PROCEDURE TO GENERATE A CONTROL VECTOR AND ADEX SYSTEM APPLYING THE SAME

Abstract

Adaptive predictive expert control procedure or system, called ADEX, that implements a control strategy in which an adaptive predictive expert controller, called ADEX controller, uses in its adaptive predictive domains a predictive adaptive model that dynamically relates the output of the process to be controlled with an integral function of the control signal that is applied to the process, instead of dynamically relating said process output with the signal that is applied to the process as conventional ADEX controllers of the prior art do. In this way, the output of said ADEX controller is an integral function of the control signal. From this integral function said control strategy uses a differential operator to calculate the real control action that is applied to the process.

Claims

1. A procedure for generating a control vector u (k) during each of a plurality of control instants k, said control vector is applied to an apparatus that performs a process with at least one input variable and at least one output variable, at least one of said input variables defines a process input vector and at least one of said output variables defines a process output vector and (k), said apparatus varies said process input vector according to the value of said control vector, said method guides said process output vector towards a setpoint vector SP (k), said method characterized by comprising the following steps: (A) generate an integral function vector U (k) of the control vector that is applied to the process u (k) by executing the sequence of operations of an ADEX controller in one of its adaptive predictive domains, whose adaptive predictive model relates the vector of process output y (k) with said vector integral function of the control vector, in order to drive the process output vector towards its SP (k) setpoint; (B) calculate a second integral function vector Uk−1 (k−1) of the control vector to be applied to the process up to time k−1; © calculating the control vector to be applied to the process u (k) using a differential operator that derives said control vector from the integral function vectors generated in the previous steps (A) and (B); (D) apply said control vector to the apparatus that performs the process.

2. A method according to claim 1, characterized by carrying out steps (A) and (B) as follows: (A) Generate a vector integral control function U (k), which represents an integral function of the values of said control vector u (k) between two control instants k+1−d and k, where d≥2, using a ADEX controller that operates in a predictive adaptive domain and whose predictive adaptive model dynamically relates the process output vector y (k) with said control integral function vector, so that the output of said ADEX controller is said vector U (k) and is calculated to guide said process output vector towards its setpoint vector SP (k); (B) Generate a second integral function vector Uk−1 (k−1), by means of an integral function of the values of said control vector u (k) between the two previous control instants k+1−d and k−1.

3. An ADEX system comprising a controller computer to apply the method to generate a control vector u (k) of claim 1, during each of a plurality of control instants k, said control vector is applied to an apparatus that carries out a process with at least one input variable and at least one output variable, at least one of said input variables defines a process input vector and at least one of said output variables defines a vector output process y (k), said apparatus varies said process input vector according to the value of said control vector u (k), said system guides said output vector y (k) towards a setpoint vector SP (k), said controlling computer is configured by sets of instructions to operate as: a. An ADEX controller that operates in a predictive adaptive domain and whose predictive adaptive model dynamically relates the output vector of the process y (k) with an integral function vector U (k) of the control vector that is applied to the process, so that the output of said ADEX controller is said vector U (k) and is calculated to guide said process output vector towards its setpoint vector SP (k); b. An integrator block that acts by generating a second integral function vector Uk−1 (k−1) of the control vector to be applied to the process until time k−1. C. A differential block that derives said control vector u (k) from the integral function vectors generated by said ADEX controller and said integrator block. Wherein said control vector u (k) is applied to said apparatus such that said apparatus varies said process input vector in accordance with said control vector.

4. An ADEX system according to claim 3, characterized by configuring the instruction sets a and b as follows: a: An ADEX controller that operates in a predictive adaptive domain and whose predictive adaptive model dynamically relates the output vector of the process y (k) with a vector integral control function U (k), which represents an integral function of the values of said vector of control u (k) between two control instants k+1−dyk, where d≥2, so that the output of said ADEX controller is said vector U (k) and is calculated to guide said process output vector towards its setpoint vector SP (k); b. An integrator block that acts by generating a second integral function vector Uk−1 (k−1), which is an integral function of the values of said control vector u (k) between the two control instants k+1−5 and k−1.

5. An ADEX system comprising a controller computer to apply the method to generate a control vector u (k) of claim 2, during each of a plurality of control instants k, said control vector is applied to an apparatus that carries out a process with at least one input variable and at least one output variable, at least one of said input variables defines a process input vector and at least one of said output variables defines a vector output process y (k), said apparatus varies said process input vector according to the value of said control vector u (k), said system guides said output vector y (k) towards a setpoint vector SP (k), said controlling computer is configured by sets of instructions to operate as: a. An ADEX controller that operates in a predictive adaptive domain and whose predictive adaptive model dynamically relates the output vector of the process y (k) with an integral function vector U (k) of the control vector that is applied to the process, so that the output of said ADEX controller is said vector U (k) and is calculated to guide said process output vector towards its setpoint vector SP (k); b. An integrator block that acts by generating a second integral function vector Uk−1 (k−1) of the control vector to be applied to the process until time k−1. C. A differential block that derives said control vector u (k) from the integral function vectors generated by said ADEX controller and said integrator block. Wherein said control vector u (k) is applied to said apparatus such that said apparatus varies said process input vector in accordance with said control vector.

