WO1997044717A1 - Digital method of regulating linear regulation processes, in particular suitable for rapidly and precisely regulating the position and rotational speed of electric motors - Google Patents

Abstract

The invention concerns a digital method of regulating linear regulating processes which is suitable in particular for regulating the position and speed of loads moved by an electric motor, the rotational speed and position of the motor being regulated simultaneously. The regulation can also follow a continual variation in the reference variable, e.g. for continuous path control systems or when, on multi-axis machines, the movements according to the different axes are to be adapted to one another. As a function of the settling time available for the respective regulating process, the regulator calculates a rectilinear curve of the correcting variable (of the motor current) which leads to the target in a dead beat manner. The regulation is highly precise, rapid, stable and robust. In comparison with conventional controllers (of the PD and possibly the PID type) the advantages are the shorter settling times, lack of inherent instability, greater rigidity, easier adjustability and fewer motor energy losses. In addition, it is known in advance when the regulating target will be reached. The digital regulator can be constructed simply and economically with a microcomputer.

Description

 description

Numerical control method for linear control processes, particularly suitable for fast and exact position and speed control of electric motors.

description

The invention is explained on the basis of a position control according to FIG. 1. It can be transferred analogously to other linear control processes, especially if the controlled variable results from the double integration of the manipulated variable over time. The example of the position control is therefore not to be understood in a restrictive sense.

The motor 1 moves the load 2, the position of which is to be regulated. The actual position of the load 2 is determined with a position measurement 3, for example by an incremental rotary encoder, and is reported to the controller 5 as a controlled variable 4. The task of the system is to set the control variable 4 (= actual position value = Sist) quickly and precisely to the reference variable (= desired position value = target position = S _ΞO ιι), which is given to the controller 5 by the external control system 7. For this purpose, controller 5 forms manipulated variable 8 in the form of a value for motor current 9. The corresponding motor current is impressed on motor 1 by power amplifier 10. It causes a torque on the motor axis and thus an acceleration of the load 2, which shifts the load 2 into the target position.

In addition to the position setpoint, the controller 5 can be given a speed setpoint 11 (V _so ιι) as the second reference variable. Load 2 then reaches the destination at the desired speed. In this way, any trajectory curves (S _so ιι = f (t) and V _so ιι = f '(t)) can _be traversed by the controller 5 actuating an uninterrupted sequence of support points of the trajectory. Such control loops are state of the art (e.g. Ludwig Merz et al.: Basic course in control engineering, 9th edition, R. Oldenbourg Verlag, 1988, p. 268 and Hans-Jürgen Schaad: Practice of digital drive control, Franzis-Verlag, 1992, p 17). Conventionally, PD or PID controllers are used for this purpose, some of which are nested several times (cascade control). However, these regulations either tend to overshoot in the target position or the load creeps too slowly to the target position, which leads to long settling times. The time behavior can be with the

The method from US Pat. No. 4,694,229 can be improved, but with all known controllers the time of arrival cannot be predicted exactly and the arrival can be delayed if external interference influences the course of movement. In addition, the control characteristic causes an unnecessarily high energy loss of the motor.

The invention has for its object to develop a control method that avoids the disadvantages just mentioned and that can be characterized as accurate, fast, stable, free of overshoots, robust, energy-saving and simple. The task is solved by the teaching of the claims.

When discussing the control properties, the

Figures 2 to 14 referenced. They show an example of the temporal course of the three variables motor current (iMotor) »load speed (Vi _st ) and distance of the load from the target (Si _st - S _So iι) under different operating conditions:

Figure 2: New control principle under ideal conditions Figure 3: Triangular speed profile Figure 4: Course with negative starting speed Figure 5: Course with positive starting speed Figure 6: Constant "inertia" is 33% too high Figure 7: Constant "inertia" is 33% set too low Figure 8: Speed disturbed by external influences Figure 9: The position is disturbed by external influences Figure 10: From standstill to a positive top speed Figure 11: Identical start and end speeds Figure 12: Course at a negative top speed Figure 13: Constant acceleration according to equation (11) Figure 14: Linearly decreasing acceleration according to equation (12)

The starting point is the well-known physical knowledge that the speed of a body results from the integral of the acceleration and that the integral of the speed describes the distance covered. From these natural laws of motion theory, two conditions can be formulated for the course of the acceleration of the load a _load (t), which must be fulfilled so that the control goal (S _so ιι, V _so ιι) is actually achieved when the settling time t _{a has} expired:

Vi _s t + / / aiast (t) dt = V _ao li d)

Sut + / SSM ⁽ 2 ⁾

This means: t _a = settling time until the target position is reached [s] acceleration of the load [m / s ² ]

Vi _s t = actual speed value [m / s] = start speed (at time t = 0)

V _so ιι = speed setpoint [m / s] (at time t = t _a ) Si _Ξt = actual position value [m] = start position (at time t = 0)

+ k'2 x t mit 0 < t < t_a und (3)As can be verified by inserting (3) in (1) and (2), the following line equation (3) was used to find a function for a _Las t (t) that fulfills both equations (1) and (2): Q> load (t)

+ k'2 xt with 0 <t <t _a and (3)

kι = 6 x

fc ₂ = 12 ^{x, 8t 8} ° "+ 6 x ^* ° _', ^LSL (3b)

The linear course of the acceleration is advantageous for the energy consumption of the motor (see below) and leads to a relatively simple control algorithm for calculating the motor current. However, variants of this equation with functions of a higher order can also be used if they also comply with equations of motion (1) and (2).

