WO2019002587A1 - Unité de régulation, système mécatronique et procédé pour la régulation d'un système mécatronique - Google Patents

Unité de régulation, système mécatronique et procédé pour la régulation d'un système mécatronique Download PDF

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Publication number
WO2019002587A1
WO2019002587A1 PCT/EP2018/067668 EP2018067668W WO2019002587A1 WO 2019002587 A1 WO2019002587 A1 WO 2019002587A1 EP 2018067668 W EP2018067668 W EP 2018067668W WO 2019002587 A1 WO2019002587 A1 WO 2019002587A1
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Prior art keywords
manipulated variable
mechatronic system
value
values
mechatronic
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PCT/EP2018/067668
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German (de)
English (en)
Inventor
Torsten Bertram
Artemi MAKAROW
Martin Keller
Christoph Rösmann
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Technische Universität Dortmund
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Publication of WO2019002587A1 publication Critical patent/WO2019002587A1/fr

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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/048—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators using a predictor
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/30—Nc systems
    • G05B2219/45—Nc applications
    • G05B2219/45092—Analysing or chemical synthesis robot, moving samples from station to station

Definitions

  • the present invention relates to a method for regulating a mechatronic system, in which a manipulated variable value to be set is determined and set for at least one manipulated variable on the basis of a model of the mechatronic system, and a control unit for a mechatronic system, which is set up for carrying out such a method and a mechatronic system with such a control unit.
  • PID controllers For fast and precise control of mechatronic systems, classic control concepts (PID controllers) can be used. Mechatronic systems are usually characterized by a non-linear system behavior. In order to meet the high demands on the system behavior, the number of controller parameters and thus the complexity of the classic PID control concept should be greatly increased. As a rule, the integral and proportional amplification is extended by non-linear characteristics. The design of such controllers is not intuitive and is associated with a very high cost. In addition, the controller found is usually not robust due to the complexity of changes in the controlled system behavior. A subsequent adaptation of the System behavior by changing the controller parameters is therefore generally only feasible by a process expert or developer.
  • Model Predictive Control is a control concept that is already used in industry.
  • the prediction of the future system behavior in each sampling step ie a specific time interval, achieves a very high degree of control quality.
  • entry, exit and state restrictions can be explicitly taken into account.
  • the effect of changing the controller parameters on the system behavior is usually very intuitive.
  • approaches such as move-blocking, for the reduction of the optimization parameters on the prediction horizon, or other approaches such as the explicit model-predictive control can be used.
  • a particular gradient-based solution algorithm must determine the optimum control sequence for the selected prediction horizon in terms of a quality measure.
  • a mechatronic system is understood in particular to mean an electronic and mechanical components-containing system.
  • a mechanical actuator can be electrically controlled.
  • a method according to the invention is used to regulate a mechatronic system, in which - similar to the classical model predictive control (MPC) - a manipulated variable value to be set is determined and set using at least one manipulated variable for a model, in particular a dynamic model of the mechatronic system.
  • MPC model predictive control
  • the inherently continuous manipulated variable value range or value range for the manipulated variable
  • a predetermined number of manipulated variable values are preset within a respective predetermined value range.
  • a course, in particular with one degree of freedom in the prediction horizon, of at least one state variable (of a state vector) of the mechatronic system is then determined over the prediction horizon.
  • a course may, for example, be a course based on a (numerical) integration or else an approximation (collocation).
  • These courses, ie the generated trajectories, the individual states or state variables, are evaluated with the aid of the quality measure, which, for example, punishes the deviations of the states from a predetermined desired course. In this way, in the course of a comparison with a desired course, that course is selected which delivers the lowest quality value and thus, for example, comes closest to the desired course.
  • the manipulated variable value of that at least one manipulated variable that corresponds to the selected curve is then set.
  • the desired value recorded in the current sampling step can be kept constant over the prediction horizon (static reference, point-to-point control). If the future desired course (target trajectory) This information can then be used on the prediction horizon (dynamic reference). The latter case is also known as trajectory following regulation.
  • the proposed method is based on the model predictive control already mentioned. In contrast, however, a gradient-based optimization calculation is no longer performed in each time interval or sampling step. Rather, in a prediction horizon, and thus in particular in one or more time intervals or sampling steps, only a predetermined number of manipulated variable values are preset within a predetermined value range, i.
