. Brown et al., In "A Constrained Nonlinear Multivariable Control Algorithm", Trans I ChemE, vol. 68 (A), September 1990, pp. 464-476, describe a non-linear controller that includes a specified level of acceptable output values within whcontrol actions are inhibited. However, Brown and collaborators do not test what input values achieve a minimum cost while also achieving exit control.

The prior patent art includes many teachings of the use of model-based control systems that employ both linear and non-linear expressions to relate control and manipulated variables. U.S. Patent No. 4,663,703, issued to Axelby et al., Discloses a reference predictive model controller that employs a pulse model of a sub-system to simulate and predict future outputs. The system includes adjustable gain and control feedback loops that adjust to make the dynamic system appear to have constant characteristics, even when its dynamic characteristics are changing. U.S. Patent No. 5,260,865, issued to Beauford et al., Describes a control system based on a non-linear model for a distillation process "that employs a non-linear model for calculating vapor flow rates and distillation velocities". process. Sanchez (U.S. Patent No. 4,358,822) discloses an adaptive-predictive control system where a model determines a control vector by being applied to a process to cause a process output to be at a desired value at a future time in the weather. The parameters of the model are updated on a real time basis to make the output vector approach the real process vector. U.S. Patent No. 5,268,834, issued to Sarner et al., Employs a neural network to configure a plant model for control purposes.

The extension to plant operations of model-based control systems is not a direct problem when the operation of the plant comprises a dynamic, non-linear process and involves a multiplicity of manipulated and control variables. Until recently, process control computers of reasonable size and cost lacked the processing capacity to handle solutions of the many simultaneous equations that result from the modeling of such dynamic plant processes. Reference synthesis techniques have been developed for application to non-linear control problems (for example, to pH control problems). In a reference system synthesis technique, it is desired to have a non-linear plant system following a reference path, and to reach a fixed point according to a first or second order path once the plant delay has expired. Bartusiak et al., In "Non-Linear Feed Forward / Feedback Control Structures Designed by Reference Systems Synthesis", Chemical In ineerincr Science, vol. 44, No. 9, pp. 1837-1851 (1989), describe a control process that can be applied to a highly non-linear plant operation. Fundamentally, Bartusiak et al. Represent a plant to be controlled by a set of differential equations. The desired behavior of a closed loop control system is represented as a set of integro-differential equations that can be non-linear by design. The desired behavior is called a reference system. Bartusiak et al. Achieve desired closed-loop behavior results by adjusting manipulated variables so that "the system behaves as closely as possible to the reference system. The action of the manipulated variable is determined by matching or, in general, minimizing the difference between the open loop system and the desired closed loop system. The desired behavior of the plant is then defined. The control variables are specified together with a tuning parameter that controls the ratio at which the control variable reaches a fixed point. More specifically, the desired parameter of the plant output is set and the rate at which the control system reaches the desired output parameter in the control phase is dictated by the tuning parameter. In this way, the control function is excited to make the output reach the value of the specified parameter, independently of the cost functions of the manipulated variable. The result does not take into account variations in the costs of the manipulated variable that would allow not only an effective control of the operation of the plant, but also the minimization of costs. Accordingly, it is an object of this invention to provide an improved method for the control of non-linear processes that allows tuning parameters to be applied to control variables. It is another object of this invention to provide an improved method for controlling non-linear processes, where the control methodology allows the minimization of input costs of manipulated variables while simultaneously achieving the desired control variables. Compendium of the Invention A system controls a plant process that includes manipulated variables (for example, input states) and control variables (for example, exit states). The system includes sensor circuits for providing measurements of the control variables and a memory for storing a correction time constant and upper and lower limits for at least one control variable. The upper and lower limits are separated by a band of values within which the control variable is considered acceptable. A processor includes data that describes a process model that relates manipulated variable costs to the control variables and, when the solution is reached, it also provides predicted values for the control variable. The logic inside the processor responds to a measured value function of the control variable that is outside the band of values, to determine manipulated variables of minimum cost that result in a return of the predicted value of the control variable within the the acceptable band of values. The control instruments within the plant are operative to alter the manipulated variables (and input states) according to del-processor signals. Brief Description of the Drawings Figure 1 is a block diagram of a system embodying the invention. Figure 2 is a diagram of the control functions employed in the invention. Figures 3 and 4 are flow charts useful in understanding the operation of the invention. Detailed Description of the Invention In the following, the following terms will be used in the description of the invention: Process model: a process model defines the operation of the plant system and is formulated in a continuous time domain in the form of algebraic and differential equations. Discretization of manipulated variables: the manipulated movements are discrete variables over time. A zero-order hold function is used to provide discrete manipulated movement variables for use in the process model. Reference trajectory: a reference trajectory provides the specification of the performance of a controller as a response rate of control variables.

