DE3316761A1 - Predictive control method - Google Patents

Abstract

The proposed ''predictive control method'' optimises the control behaviour of controllers whose control paths contain dead times. Typical representatives of these are converters which, from the control-engineering viewpoint, even have variable dead times, that is to say are time-variant transmission elements. The basic principle of the predictive control method is the prior calculation of the behaviour of the control path for the time period following the dead time. The drive signal (control voltage) for the control path is derived from the result of this prediction. Fig. 5 demonstrates the predictive method on a current controller for a line-controlled converter. By making reference to the next subsequent converter switching state, the controller calculates the required load current behaviour. As a result of the comparison of this ''precalculated'' signal with the actual current signal, the change-over time for the converter can be determined. <IMAGE>

Description

Designation: "Predictive control method"

Publications considered for the patent application: / 1 / R. Jötten The calculation of single and multiple integrating control loops in the Drive technology AEG-Mitteilungen (1962), pp. 219-231.

/ 2 / D. Schröder Dynamic properties of converter actuators with natural commutation control technology and process data processing, issue 4, 1971, Pp. 155-162.

/ 3 / D. Schröder Analysis and Synthesis of Automatic Control Systems with controlled converters 5th IFAC Congress 1972, pp. 1-8.

Session 22.1 / 4 / Patent Application Papers No. 32 20 198.2 and No. 32 06 684.8 State of the art There are many publications from the literature known to deal with the problem of control and regulation when converter actuators are included in the control loop. The problem can be seen particularly clearly, if control loops close to the converter actuator are considered, these are for example the voltage and current control loops. The difficulty with such Control loops consists in the fact that the actuators are generally dynamically non-linear work e.g. the duty cycle of the actuator is not constant.

Since such control loops cannot be processed with linear control theory appropriate simplifications had to be made. A simplification in principle is the linearization at the operating point, i.e. there are only very small changes of the signals around the operating point assumed / 1 /. This approximation lies on the "safe side" of the parameter estimates and thus uses the actuator properties only limited.

Due to the increasing demands on the dynamics of control loops with converter actuators an attempt was made to find more general approximations. An improved approximation takes into account the large-signal behavior of the actuators / 2 /. This approximation is aware of the linearization at the working point and in the mathematical approach, for example, all working points, all permissible amplitudes of the triggering signal, all permissible points in time of the signal change etc. approved. The result is a complex mathematical relationship between the influencing parameters on the one hand and the desired result of the waiting time on the other hand.

Since with the linear control theory such complex relationships can only be taken into account to a limited extent, a new approximation of the complex Relationships sought and found on a statistical basis. With this statistical Approach results in results that correspond to reality much better than with the approximation of the linearization. But be on it at this point pointed out that with the second approximation only a Correspondence between theory and practice is to be expected.

As already shown in the literature / 2 /, the in the actuators Dynamics contained only in the statistical mean, but not fully exploited in individual cases. This is a disadvantage that is already included in the approach.

The problems become even more difficult if apart from the non-flawless one Area of the current also the gap area of the current is taken into account. There are also a large number of publications and for this problem Proposed solutions. The peculiarity of this problem is that apart from the actuator behavior also the load parameters are of great influence, so that the mathematical description is even more complex than in the previous task / 3 /. Based on these Difficulties are then very many compromises in the practical implementation has been accepted between the effort and the dynamic results. Exemplary some difficulties are mentioned: Identification of the working point (stationary and dynamic), controller implementation and parameter modification in the controller (stationary and dynamic). For example, several variations of the solution use the mean current value and partly the regulator output voltage for identification. In / 4 / it is shown which disadvantages cannot be avoided due to this implementation. aside from that are presented in / 4 / new ways of solving some of the disadvantages of the previous solution avoid.

In general, however, it can be stated that with all previous solutions Approximations were used so that in practice undesirable deviations cannot be avoided by the design goal.

A fundamentally different approach is to use the actuator to approximate in the different work areas by characteristic curves and that to approximate dynamic actuator behavior through dead times. The device-related But effort increases very quickly if the dynamic results are reasonably satisfactory are required. "Feed forward-feedback" structures also tend to be less favorable Results compared to the above solutions.