  • the value range for manipulated variables that is limited and initially continuous in this way is discretized so that only a fixed number of manipulated variable values is possible.
  • Xk + 1 Xk + f (Xk + 1; Xk; Uk ) -At, or the progression of the state variables over time can be determined by means of basic functions such as poly- nomial functions. These basic functions are defined in such a way that constraints and the state differential equation are maintained at the interpolation points.
  • u k denotes manipulated variable values which lie within a range of values, that is to say u min ⁇ u k ⁇ u ma x.
  • these manipulated variable values are discretized. In order to This results in a certain number of the mentioned courses.
  • each of these trajectories ie each of these courses, can be checked with the quality measure.
  • the quality measure can be chosen arbitrarily, since no gradient-based solution algorithm is used in the process. Smoothness requirements for the optimization problem do not exist.
  • the manipulated variable value of that trajectory which delivers the smallest value of the quality measure and thus comes closest to the desired course is then selected and given to the controlled system in the next step, ie set as manipulated variable. If several states or state variables of the mechatronic system are evaluated, then this procedure must be carried out for each state.
  • the quality measure then consists of several terms to evaluate the individual states. Weights in front of the individual quality parameters can be used to allow the deviations of individual states from their respective target profiles to be incorporated into the evaluation to different degrees.
  • This prediction, evaluation and selection process can take place in each time interval or sampling step. Due to the value discretization of the manipulated variable, a gradient-based online optimization is not required. Rather, it is sufficient to test all possible manipulated variable values proposed by a suitable search algorithm and to select the most suitable manipulated variable value according to a selection criterion, for example a minimum operator. The number of calculations per time interval is This is known in advance exactly (when all manipulated variable values are tested) and therefore guarantees the real-time capability of the method. Due to the discretization of the originally continuous manipulated variable value range, the model predictive trajectory control (MPTSC) represents a suboptimal solution in comparison to the classical MPC. The minimum manipulated variable intervention is limited to the discretization step size. However, the real-time capability can be guaranteed.
  • MPTSC model predictive trajectory control
  • Two strategies can be used to reduce the influence of suboptimality by value discretization.
  • the discretization step size can be reduced so that more manipulated variable values are generated.
  • This increases the computing time requirement.
  • the error due to the approximation with a finer value discretization may possibly be neglected in comparison to the error through the determination of the states and the model error of the prediction error.
  • Another strategy is the adaptive manipulated variable discretization.
  • the particular equidistantly discretized manipulated variable value range is mapped to a new set of values in each sampling step.
  • the discretized manipulated variable value range describes the definition quantity of a function in each sampling step.
  • the set of values of this function describes the manipulated variable values to be tested in one sampling step.
  • Such a function can be described, for example, via several polynomial functions.
  • conditions can be set to this adaptation function.
  • the current control error device between setpoint and actual value
  • at least one state variable of the mechatronic system and / or a past history of the at least one manipulated variable (ie its history) are taken into account.
  • a finer discretization can be carried out with a small control error than with a large control error.
  • the minimum and maximum manipulated variable value should preferably always be contained in the adaptive manipulated variable value quantity. In this way, an adaptation of the manipulated variable discretization is possible, i. a quasi-continuous manipulated variable value range is achieved
  • switches can be introduced on the prediction horizon.
  • the respective predetermined number of manipulated variable values within the respective predetermined value range is predetermined for at least two of the several subsequent time intervals on the prediction horizon.
  • the respective predetermined number of manipulated variable values can be individually specified for each of the at least two time intervals.
  • a non-linear model can also be used, but a numerical integration must be performed at runtime.
  • a nonlinear model has the advantage that the image quality is usually higher.
  • MPTSC has the advantage that the model can be arbitrary and does not have to meet any smoothness requirements. Even data-based models can be used here. As an example, neural networks should be listed here. With such models, if they are adapted during control, a controller adaptation becomes possible.
  • the MPTSC is a sub-optimal method compared to the conventional MPC (mathematically, MPTSC is always optimal in formulating the adjusted optimal control problem), it has the ability to explicitly consider and adhere to state constraints, as shown in the experiment.
  • the optimum manipulated variable can be determined in each controller cycle by simply testing the existing manipulated variables.