Objective function: an objective function defines an optimal control performance. The objective function includes penalties for violation of fixed control points and functions of economic cost (profit). Manipulated variable limits: the manipulated variable limits are set to reflect limits or secondary controller states such as range limits, fixed point limits and anti-accumulation conditions. Feedback: Feedback is incorporated into the reference trajectory as a polarization value that represents an error between the process measurements and the model predictions. State estimation: the predictions of states and outputs of the process model are provided in each controller scan by integration of the dynamic model, based on current values of manipulated variables and forward feed and the predictions derived during a previous time of exploration controller. Initialization: initialization of controller outputs is provided by reading current values of the variable manipulated in each scan and providing controller movements as increments to the values. When the controller program is running (either in a closed or open loop), the states and outputs of the model are initialized to predicted values during a previous scan of the controller.

When the program is turned on for the first time, the states and outputs of the model are initialized by solving a stable state model for the current manipulated and forward feed values. Turning to figure 1, the digital computer-based control system monitors a process that occurs in the plant 12. The process values are fed to a non-linear controller function 14 resident within the digital control system 10. A model process 16 is stored within the digital control system 10 and manifests a series of non-linear equations that provide a reference system for the non-linear controller 14. A plurality of control parameters 18 provide constraints for the control values derived by the non-linear controller 14. By comparing the process value measurements with the predicted values derived through a solution model 16 (with control parameters 18), the correction values are derived and applied as control inputs to the plant 12. In figure 2, the non-linear controller 14 includes a process model 16 that defines a change in the rate of process states by changes in manipulated system variables, independent variables and polarization values. The non-linear controller 14 further includes one or more tuning values that define response characteristics of the closed loop process. More specifically, each response characteristic of the process defines a path to be followed by a control variable in response to changes in the manipulated variables. An optimization function 19 determines minimized manipulated variable costs that achieve the desired response path, given the differences between the measured values and the projected values derived from the process module 16. Subsequently it will be understood that the non-linear controller 14 establishes boundary limits for one or more control variables (eg, outputs) of the plant 12. Once the upper and lower limits for a control variable are established, the non-linear controller 14 implements a control procedure that compares a measured rate of change between a control variable and a desired movement rate of the control variable in relation to at least one of the limits. If the control variable is within upper and lower limits, no control action is taken. If the control variable is out of bounds, the comparison of the measured dynamic change rate and the dynamic change rate of the model allows derivation of an error rate of change. That value of the error rate is then used by an objective function to allow the determination of a set of manipulated variables that will exhibit a minimum cost to obtain a return of the control variable within the upper and lower limits. Using the upper and lower limits to define an acceptable range of values of the control variables, various manipulated variable costs can be tested to determine which combination allows a return of the control variable within the limits while "which, at the same time, minimizes the costs of the manipulated variables. Turning to Figures 3 and 4, a description of the operation of the non-linear controller 14 will be presented. The non-linear controller 14 runs on a general-purpose computer that is integrated into the plant 12. The non-linear controller 14 runs at a frequency or specified scan rate, for example once per minute, whereby the control variables are monitored and the manipulated variables are calculated in order to derive movements for each of them, to implement a control action. The procedure begins by reading plant data in a digital control system 10 (box 30). These data include current values for the control variables, manipulated variables and auxiliary variables or forward feed. The measurements of the plant are supplied either by field instruments or via off-line laboratory analysis. Next, the current measurement values of each control variable are compared with a corresponding model prediction. A polarization value that represents the lack of congruence between the plant and the model is calculated as the difference between the measurements and the predicted values (box 32).

As shown in box 34, the input data are immediately validated (for example, abnormal conditions such as unavailable measurement values or out-of-range values are discarded). It also carries out data conditioning and includes filtering and setting limits of manipulated variables, based on limits specified by the operator and state values of the plant control system. At the beginning of the operation of the non-linear controller 14, an initialization of cold start is carried out (see decision box 36). The values for the independent variables, either manipulated or feed forward, are read from a database stored within the digital control system 10 (box 38). An initialization action calculates model states and plant outputs that represent plant conditions such as temperature, composition and product properties. The model can be in any mathematical form. A state-space model will be used hereinafter for the purpose of describing the procedure. Each state is defined by a vector value "x" and the plant outputs are represented by vector values "and". The independent variables are represented by the value "u", as follows: 0 = F (x, u) (1) y = H (x) (2) The values for the plant states are then used as initial values for the non-linear controller 14 (see boxes 40 and 42). The state values are then estimated and written to the memory (box 44). At this point, the non-linear controller begins the operation of the process control algorithm (box 46). As shown in Figure 4, the control process reads the hardware process data from the plant control system (box 48) to determine the current status of the process. These data include the following: Initial values for each model state. Initial values for predicted plant departures. Polarization values that represent plant / model errors.