Another way is to simulate the system on the computer. In in this case, however, an approximation of the dynamic one must also be used for the actuator Behavior can be found or the actuator must be simulated in the structure. In the first case - the approximation - the old problem persists. In the second Case - the simulation - can be the effort for that Simulation considerable increase. Almost independent of the complexity of the simulation, the problem remains As in the simulation, the next ignition point of the valve (s) is found will. Here, too, various examples are given in the literature. In general the task is to determine the ignition point as precisely as possible in order to Generate system disturbances not caused by the simulation. The one dealt with here With these means, however, the question of the optimal dynamic ignition point only becomes treated within the framework of the theories presented above. It remains to be stated that basically solutions have been used so far that are based on linear control theory go out. When trying to work with sampling theory, linearization becomes general assumed in the operating point. This means that the scope of the solutions is the same restricted.

The aim of the considerations should be how with new methods and devices a general solution to the above problems can be achieved. A new tool is the microcomputer. There are a number of publications in this area as well before. In these implementations, however, the above-mentioned methods are used has been or has been transferred to the microcomputer. The disadvantages of these solutions are on the one hand by the restrictions in the approximations and on the other hand increased by the sometimes considerable computing times of the microcomputers. In The methods and solutions presented here are intended to avoid the disadvantages, by adapting the dynamic behavior of the microcomputer to the dynamic behavior of the actuator fully adapts, this is done by a predictive solution.

The new method with prediction To get the new method in a simple An example to explain a system with a converter actuator with natural Commutation and an ohmic-inductive load, which is also a counter voltage should contain. The example therefore corresponds to a drive system, that consists of a converter actuator and a direct current shunt machine consists. For further simplification, it is assumed in the explanations that the Parameters of the load such as the ohmic resistance, the inductance and the counter voltage are constant. But these are not fundamental necessities for the application of the procedure, but this simplification is only from didactic Reasons accepted. Another didactic restriction that the counter voltage should be a direct voltage that does not change over time is also not necessary.

The counter voltage may also vary over time, e.g. sinusoidal be with variable frequency as with three-phase machines. The actuator can also be other than an actuator with natural commutation, i.e. an actuator with load commutation or a self-guided actuator.

The new method for controlling power converter actuators works on the assumption that the valves of a converter have a switching character, i.e. have either an infinitely small or an infinitely large resistance. On this condition, the connection between the electrical network and the load created by the converter (see Fig. 1) by a Equivalent circuit diagram or a model can be described (see Fig. 2). The number of different possible models is indicated by the number of different possible Switching states of the converter are determined. A six-pulse converter on the three-phase network has e.g. 6 basic switching states (sole time of the valves), which are represented by 6 equivalent circuit diagrams can be described. However, these equivalent circuit diagrams differ in this case only in the phase position of the supply voltage (see Fig.

3).

The individual equivalent circuit diagrams or models are valid as long as the converter is in the corresponding switching state. Current and voltage curves can then be determined from a differential equation established by the model, whereby initial values must be taken into account. The differential equation valid for the model in Figure 3 is: x = location id (X = xo) = 1o The associated signal curves are shown in Fig. 4.

As noted above, a further didactic prerequisite is that the parameters L, R and Ue do not change while the differential equation is valid, i.e. while the converter is in a switching state. The solution of the differential equation is then composed of a homogeneous and a particulate part. The homogeneous part is dependent. from the initial values of the model, the particular part from the perturbation function. The solution of the differential equation (1) is therefore composed as follows: homogeneous part particulate part To simplify the analysis, the counter-voltage possibly present in the load was regarded as the supply voltage. In this case, the particular part of the solution is made up of a sine function and a constant component. The homogeneous solution is an exponential function (model: two-pole 1st order), the initial value of which depends on the initial values of the model.

The parameters A, B, C, s and t can be derived from the parameters of the Model (Fig. 3) and from desired boundary conditions (e.g. initial values, mean values) determine. Therefore, the converter behavior can be related to a specific Switching status at any time - even before the relevant switching status actually occurs present - calculate.

The control method according to the invention with prediction now calculates that Desired converter behavior, with the next expected converter switching state is taken into account. Are there suitable conditions for the transition to this switching state? before, the converter is switched over.