  • the online optimization can be carried out here with the minimum operator (the computation time is small here in comparison to gradient-based optimization algorithms). If several degrees of freedom are to be realized on the prediction horizon (switches), then the number of trajectories to be tested increases (due to the combinatorics).
  • MPTSC with the minimum operator in terms of the necessary computational time from a certain point is no longer worthwhile compared to a gradient-based algorithm.
  • the at least one state variable preferably comprises a rotational speed, a torque or a force of an electric motor of the mechatronic system or a speed or a position of an actuator of the mechatronic system.
  • the proposed method can thus be used in particular for an electric motor or a linear drive with an actuator.
  • An electric motor in turn can be used for example as a servomotor.
  • MPC multivariable system
  • a robot arm or other movable component of an industrial robot
  • has individual servomotors and such a robot arm or robot may be considered a mechatronic system besides the single servomotor, if such a robotic arm or robot is moving or perform a task, a kinematic dynamic model of the entire robotic arm or robot can be used at run time of the control, which means that in each sampling step the manipulated variables for each individual servomotor are determined simultaneously in the joint space of the robot, in which target profiles for each joint are specified (for example in the form of positions, speeds, accelerations or moments), MTPSC can also be used with target specifications in the working space, ie in the coordinate system of the end effector or gripper
  • two alternative architectures with the MPTSC as controller are proposed.
  • MTPSC contains only a model of movement in the working space, for example movements with respect to the translational and rotational degrees of freedom of the end effector and state / command value restrictions (such as maximum speeds, accelerations, forces, moments, avoidance of collisions with obstacles).
  • the determined manipulated variables (such as speeds of the end effector) can then be transformed via the robotic Jacobi matrix into the necessary joint speeds or accelerations in the current scanning step. These can then be controlled with conventional robot servo-motor controllers or with another lower-level MPTSC in the joint space.
  • Another possible architecture is an MPTSC with a holistic (kinematic / dynamic) robot model define, which determines the associated manipulated variables for each servomotor for a given target trajectory in the working space.
  • Mechatronic systems usually have cascaded control concepts, conventionally based on classic PID control concepts.
  • the outer cascade is a (mostly complex) speed, torque, force, speed or position controller.
  • the inner cascade usually regulates state variables with fast dynamics, such as the electric current.
  • the inner cascade is then usually followed by power electronics with a modulator.
  • the modulator translates the continuous control signal (or the continuous control variable) into a discrete signal.
  • a linear drive is usually the pulse-width-modulated actuator voltage. Electric motors are usually the switch positions of the inverter.
  • the proposed method can now be used to replace the entire cascade structure or just individual controllers or control loops within an existing controller cascade. In the event that the entire cascade is replaced, the MPTSC can directly determine the control value or the original, outermost cascade. This manipulated variable or manipulated variable value can then be converted by the modulator into a discrete actuating signal.
  • the proposed strategy of adaptive manipulated variable discretization can be used if a value-continuous manipulated variable range is required.
  • the presented strategy of switching or the use of different phases and / or Stands between the switching times can be used as a supplement to increase the control quality or for better approximation of classic MPC.
  • the set of values of the manipulated variable of a controller permits only discrete values (for example PWM)
  • PWM discrete values
  • preferably only the strategy with the switching or the use of different phases and / or distances between the switching times is used.
  • the number of trajectories to be evaluated for this case is calculated as 2 n + 1 .
  • N describes the number of switches.
  • special evaluation criteria may preferably continue to be used. For example, the cutting of the desired size of a predicted state trajectory can be punished (sign change weight). Thus, only those manipulated variable values are weighted more heavily, which lead to overshoot. For the discrete case, an integrally similar fraction can be realized to eliminate a steady state error.
  • the deviation of at least one state variable from its desired course of a past sampling step can be evaluated and compared with the current deviation.
  • the manipulated variable (high level, low level for the voltage), which increases the sum of the two values, is punished more strongly. This allows a further improvement of the control while maintaining the real-time capability.
  • the invention further provides a control unit for a mechatronic system, which is set up for carrying out a method according to the invention, and a mechatronic system having such a control unit.
  • a control unit can be integrated, for example, in a computing unit of an electric motor, in particular a servomotor, or a linear actuator or linear drive, in particular a control unit.