6. An ADEX system according to claim 5, characterized by configuring the instruction sets a and b as follows: a: An ADEX controller that operates in a predictive adaptive domain and whose predictive adaptive model dynamically relates the output vector of the process y (k) with a vector integral control function U (k), which represents an integral function of the values of said vector of control u (k) between two control instants k+1−dyk, where d≥2, so that the output of said ADEX controller is said vector U (k) and is calculated to guide said process output vector towards its setpoint vector SP (k); b. An integrator block that acts by generating a second integral function vector Uk−1 (k−1), which is an integral function of the values of said control vector u (k) between the two control instants k+1−5 and k−1.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0022] For a better understanding of the invention, the following figures are included, which represent an exemplary embodiment and should not be considered more than a way to illustrate and clarify the invention.

[0023] FIG. 1 shows the general and conceptual structure of an ADEX system with integral control function according to one embodiment.

[0024] FIG. 2 shows a graph of trend curves for two consecutive periods of time. During an initial period of 6 minutes, the trend curves represent the result of a direct application of an ADEX controller with a control period below the modeling threshold to a simulated process. During a second period, after 6 minutes, the trend curves continue to represent the result of the direct application of the same ADEX controller to said simulated process, but in this second period the control period of this ADEX controller has been changed to a value above the modeling threshold. The trend curves in the upper part of the figure represent the evolution of the process output (thick line) and its set point (thin line), the scale for both curves is on the ordinate axis on the left side. The trend curve in the middle represents the control signal generated by the ADEX controller and applied to the process, the scale is on the ordinate on the right side. The trend curve at the bottom is only to indicate when the control period has changed.

[0025] FIG. 3 also shows a graph of trend curves for two consecutive time periods. The results presented in the initial period of 6 minutes are equivalent to those presented in the initial period of FIG. 2, that is, the result of a direct application of the same ADEX controller of FIG. 2 with a control period below the modeling threshold to the same simulated process. During the second period of 6 minutes, the control signal applied to the process is changed to that generated by an ADEX system with integral control function of the present invention and the control period remains the same as that used during the initial period. The trend curves have a meaning equivalent to those in FIG. 2.

MODES OF EMBODIMENT OF THE INVENTION

[0026] An embodiment of the invention is briefly described below, as an illustrative and non-limiting example thereof.

[0027] At any control instant k, the human operator can choose to apply manual control or automatic control to the process variable to be controlled; both forms of control are shown in FIG. 1 and are described with reference to said figure below:

[0028] 1. Manual control: under manual control, the control signal u (k) is applied directly from the operator (2) to the apparatus (4) carrying out the process being controlled and to the integrator block A (7) as shown on the road (1). A sensor (5) associated with the apparatus (4) measures the process output variable y (k) to be controlled. This variable y (k) is applied as an output variable of the process to be controlled, as shown in path (6), to the ADEX controller (9). The integrator block A (7) calculates a control integral function in k−1, U (k−1), integrating said control signal u (k) between two previous control instants, k−δ and k−1, where δ is an integer that represents the integration interval in control periods, where δ≥2. Said integral control function at k−1, U (k−1), is applied as controller output at k−1 to the ADEX Controller (9). Therefore, under manual control, the ADEX Controller (9) receives as inputs: 1) said process output variable y (k), and 2) said integral control function in k−1, U (k−1). This allows the ADEX Controller (9) to operate in the identification mode for adaptive predictive domains (AP) described in U.S. Pat. No. 6,662,058 B1. Said identification mode will adjust the parameters of the adaptive predictive model (AP) for the corresponding operating domain of the ADEX controller (9), in such a way that said AP model will represent a dynamic relationship between said process output variable y (k) and said integral control function U (k−1) and, therefore, will be able to predict future values of said process output variable y (k) based on a future sequence of values of said integral control function U (k−1). Automatic control: under automatic control, the SP setpoint value (k) for the process output variable y (k) is applied directly from the operator (2) to the ADEX Controller (9), as shown in the path (8). Also, the measured process output variable y (k) is applied to the ADEX controller (9) from the sensor (5) as shown in path (6). This allows the ADEX Controller (9) to operate in the automatic mode for adaptive predictive domains (AP) described in U.S. Pat. No. 6,662,058 B1. In this automatic mode, from the process output variable y (k) and its SP (k) setpoint, the ADEX controller (9) generates as controller output an integral control function in k, U (k), which in this case represents the integration of said process control signal u (k) between two control instants, k+1−d and k. The output U (k) of the ADEX Controller (9) is applied to the Differential Block (10) that calculates the control signal u (k) that is applied to the process. The integrator block B (11) calculates a second integral function Uk−1 (k−1) integrating said control signal u (k) between the previous control instants, k+1−d and k−1. Said second integral function Uk−1 (k−1) is subtracted from said control integral function in k, U (k), within the differential block (10) to generate the control signal u (k) that is applied to the apparatus (4) that carries out the process being controlled. The specific operations that the ADEX System of this invention will carry out at each control instant k to automatically control the process output variable y (k) are described below: [0029] (a) Measurement by the sensor (5) of the process output variable carried out by the apparatus (4) to obtain the process output variable y (k) to be controlled. [0030] (b) Calculation of the integral control function in k, U (k), by the ADEX controller (9) as controller output. This controller calculates the integral control function U (k) from the value of the output of the process to be controlled, y (k), and the value of its setpoint in k, SP (K), applied directly from the operator (2) to the ADEX Controller (9), and executing the sequence of operations described in U.S. Pat. No. 6,662,058 B1 for ADEX controllers in predictive adaptive domains of operation. [0031] (c) Calculation of said second integral function Uk−1 (k−1) by means of the equation that determines the operation of the integrator block B (11) within the differential block:
where Uk−1 (k−1) is obtained integrating the previous control signals u (k) from time k−1 to time k+1−d, and δ≥2 is an integer conveniently selected by the ADEX system designer. [0032] (d) Calculation of the control signal u (k) in the differential block by means of: [0033] (e) Application of the control signal u (k) to the apparatus that performs the process.

