Method for sequential predictive control, first solving a cost function and subsequently a second cost function for two or more control objectives

Abstract

A sequential or cascading predictive control method is provided, including first solving a cost function and then a second cost function for two or more control objectives. The method includes separating the cost function into at least two or more cost functions, depending on the number of defined control objectives. The method additionally includes controlling a first variable with a unitary cost function, a single term or nature of the control objectives. The method also includes determining the possible states that minimize the cost of the first objective to be controlled. Considering only the options given through this determination, a second variable is controlled with a cost function that minimizes the cost function thereof.

Claims

1. A sequential or cascading predictive control method for converters/inverters first solving a cost function and then a second cost function for two or more control objectives, wherein the converter / inverter is an induction machine, wherein the method comprises: a. defining a mathematical model of a load/network (M.sub.carga); b. defining a mathematical model of a converter/inverter (M.sub.inversor); c. defining first control objectives for the load/network (x.sub.c1, x.sub.c2); d. defining second control objectives for the converter/inverter (x.sub.il, x.sub.i2); e. defining a cost function for each of the first control objectives if the first control objectives are of a different nature; f. defining a single cost/network cost function (G.sub.c1, G.sub.c2) if the first control objectives are of the same nature; g. defining a cost function for each of the second control objectives if the second control objectives are of a different nature; h. defining a single cost function for the converter/inverter (g.sub.i1, g.sub.i2) if the second control objectives are of the same nature; i. evaluating possible states for the load/network using Mcarga, and evaluating g.sub.c1, determining the two states that minimize the cost function g.sub.c1, then subsequently evaluating g.sub.c2 for the preselected states and determining the state that minimizes g.sub.c2; j. selecting redundancies of the converter/inverter for said status and evaluating g.sub.il using the Minversor selecting those that minimize the cost function g.sub.c1, subsequently, of the redundant states that minimize g.sub.il evaluate g.sub.i2 obtaining the state that minimizes g.sub.i2; k. applying the state resulting from the previous step to the inductive machine; and l. subsequent to applying the state to the inductive machine, controlling the inductive machine to transport electric energy.

2. The method according to claim 1 wherein one of the first and second control objectives is Torque.

3. The method according to claim 1 wherein one of the first and second control objectives is Flow.

4. The method according to claim 2 wherein the mathematical model of the Torque is: $T_e^{k+1}=\frac{3}{2}{N}_p{\psi }_s^{k+1}.Math.i_s^{k+1}$ wherein N.sub.p is the number of pole pairs of the machine, and the superscript k+1 indicates that it is the estimated value at the next instant of the sampling time k.

5. The method according to claim 3 wherein the mathematical model of the Flow is: ${\psi }_r^{k+1}=\frac{L_r}{L_m}{\psi }_s^{k+1}-\frac{1}{\lambda L_m}{i}_s^{k+1}$ wherein L.sub.r is the rotor inductance, L.sub.m is the rotor-stator mutual inductance and λ is a factor given by the resistance, inductance and permeability of the machine, all known as machine parameters.

6. The method according to claim 5, wherein cost function g.sub.1 is determined by:
g.sub.1=(T.sub.m−T.sub.r).sup.2 wherein the subscript m indicates that the variable is measured and the subscript r is the reference value.

7. The method according to claim 1, wherein a first variable to be controlled is Torque, whose reference value is given in this case by linear control of angular velocity of the machine, and the method further comprises: determining two possible driving states of the converter/inverter that minimize the Torque; and proceeding with the predictive control of Flow, which minimizes the cost function thereof considering only the two options delivered by the Torque control process and where the state that minimizes the error in the electric flow of a stator is the one that is applied in the system.

8. The method according to claim 1 wherein the converter / inverter is a three phase machine.

9. The method according to claim 6, wherein cost function g.sub.2 is determined by:
g.sub.2=(φ.sub.m−φ.sub.r).sup.2 wherein the subscript m indicates that the variable is measured and the subscript r is the reference value.

Description

BRIEF DESCRIPTION OF THE FIGURES

(1) FIG. 1 (Prior Art) shows a standard predictive control scheme.

(2) FIG. 2 shows a block diagram of the sequential predictive control of the present invention for an induction machine.

(3) FIG. 3 shows graphs of different parameters of the sequential predictive control of the present invention for an induction machine, where (a) Flow; (b) Torque; (c) Angular velocity; (d) Current in phase a of the machine.

(4) FIG. 4 shows graphs of different parameters of the sequential predictive control of the present invention for an induction machine, where (a) Voltage of a phase a (υaN); (b) Tension between lines (υab); (c) Current in phase a of the machine.