  • the arithmetic unit can then be arranged, for example, on the corresponding mechatronic system.
  • FIG. 1 and 2 show schematically classical model predictive regulations in various embodiments or with different degrees of freedom in the prediction horizon.
  • FIG. 3 a schematically shows a method according to the invention in a preferred embodiment.
  • FIG. 3b schematically shows the control unit from FIG. 3a in a more detailed representation.
  • FIG. 4 schematically shows a method according to the invention in a further preferred embodiment.
  • FIGS. 5a and 5b each show part of a method according to the invention in a further preferred embodiment.
  • FIG. 6 shows an exemplary polynomial function for adaptive manipulated variable discretization.
  • FIG. 7 shows a comparison between desired and actual course of a controlled variable when using a method according to the invention. Detailed description of the drawing
  • FIG. 1 shows in simplified form the principle of a model-predictive control on which the invention is based.
  • the time t which is plotted to the right, divided into time intervals AI.
  • To the left is the past history of the state or the controlled variable.
  • the index k describes the controller clock or the sampling.
  • the time intervals At relate to the prediction horizon.
  • the manipulated variable value range is continuous here.
  • a prediction horizon n p the plurality of time intervals, here up to the time t N , a predicted curve V pr for at least one state.
  • the manipulated variable u has an individual value for each of the time intervals. Only the first manipulated variable value is used for controlling the controlled system. The next time t k + i, the calculation is made again.
  • FIG. 2 shows a modified variant of the model-predictive control shown in FIG.
  • FIG. 3 a shows schematically a method according to the invention in a preferred embodiment, illustrated here by the example of a block diagram of a brushless DC motor 100, in particular a servomotor (integrated state determination).
  • the Servomotor to be controlled here has a superimposed position control, for example, for a position or an angle of a shaft, and a subordinate current control, wherein the control according to the invention is applied here only in the position control 300.
  • the position control can also be exchanged with a speed control, but here only one possible embodiment is shown. However, then the speed and not the position must be determined in each sampling and passed to the controller.
  • the controller 300 or a control unit with such a controller receives as input at least one setpoint for the position (or speed), s so n, and outputs a setpoint for the current, i so n, as a manipulated variable.
  • This desired value for the current is passed to a current controller 31 0, for example a PI controller.
  • suitable sensors provide information about the current magnetic flux.
  • the rotor position must be determined using other physical parameters, such as the counter voltage.
  • an inverter 1 10 the information about the magnetic flux and the set target value for the current, ison, converted into a switching pattern for the power semiconductors.
  • the Hall signals IH a , IH b and IH C provide information about the current rotor position, which is needed to generate a new switching pattern for the power semiconductors.
  • the switch positions and thus the manipulated variables U a , U b , U c are mostly pulse-width-modulated voltage signals.
  • a controlled system 320 then results in an actual value for the position (or speed), s is .
  • the actual value s is the position is returned to the controller 300.
  • the current controller contains information about the magnetic flux of the individual phases.
  • a state vector x k shown here only by a first, individual state or a single state variable xi, is given from the controlled system 320 to the controller 300.
  • the actual value of the position or (velocity), s is, can also be contained in the state vector x k and does not necessarily have to be returned as a single signal.
  • the control unit 300 should map the current controller 310 (including 1 1 0) and the controlled system 320 (including 120) with a dynamic model. In this particular case, the model would map the input i so n to the position s ist
  • control unit 300 of Figure 3a is shown in somewhat greater detail, in particular with respect to individual modules and their operation.
  • the target value for the position, Sson is first fed in the control unit 300 to a module 301, in which several Rere manipulated variable values are generated.
  • a module 301 in which several Rere manipulated variable values are generated.
  • the various state trajectories are determined.
  • the one with the lowest quality value is then selected from these trajectories, so that then a suitable setpoint value for the current, i soN , can be output as the manipulated variable.
  • the model for predicting system behavior can be determined using the familiar system identification tools.
  • the model structure is usually assumed from a priori knowledge about the controlled system. This knowledge can be obtained from physical modeling or non-parametric system identification.
  • the model parameters can be identified by the use of optimization algorithms.
  • a measured time course of the inputs and state variables can be used as a basis for offline generation of an optimal mapping in terms of a quality measure. In most cases, the deviation from simulated and measured state variables is evaluated.