Parameters of the model. Current values measured from independent variables. Fixed points or target values for control variables and restrictions. Borders for manipulated variables. Conditions of entry status. The values for the model states and the predicted outputs of the plant are either the previous values of a last run of the controller or of the initialization values of the cold start. The control variable (s) (for example, an output to be controlled) and the fixed restriction points are captured by the operator. The fixed points are captured as an upper limit value and a lower limit value. The use of these values allows the adjustment of the manipulated variables (inputs) in order to achieve a minimized cost to reach a value of control variable within the values of the upper and lower limits. The values of the parameters of the model are predetermined. The current measured values of the independent variables are derived from field instruments in the plant or laboratory analysis. The borders of the manipulated variables are, as indicated above, based on limits specified by the operator and state values of the plant control system. The mode of operation of the controller is then set (box 50). A controller mode allows to calculate model predictions and derive control signals, without applying the control signals to the plant. Subsequently, it will be assumed that the digital control system is established in a fully operational mode, where the manipulated variables will be actively controlled according to model calculations and measured system states. The input data is converted to a form for use with the control model / system (box 52) and a state estimation procedure (box 54) is initiated. Each state is estimated using a dynamic model of the plant. In the state / space model shown later in equations 3 and 4, the states are represented by the variable "x", the outputs of the plant are represented by the variable "y", and the independent variables are represented by "u": dx / dt F (x, u) (3) y = H (x) (4) Equation 3 indicates "that the rate of change of the model states is a function of the model states themselves and the independent variables. Equation 4 indicates "that the output is a function of the model states. Model estimates are obtained by integrating equations 3 and 4 of the last run of the nonlinear controller 14 to the current time. A preferred method of calculation involves orthogonal positioning, where equations 3 and 4 are divided into time segments, thereby allowing differential equations to be solved in parallel, over the same time increment. The control calculations carried out by the non-linear controller 14 are carried out employing sequential quadratic programming techniques (box 56). The control calculations determine the future movements in manipulated variables that give a better congruence with the control performance specification during a time horizon towards the future. The non-linear controller 14 uses the model of the plant, a reference trajectory that defines a specified performance of the controller, an objective function (which will be described below), and the boundaries of the manipulated variables. The movements of the manipulated variables are discretized during a time horizon towards the future.

The model shown in equations 3 and 4 is used. As indicated above, the variable "u" represents independent variables and a subset of them is that of the manipulated variables (that is, inputs). The values for all the independent variables are obtained by a "zero-order hold function" of manipulated variables discretized Uk at each time step k. A zero-order hold function assumes that the value of the manipulated variable remains constant between executions of the program. The reference trajectory specifies the controller's performance to alter the control variables according to applied constraints. The reference trajectory equations 5 and 6 below express a relationship between the change rates of the control variables and the error (or difference) between a fixed point of control variable and the measured controlled variable. dyk / dt = (SPHk- (yk + b)) / T + Vh? k -Vhnk (5) dtk / dt = (SPLk- (yk + b)) / T + Vlpk-Vlnk (6) k = 1 a K Vlp greater than or equal to 0.0 Vln equal to or greater than 0.0 Vhp equal to or greater than 0.0 Vhn equal to or greater than 0.0 where: SPH = upper limit for control variable or restriction; SPL = lower limit for control variable or restriction; y = predicted control variable; b = polarization that relates the error in prediction and measurement; Vhp = positive variation of measured variable of SPHj Vhn = negative variation of measured variable of SPH; Vlp = positive variation of SPL measured variable; Vln = negative variation of SPL measured variable; k = time step towards the future; K = time steps to the future in the time horizon used by the controller; T = time constant for the desired closed loop response speed of the controlled variable. Each of the variables Vlp, Vhp, Vln and Vhn will be called in the following variable "of violation". Each variable of violation allows to convert an inequality into an equality relation and allows to prioritize the restrictions through the application of weight functions in the objective function. The objective function (that is, the relation to be satisfied by the control action) is given by: Min Sum (h * Vhpk + WI * Vlnk) + C (x, u) (7) where: Wh, Wi = weights of penalty; Vhpk, Vlpk = violation variables, as defined above; C (x, u) = cost penalty function. Equation 7 expresses a sum minimization function for use when a violation of either the upper limit of the control variable or the lower limit of the control variable has occurred. Equation 7 applies weight factors "that allow a positive violation value or a negative violation value to be emphasized (or de-emphasized), as the case may be. Equation 7 also includes a term (ie, C (x, u)), which is a cost function "that depends on the manipulated variable states u and model x. The control system solves equation 7 and evaluates a sum that results from each solution when several changes are attempted in the manipulated variables. The objective is to achieve a return of the control variable and within the boundaries defined by the upper limit (SPH) and the lower limit (SPL). Since SPH and SPL are separated by a range of values that define an acceptable range of the control variable, several possible changes in the manipulated variables can be calculated to determine which combination results in the lowest cost for the manipulated variables while achieving a return from the control variable to the acceptable range. When the manipulated variables (in any control action) allow a return of the plant output into the range between SPH and SPL, each of the first two expressions in equation 7 is canceled and the solution of the function is strictly related with the costs represented by the manipulated variables.