(5) FIG. 5 shows a flow chart of the sequential predictive control for an induction machine.

DETAILED DESCRIPTION OF THE INVENTION

(6) The present invention provides a sequential or cascade predictive control method, first solving a cost function and then a second cost function for two or more control objectives (see FIG. 5), comprising: a) separate the cost function into at least two or more cost functions, depending on the number of control objectives; b) define control objectives; c) first control a variable with a unit cost function, a single term or nature of the control objectives; d) determine the possible states that minimize the cost of the first objective to be controlled; Y e) control a second variable with a cost function that minimizes its cost function considering only the options given in the point d).

(7) On the other hand, for an application that involves power electronics, specifically for inverter/rectifier applications, the method is defined as follows:

(8) 1. Define the mathematical model of the load/network (M.sub.carga).

(9) 2. Define the mathematical model of the converter/inverter (M.sub.inversor)

(10) 3. Define the control objectives for the load/network (x.sub.c1, x.sub.c2)

(11) 4. Define the control objectives for the inverter converter (x.sub.i1, x.sub.i2)

(12) 5. If the objectives of load control are of a different nature (voltage, current, power, harmonics) define a cost function for each of them. If they are of the same nature (only currents, only voltages, only powers, etc.) define a single cost function for the load/network (g.sub.c1, g.sub.c2)

(13) 6. If the control objectives of the converter/inverter are of a different nature (voltage, current, switching frequency, losses) define a cost function for each of them. If they are of the same nature (only currents, only voltages, only losses, etc.) define a single cost function for the converter/inverter (g.sub.i1, g.sub.i2)

(14) 7. Using Mcarga, evaluate the possible states for the load/network and evaluate g.sub.c1 determining the two states that minimize the cost function g.sub.c1 then evaluate g.sub.c2 for the preselected states and determine the state that minimizes g.sub.c2.

(15) 8. With the resulting state, select the redundancies of the existing converter/inverter for said state and evaluate g.sub.i1 using the M.sub.inversor by selecting those that minimize the cost function g.sub.c1, subsequently, of the redundant states that minimize g.sub.i1 evaluate g.sub.i2 obtaining the state that minimizes g.sub.i2.

(16) 9. Apply resulting state from the previous step.

Application Example

(17) The present invention provides a method of sequential predictive control as shown in FIG. 2, where the application is for an induction machine consisting of first controlling a variable with a unitary cost function (a single term or control objective) and then the following terms. In this case of the control of an electric machine, the first variable to be controlled is the Torque, whose reference value is given, in this case, by the linear control of the angular speed of the machine. The two possible driving states of the converter that minimize the Torque are determined and then the predictive control of the Flow is carried out, which minimizes its cost function considering only the two options delivered by the Torque control process. The state that minimizes the error in the Stator Electric Flow is the one applied in the system.

(18) Using the method of sequential predictive control of the present invention, the control of the induction machine was performed, which presents control objectives where the cost function contains equally important terms, in this case a term of greater importance cannot be distinguished than the other, the most complex control when defining the weight factor. The results of the simulation of the control performed are shown in FIG. 3 and FIG. 4.

(19) The equations that describe the system for modeling the torque and electrical flow of the machine stator are given by:

(20) ${\psi }_r^{k+1}=\frac{L_r}{L_m}{\psi }_s^{k+1}-\frac{1}{\lambda L_m}{i}_s^{k+1}$$T_e^{k+1}=\frac{3}{2}{N}_p{\psi }_s^{k+1}.Math.i_s^{k+1}$

(21) Where Lr is the rotor inductance, Lm is the mutual rotor-stator inductance and λ is a factor given by the resistances, inductances and permeability of the machine, Np is the number of pole pairs of the machine, all known as machine parameters, and the superscript k+1 indicates that it is the estimated value at the next instant of the sampling time k.

(22) The cost functions g.sub.1 and g.sub.2 are determined by:
g.sub.1=(T.sub.m−T.sub.r).sup.2
g.sub.2=(φ.sub.m−φ.sub.r).sup.2

(23) Where the subscript m indicates that the variable is measured and the subscript r is the reference value.

(24) It should be noted that this sequential predictive control SMPC (Sequential Model Predictive Control), can be used to control any system, regardless of its nature, as long as there are equations that model the behavior of the system and that allow predicting it, in the case of electrical systems, all of them can be controlled without problems by the SMPC, even those with terms of equal importance in the control objectives, such as the case of the induction machine.