The following procedure results from the example of the six-pulse converter (Fig.5): In the time before a certain switching state of the converter is present, is based on the equivalent circuit that is expected to be the next Switching state heard, a desired signal course "pre-calculated" (see dashed Course in Fig. 5). As soon as the actual converter signal matches the "pre-calculated" matches, the converter is brought into the switching state that corresponds to the "advance calculation" was the basis. From this point in time, the "advance calculation" is based on the next expected Converter switching status and the corresponding Equivalent circuit diagram. An important property of the method according to the invention is the independence of the converter operating areas (in this case: gap and non-void area; see Fig. 5).

In fig. 6 and fig. 7 it is shown how the procedure in the case of a Converter current control works: Since the "pre-calculated" signal curve both of the next expected converter switching state as well as the desired converter behavior (e.g. average current value), there is a sudden change in the "pre-calculated" Signal curve either with a change in the switching state or a change the desired converter behavior. The control properties of the procedure are optimal: The desired converter behavior is achieved as quickly as possible and without overshoot achieved.

The mode of operation shown in Fig. 6 and Fig. 7 is as follows: From the comparison of the "pre-calculated" and real signal it is determined whether a favorable switching time is present. This determination takes place at short time intervals again and again. Another possibility, however, is the following way of working: From the Difference between the "pre-calculated" and the real signal becomes an expected one optimum switching time determined. The result is sent to the converter actuator, which in this case contains a conventional tax rate (e.g. via a control voltage). The switchover then takes place at the pre-calculated point in time.

The converter control method according to the invention can be based on use all types of power converters. The structure shown in Fig. 8 represents a Possibility of implementation. The advance calculation unit (1) calculates the desired based on the next expected converter switching state Converter signal. The control circuit (2) compares this signal with the actual value. As soon as there is a suitable time for the converter switchover, it switches the controller (usually only a two-position controller is required for this) the converter around. If necessary, the correction unit (3) can be used to make adjustments to the "forecast" - Parameters can be made to the current load condition.

The above-described application of the method is only shown in connection with converter actuators, but it can also be shown in Can be used in connection with other actuators and lines. In particular in connection with transmission elements that have scanning properties or dead times the advantages of the forecast can be used.

From the previous explanations it can be seen that the signal processing Part and the power-converting part or the mechanical part of the overall system are in different time ranges. During the power converting part and the mechanical part of the system is in the real time domain the signal processing part is one or more time segments in the future. The new regulation or control method should therefore be called a method with prediction will. With this procedure - as the didactically simple example shows - For example, problems of the static and dynamic non-linearities of the actuator or the problem of discontinuous and non-discontinuous flow is completely eliminated. The actuator with the load can be used to the absolute limits of its dynamics because every time the setpoint changes, the system follows the setpoint as quickly as possible and without overshoot. Should have static and dynamic non-linearities in the load are included, then these non-linearities can also be taken into account.

Another question - the influence of the disturbance or the disturbance behavior - can also be explained using the attached images. From Figure 6 it can be seen that, for example, in stationary operation in each case the precalculated course of a Signal is compared with the real course of the same signal.

Let us also assume, for didactic reasons, that a current control - as described above - should be present and that the fault, e.g. a mains voltage dip is present. Of course, the valve that has already been ignited can cause this break-in no longer take into account, so that, for example, a reduction in the current curve must occur. Due to the lowering of the current profile, however, the real profile becomes of the "current actual value" signal, the precalculated signal curve earlier in time meet, so that an advance of the ignition point automatically and in the correct Direction takes place. In contrast to the previously known control methods with e.g. PI controllers will be in present example immediately and proportionally - not with the disturbance transfer function as with the PI controller - reacts. Should the grid failure several time steps remain, then correcting the forecast the old state can easily be restored.

From the previous representations it can be seen that with the predictive control process ensures optimal behavior of the overall system will.

Of course, the question of to what extent must now be clarified the point in time of a setpoint change in the example has an influence on the behavior of the overall system. From the pictures in this chapter it can be seen that the setpoint changes always for the optimal behavior of the overall system before the optimal ignition point have to lead. If, on the other hand, there is a change in the setpoint value after the optimum ignition point (asynchronous systems), then the valve that had the optimal ignition timing had, although ignited immediately, but in this case - is - under the given external Boundary condition - only suboptimal behavior possible in the relevant ignition period; all other ignitions are again optimal.

Since in general, however, the higher-level systems nowadays in general can also have digital signal processing by synchronizing the systems this effect can easily be avoided.