[0034] In its implementation, the ADEX System of the present invention can be applied to a scalar process output variable, y (k), as previously considered, or to a process output vector, y (k), composed of n components of scalar output, which are n scalar process output variables. In this case, the ADEX system can be applied to each of said n scalar components of the process output vector, as described above, but taking into account the multivariate nature of the process, said ADEX controller can be a multivariable ADEX controller that guides said process output vector y (k) towards its setpoint vector SP (k). Said multivariable ADEX controller calculates as its output a vector integral function of control in k, U (k), which will be applied to a multivariable differential block in which an integrator block will calculate a second integral function vector Uk−1 (k−1) by means of:

[0035] where u (k−i) is the control vector that has been applied at times k−i to the apparatus that develops the process and the control vector u (k), which is applied to the apparatus that performs the process at time k, is calculated in said differential block by means of:

EXAMPLE

[0036] The performance of the ADEX system with integral function of the control signal of the present invention will be illustrated by controlling a simulated mono-variable process, with one input, u (k), and one output, y (k), both at time k, which are measured as increments of their values when the process is in a state of equilibrium, considering that the process is in equilibrium when both input and output variables are equal to zero. When the control period is equal to 1 second, the dynamics of the simulated process can be described by the following equation: y(k)=y(k)+0.1u(k−1)+0.1u(k−2)+0.2u(k−3)+0.2u(k−4)(5) To illustrate the performance of the ADEX system of the invention, the simulated process will be controlled in the different scenarios described below:

[0037] In a first scenario, an ADEX controller operating in a predictive adaptive domain is used to control the simulated process, using the sequence of operations described in U.S. Pat. No. 6,662,058B1 and with a control period of 1 second and a prediction horizon of 5 control periods. The parameters of the driver block of the ADEX controller, which generates the desired path for the process output, are the same as those of a second order model with a time constant equal to 1, 5 control periods, a gain and a ratio of damping equal to 1, and the adaptive predictive model (AP), which relates the output of the process with the control signal, is of the first order with two parameters so that it calculates the a priori estimate of the output of the process at the instant by the equation:

[0038] As described in the previously cited patents, the ADEX controller adaptation mechanism will adjust the parameters of this model to make said a priori estimate of the process output converge towards the process output itself.

[0039] Using this same AP model, the prediction of the process output at time from the control signal u (k) applied at time k is given by:

[0040] The control signal u (k) generated by the ADEX controller at instant k will make the predicted output of the process at instant k equal to the desired output generated at instant k by the driver block for that same instant k+1, yd (k+lk). Therefore, equating said desired output to said predicted output in equation (7) and solving, u (k) will verify the following equation:

[0041] In a second scenario, an ADEX controller operating in a predictive adaptive domain is used to control the simulated process, with the sequence of operations of patent U.S. Pat. No. 6,662,058B1, which has the same configuration as the ADEX controller in the first scenario, except that the period control is equal to 2 seconds.