  • the found parameters can be assumed to be constant or adapted to the current system behavior with a suitable online optimization algorithm (model adaptation).
  • FIG. 4 schematically shows a method according to the invention in a further preferred embodiment, in this case using the example of a linear drive 200.
  • the regulation according to the invention is applied here to the entire control concept.
  • An additional current regulator is not needed.
  • On a cascaded control concept is waived. This procedure is suitable for linear drives, since satisfactory control quality can be achieved with a few degrees of freedom or only one degree of freedom in the prediction horizon at a prediction horizon of several scanning steps.
  • the controller 400 or a control unit with such a controller receives here as input at least one setpoint for the position, s so n, but the manipulated variable is not the current, but directly the pulse width modulated voltage U for an electromagnetic actuator. Again, the voltage can be given pulse width modulated.
  • the control unit 400 should map the controlled system 420 with a dynamic model.
  • W: ⁇ -1, -0.9, -0.8, ⁇
  • a curve V of the state variable can be determined.
  • the target value V so n is a static reference to the prediction horizon.
  • FIG. 5b schematically shows a further part of a method according to the invention in a further preferred embodiment.
  • the trajectory family for the first state x ⁇ is shown above the prediction horizon.
  • the target curve V so n in this example is the sampled target variable at time k, which is kept constant over the prediction horizon, if there is no information about the future development of the target curve.
  • curves V, V are shown, as they can be shown for different specific control variable values, as shown by way of example in FIG. 5b below (where, by way of example only, manipulated variable values ui, u 2 and u 3 are shown for a value range W). With V is also an actual history of the state shown.
  • FIG. 6 shows a possible adaptive manipulated variable discretization, as it can be used in the context of the invention.
  • the equidistant manipulated variable discretization (right value axis) is mapped to an adaptive manipulated variable discretization (high value axis).
  • each individual curve is composed of two polynomials.
  • the polynomial order the width of the area in which there is a small curve change.
  • a fine discretization takes place around the last manipulated variable u k -i.
  • u k -i, i 0.7
  • u k -i, 2 0
  • FIG. 7 shows the control behavior of a servomotor (brushless DC machine) over time t.
  • the state (xi) position in rad (or in general the first state from a state vector) is an erroneous desired course (here for a position s so n) specified.
  • the second state (x 2 , here a speed in rad / s) is regulated to a zero value.
  • the second state becomes x 2 ⁇
  • the manipulated variable value range is limited to u ⁇
  • FIG. 7 shows the associated manipulated variable profile of the general manipulated variable u, which may in particular be the nominal current i soN in amperes.

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Abstract

L'invention concerne un système mécatronique, une unité de régulation et un procédé pour la régulation d'un système mécatronique, par exemple un robot, un moteur linéaire ou un servomoteur, des valeurs de grandeur de réglage (U1, U2, U3) pour plusieurs intervalles de temps successifs, c'est-à-dire pour un horizon de prédiction (np), étant prédéfinies dans une plage de valeurs déterminée au préalable, par exemple plusieurs positions de consigne, l'allure respective future (V,V',V") d'une grandeur d'état (x1) étant déterminée au moyen d'un modèle dynamique du système mécatronique pour chacune des valeurs de grandeur de réglage prédéfinies (U1, U2, U3), par exemple l'allure du trajet à l'aide de positions déterminées par le modèle, les allures déterminées (V,V',V") étant comparées à une allure de consigne (Vsoll) et une mesure de qualité de l'allure respective (V,V',V") étant déterminée à partir de cette comparaison, la valeur de grandeur de réglage (U1, U2, U3) prédéfinie pour laquelle la mesure de qualité déterminée de l'allure respective (V,V',V") présente la valeur de qualité la plus petite étant choisie, c'est-à-dire l'allure déterminée (V,V',V") qui est la plus proche de l'allure de consigne (Vson), et la valeur de grandeur de réglage (U1, U2, U3) choisie étant réglée comme grandeur de réglage pour la régulation du système mécatronique.
PCT/EP2018/067668 2017-06-30 2018-06-29 Unité de régulation, système mécatronique et procédé pour la régulation d'un système mécatronique WO2019002587A1 (fr)

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