In order to determine the load acceleration a _load using this method, it is necessary to know the settling time t _a . t _a indicates the time that the system needs for the current control process to reach the target position. The essential element of the new controller is therefore a time register (cf. FIG. 12 in FIG. 1) which provides the value t _a for the calculation. As soon as the control system specifies a new target position, the time register must be initialized. There are basically two options:

a) t _a is specified as part of the command variables by the control system (cf. FIG. 1, switch position "a"). This is recommended if the control system knows the point in time at which the load should have reached the target position, for example on machines that are subject to a certain work cycle. In the case of a multi-axis robot, the same value for t _{a can be} specified for all axes. Axes that only have to travel a relatively short distance then carry out the movement accordingly smoothly, ie without jerks, with little wear and energy saving. b) t _a is determined automatically by the controller (cf. FIG. 1, switch position "b"). This procedure is recommended if the target position is to be reached as quickly as possible or if a conventional controller (eg PD controller) is to be replaced and the control system is therefore not prepared for communicating the arrival time t _a .

If the permissible maximum values are assumed for the acceleration of the load a _load (or for the motor current iMotor / see equation (5)), then by changing equation (3) it can be calculated which settling time t _a is required for the movement sequence at least . The consideration only needs to be made for t = 0 and t = t _a , because due to the linear course of the acceleration, the maximum of the acceleration only at one of the two

End points of the movement can occur. The result is two quadratic equations, the solutions of which limit the permissible value range for t _a . The smallest possible value for t _a must be selected from these solutions, which still ensures that the system is only required to accelerate within its physical limits (eg maximum engine torque).

After initialization, the controller must constantly update the content of the time register 12, e.g. by the

Regulator reduces the settling time t _a at regular intervals by the amount of the elapsed time.

The controller calculates the desired load acceleration according to equation (3) with t = 0:

aLast (4)

All the values required for this are known: S _ΞO n and V _so ιι were specified by the control system, t _a is taken from the time register, Si _Ξt is a measured controlled variable and V ± _st can either also be measured directly (eg with a Tachometer generator) or Vi _s t is derived from the actual position values (Vi _St = Δs _ist / Δt).

The motor current I _Mo t _or is to be set so that the load acceleration determined with equation (4) results. In commercial servo motors generally is a linear relationship between the motor current and the motor torque, the motor current i that is _engine load and the acceleration a _La st are proportional to one another:

I _M otor = inertia xa _load (5)

The following mean: lMotor = motor current [A] Inertia = system-specific constant [As ² / m], proportional to the moment of inertia of the moving masses and inversely proportional to the motor-torque constant a _Last = load acceleration [m / s ² ]

Equation (4), (10), (11) or (12)

This simple, proportional relationship applies in good approximation to the system shown in FIG. 1. In other applications, e.g. Equation (5) must be adapted accordingly if friction, spring or weight forces exert a significant influence or where a non-linear motor characteristic has to be compensated.

The controller must continuously re-evaluate equations (4) and (5) in real time and thereby continuously update the manipulated variable I _motor . He can, for example, by a

Microcomputers can be realized, which executes this control algorithm cyclically or periodically. The actually continuous course of the manipulated variable is approximated by a time-discrete, step-shaped course. The approximation is more successful the more the calculation is repeated. A system-specific cycle time (e.g. 500 μs) should not be exceeded so that no deviation from the ideal course is noticeable. Since the settling time t _{a is} automatically reduced continuously, and since the current measured values of the controlled variables (Si _St , V _lst ) are used for each new calculation, the controller always appears to be at the beginning of the movement sequence (t = 0 in the sense of the equations (1) to (3)), and it can always be calculated with equation (4). Equations (1) to (3) only serve to explain the relationships and are not required by the controller to determine the motor current I _motor .

Equation (4) contains a pole for t _a = 0. In conjunction with delay times in the control loop (caused, among other things, by a dead time of the power amplifier, the inductance of the motor and the computing time for the control algorithm), instability arises for very small values of t _a .

Therefore, t _a should not be reduced to zero. If the load is to stand still in the target (V _so ιι = 0), t _a can be limited to a suitable minimum value. In practice it has proven useful to use about four times the value of the delay times mentioned. The target position is then safely reached after a very short calming period. The delay times should be kept as short as possible so that a lower minimum value is used and the control achieves high rigidity in the end position. If the movement is part of a trajectory and the load should cross the target position (V _so ιι ≠ 0), you can switch to the next segment of the trajectory shortly before reaching the target.