The optimization solution of equation 7 is subjected to additional borders of manipulated variables as expressed later in equations 8 and 9. ulb less than uk less than uhp (8) ABS (uk-u (k-1) less than dub (o) where: uhb = upper border in a manipulated variable; ulb = lower border in a manipulated variable; dub = border or change in u between steps of time. Once "an acceptable solution has been achieved, the outputs, which consist of manipulated variable values for each time step in the future, are checked against the system constraints (box 58). Assuming the validity of the output data, the data is then written to the memory (box 60) and the calculated manipulated values are sent to the plant (box 62) to operate the field control elements (eg, valves). It should be understood that the foregoing description is only illustrative of the invention. Various alternatives and modifications can be designed by those skilled in the art, without departing from the invention. Accordingly, the present invention is intended to encompass all those alternatives, modifications and variations that fall within the scope of the appended claims.

Claims

CLAIMS 1. A system for controlling a plant process "including manipulated variables comprising input states, and control variables comprising output states, said system comprising: sensor means for providing measurements of at least said control variables; memory means for storing upper and lower limits and a correction time constant for at least one control variable, said upper and lower limits separated by a band of values wi which said at least one control variable is considered acceptable; processing means coupled to said sensor means and said memory means and including data describing a model of said plant process, said model relating the costs of manipulated variables with the control variables and, upon the occurrence of the solution, additionally providing predicted values for said at least one control variable, said processor means further including logical means responsive to a measured value function of said at least one control variable that is outside said band of values, to generate control signals to alter said variables manipulated in one direction to achieve a minimized cost thereof, said manipulated variables being altered in one direction to cause a predicted value of said at least one control variable to be wi said band of values; and control signal means responsive to said control signals to operate instruments in said plant to control said manipulated variables. The system for controlling a plant process, as defined in claim 1, wherein said memory means additionally stores data describing a path response function for said model which prescribes a rate of return for said control variable to said band of values considered acceptable when said upper limit is violated by said control variable, and a trajectory response function for said model that prescribes a rate of return for said control variable to said band of values considered acceptable when said lower limit is violated by said at least one control variable, both path response functions including correction time constants and expressing a relationship between measured and desired rates of change of said at least one control variable, said logic means using said data for determine said input states of minimized cost. 3. The system for controlling a plant process, as defined in claim 2, wherein said path response functions for said at least one control variable are: dyk / dt = (SPHk- (yk + b)) / T + Vhpk + Vhnk dyk / dt = (SPLk- (yk + b)) / T + Vlpk-Vlnk k - 1 to K Vlp greater than or equal to 0.0; Vln greater than or equal to 0.0; Vhp greater than or equal to 0.0; Vhn greater than or equal to 0.0; where: SPH = upper limit for control variable or restriction; SPL = lower limit for control variable or restriction; y = predicted control variable; b - polarization that relates the error in prediction and measurement; Vhp = positive variation of measured variable of SPH; Vhn = negative variation of SPH measured variable; Vlp = positive variation of SPL measured variable; Vln = negative variation of SPL measured variable; k = time step towards the future; K = time steps to the future in the time horizon used by the controller; T = time constant for the desired closed loop response speed of the controlled variable. The system for controlling a plant process, as defined in claim 3, wherein said logic means operate to provide a solution to a minimization relationship in order to determine manipulated variables of minimized cost to achieve a movement of said at least a control variable wi said band of values, said minimization ratio expressed as: Min Sum (Wh * Vhpk + WI * Vlnk) + C (x, u) where: h, i = penalty weights; Vhpk, Vlpk = violation variables; C (x, u) = cost penalty function.