Another question to be asked about the new control system is how this works Overall system behaves when limitations, e.g. maximum output voltage of the actuator, can be achieved by specifying the setpoint and the load parameters. As from the pictures This chapter can be seen, such nonlinearities caused by the Design of the power-converting and mechanical part are conditional, not compensated will. However, there are differences to the previously usual control procedures to determine. Assuming a conventionally controlled system with a PI controller is in the present case as well as with the new regulation with advance calculation the maximum control occur. But while with the conventional regulation of the Integral component of the controller, the control difference is further integrated and thus with Removal process leads to the known undesirable effects, this is the case with the new one Regulation with the advance calculation is not the case - the system behaves in a comparable manner like a controller.

This describes some of the basic properties of the new solution.

It should be pointed out again in this context, that the example of the current control was chosen only for didactic reasons.

An obvious extension of the procedure described can be on Example of speed control are shown. So far, in drive technology the controls are mainly structured as cascade control, i.e. the speed controller the current regulator was subordinate. With this solution, the necessary conditions could be met be respected. With this solution, the speed controller was basically the Current controller of the - generally limited - current setpoint supplied. The dynamic the inner control loop of the current control loop, however, essentially determined the Dynamics of the outer control loop - the speed control loop.

The new solution is now on the one hand - except for possible limitations -Ensured that-the most favorable overall behavior is always achieved, which also is also constant. Under these conditions, for example, the one presented in the example Current control loop can be assumed to be linear under all operating conditions, and The existing theories of control and automation technology can then be used be applied in full validity. Another solution is opening up Additionally. Since it is known in advance how the electricity can be built up and taken down, the optimal course of the speed can also be determined beforehand. The math Treatment and the technical implementation is analogous to that shown above Example. Whether in the implementation of the equipment, each task is assigned to a processor is assigned or other structures are implemented, is without principle Concern.

The process can also be applied to other tasks using the electricity and speed control can also be expanded.

It should be pointed out at this point that the precalculation takes place in time segments. In the example of the current control, the time step was in essentially determined by the actuator behavior, for didactic reasons each only calculated one time step in advance. If the setpoint does not change and If there are no interfering influences, the system will be in a steady state. In this case it can be seen immediately that an arbitrarily long time in advance the Ignition times can be calculated and thus determined. The control device in this case only has to monitor whether Changes have occurred and can otherwise take on other tasks. The procedure - "forecast by several time steps "- is in principle also possible in the dynamic case. This also applies to control loops such as the speed and the position Etc..

Claims (11)

Claims 0 control device for a system consisting of control device, Actuator and load, characterized in that the control device around a certain temporal amount in advance the dynamic behavior of the actuator and the load calculated with the actual signal (s) of the actuator operating in real time and the load (controlled system) compares and from the comparison of the signals that optimal control signal determined. 2. Control device according to claim 1, characterized in that the course of the actual signal (s) as well as the course of the predicted one (s) optimal signal (s) is (are) available in analytical form and thus the time (s) The intersection (s) of the signals can be calculated in advance. 3. Control device according to claim 1, characterized in that that no precalculation of the temporal intersection (s) of the signals takes place, but that the actual signal (s) directly with the precalculated signal (s) is (are) compared and, if the signals are equal, a corresponding control signal is initiated. 4. Control device according to claims 1-3, characterized in that that the actuators switching elements such as relays, transistors, Thyristors, GTO e.t.c. exhibit. 5. Control device according to claims 1-4, characterized in that that the actuators are converter actuators that are either external, load or are self-guided. 6. Control device according to claims 1-5, characterized in that that the load electrical machines such as DC machines or Three-phase machines are. 7. Control device according to claims 1-6, characterized in that that the control device only one time step in advance the behavior of the controlled System calculated. 8. Control device according to claims 1-6, characterized in that that the control device several time steps in advance the behavior of the controlled System calculated. 9. Control device according to claims 1-8, characterized in that that the control device with advance calculation (prediction) is combined with known ones Control devices to influence different variables to be controlled. 10. Control device according to claims 1-8, characterized in that that several control devices are combined with one another with advance calculation, to influence different variables to be controlled. 11. Control devices according to claims 1-10, characterized in that that the control device is implemented analog, hybrid or digital with precalculation will.