[0042] Finally, in a third scenario, an embodiment of the ADEX system with an integral function of the control signal is used to control the simulated process, which has been previously described to illustrate the invention, with a value of δ, which determines the horizon for the calculation of the integral function of the control signal, equal to 10, and an ADEX controller that has the same configuration as that of the ADEX controller considered in the first scenario, and a predictive adaptive model that, according to the invention, dynamically relates the process output with said integral function of the control signal U (k), so that in this case it calculates the a priori estimate of the process output at the time using the equation:

[0043] Using this same AP model, the output of the ADEX controller at instant k, U (k), will verify the following equation:

[0044] Where, analogously to equation (8), yd (k+lk) is the value of the desired path for the process output at control instant k+1.

[0045] The AP model described by equation (6), which estimates the output of the process y (k) and operates with a control period of 1 second, has a reduced order with respect to equation (5), which represents the dynamics of the process when the control period is also 1 second. For this control period of 1 second, the AP model of equation (6) does not have the adequate parametric structure to allow the adaptation mechanism of the ADEX controller to perform the identification of the dynamics of the process described by equation (5), because in equation (6) there are only 2 parameters and it would need to have 2 other parameters:

[0046] When the control period is equal to 2 seconds, the dynamics of the simulated process can be described by an equation of the same order as the AP model of equation (6), that is, with the same number of parameters. In this case, the adaptation mechanism of the ADEX controller will be able to successfully identify the dynamics of the process using the AP model described by equation (6).

[0047] Therefore, the 1 second control period is below the modeling threshold for an ADEX controller using the AP model in equation (6) and satisfactory control performance cannot be expected. However, if the control period is increased to 2 seconds, the same ADEX controller can achieve a good identification of the process dynamics and as a result, satisfactory control performance, that is, the control period of 2 seconds is above the modeling threshold. However, thanks to the invention it is possible to obtain a satisfactory control performance despite using a control period below the modeling threshold.

[0048] The evolution curves of FIG. 2 present the results obtained in the application of the ADEX controller, with a control period of 1 second described in the first scenario, to the simulated process during the first 6 minutes of the experiment. During the second 6 minutes, the results are shown the results obtained by the same ADEX controller when the control period is 2 seconds. The evolution curves in the upper part of the figure represent the process output evolution (thick line) and its set point (thin line); the scale is displayed on the left axis of the ordinate. The evolution curve in the lower part represents the control signal generated by the ADEX controller with control periods of 1 and 2 seconds and applied to the process, its scale is represented on the right ordinate axis. The curve in the base of the figure only indicates the instant at which the change in the control period occurs.

[0049] The evolution curves of FIG. 3 present the results obtained in the application of the ADEX controller, with a control period of 1 second, to the simulated process during the first 6 minutes of the experiment and, during the second 6 minutes, the results obtained when the control signal of said controller it is changed by the control signal to the process generated by the ADEX system with integral control function of the invention with a control period also of 1 second. The evolution curves and scales are equivalent to those described for FIG. 2.

[0050] The results presented in the first 6 minutes of FIG. 2 show how the conventional prior art application of an ADEX controller using a control period of 1 second, below the modeling threshold, does not achieve satisfactory control performance. That is, the output of the process under control oscillates with a great amplitude around its set point and the control signal also oscillates in a similar way, without any perspective for the process to approach stability. However, as shown by the results presented in the second 6 minutes of FIG. 2, when the same ADEX controller begins to use a control period of 2 seconds, above the modeling threshold, the process output stops oscillating and converges towards the set point following a desired output path. In addition, subsequent changes in the set point cause the process output to catch up with and stabilize therein following a desired output path as well, demonstrating satisfactory control performance. This desired path corresponds to the configuration of the driver block of the ADEX controller, which has been previously described.

[0051] The results presented in the second 6 minutes of FIG. 3 demonstrate that an ADEX system with integral control function can achieve satisfactory control performance using a control period of 1 second, below the modeling threshold of the conventional ADEX controller used in the first 6 minutes of this same figure. From the beginning, the process output follows a desired path to reach and stabilizes at the set point. This satisfactory control performance is reproduced in subsequent setpoint changes. Also in this case, this desired path corresponds to the configuration of the driver block of the ADEX controller, which has been previously described.

[0052] It can be seen that the desired trajectories converge towards the setpoint much faster when the process output is controlled with a control period of 1 second by the ADEX system with integral control function (FIG. 3), than when the process output is controlled by the conventional ADEX controller with a control period of 2 seconds (FIG. 2). The reason is that the driver block of an ADEX controller generates the desired trajectory depending on the control period, so that the shorter the control period, the faster the desired trajectory of the output of the process under control approaches its setpoint.

[0053] As illustrated in this simulation example, the use of ADEX systems with integral control function will allow satisfactory control performance to be obtained using control periods below the modeling thresholds of conventional ADEX controllers. The use of these “short” control periods is mandatory for a wide variety of industrial processes and therefore the use of ADEX systems with integral control function represents a significant advance in control performance for these types of industrial processes.