Figure 2 illustrates the effects of the control principle by the time course of the three variables motor current (IMotor) / speed (V _actual ) and position _error (S _1Ξt - S _S oiι) is shown graphically. In the example shown, the load is to be moved a certain distance from standstill and to stand still again at the destination (V _so ιι = 0). As expected, the control algorithm leads to a linear time profile of the motor current IMotor (see equation (3)). It can be seen that the movement is symmetrical to the center (t _a / 2) runs. The load is accelerated during the first half of the movement and decelerated again during the second half.

For conventional PD and PID controllers are high

Control speed and good damping opposing requirements, for which a compromise must be found by setting the control parameters. The new control principle combines both requirements. The control algorithm forces the path difference (Si _st - S _so n) and the speed _{Vj .st} to disappear simultaneously at the time t _{a has elapsed} . The load therefore stands still in the target position and overshoot cannot occur.

The linear course of the motor current has the advantage that the power loss of the motor is minimized. This is illustrated by the following calculation. It is based on the premise that the power loss is determined by the winding resistance R of the motor (P (t) = R x I ² (t)). Compared to a triangular-shaped speed profile, as has so far been frequently attempted in technology (see FIG. 3), there is an energy saving of 25% (see relation of equations (8) and (7)). The motor can be dimensioned correspondingly smaller. On the basis of the equation of motion (2) it can be shown that the parabolic speed profile (according to FIG. 2) initially requires 1.5 times the motor current compared to the triangular speed profile (according to FIG. 3), so that in both cases the same distance traveled after the same settling time becomes. So the energy loss is: tt

W = IR x I \ t) dt = R xf I ² (t) dt (6) oo

/ for the triangular speed profile according to FIG. 3: t _a

W = R x I ^' ll dt = R x ll xt _a (7) or for the round speed test according to equation (4) or (5) and Figure 2:

W = R x dt = 0.75 x R x 1% xt _a (8)

It means:

W = energy loss [Ws] R = motor winding resistance [Ω]

I _k = amount of the motor current in the triangular

Speed profile according to FIG. 3 [A] t _a = settling time until the target position is reached [s]

The following examples show that the control system reacts promptly, appropriately and stably even when there are deviations from the ideal conditions:

a) If the load is moving at the start of the control (Figures 4 and 5), the current curve is linear again, but no longer symmetrical to the center. The important property that the load comes to a standstill in the target position with the expiration of t _a is retained.

angibt (vgl. Gleichung (5)) , läßt sich die Trägheit im laufenden Regelbetrieb ausmessen (Trägheit= I_MotorχΔt/ΔVi_St) • Es ist daher leicht möglich, die Regler-Software so zu erweitern, daß sich der Regler auf den optimalen Wert für die Trägheit automatisch einstellt.b) If the controller uses an inertia that differs from the actual one (Figures 6 and 7), this is tolerated over a wide range, so that the precise arrival at the right time is guaranteed. The somewhat increased power loss due to the curved motor current curve has a disadvantageous effect. On the basis of the convex or concave course of the current curve, however, it can be seen that a faulty inertia is expected. Because the inertia is the relationship between the Motor current IMotor and the load acceleration

indicates (cf. equation (5)), the inertia can be measured during normal control operation (inertia = I _motor χΔt / ΔVi _St ) • It is therefore easily possible to expand the controller software so that the controller adjusts to the optimum Automatically sets the inertia value.

Inertia is the only adjustable control parameter. In contrast, with conventional PD or PID controllers, several parameters have to be adjusted, which also influence each other. Sufficient control properties are often only achieved with a high gain factor just below the vibration limit. The PD / PID control then threatens to slide into instability if the ambient conditions change slightly. The new control principle is much more robust, the settings for maintenance or commissioning can be carried out more easily and quickly.

If external disturbances suddenly change the speed (Figure 8) or the position (Figure 9), the controller immediately adjusts to the changed situation and brings about a linear course of the motor current, which leads safely to the target. Faults that occur long before the arrival time are reacted relatively gently, since the entire remaining time of t _{a is used up} to correct the situation. However, disturbances of the same size shortly before arrival lead to violent reactions of the motor current in order to compensate for the disturbance in good time. As long as the physical system limits (eg maximum engine torque) are not exceeded, the load reaches its destination without overshoot and without delaying the arrival time. This is a decisive advantage over classic controllers (eg PD controllers), in which the arrival time shifts backwards with every disturbance and in which the arrival time cannot therefore be predicted exactly. d) If the target is to be passed at a certain speed (V _so n ≠ 0), the control algorithm succeeds in simultaneously reaching the desired final speed V _so ιι as well as the desired target position S _so n (t _a) Figure 10). It is not necessary for the movement to start from a standstill (cf. FIG. 11), and negative speeds or distances are also processed correctly, even if the end point of a positive distance is to be crossed with a negative speed (backwards) (see Figure 12).

With the control principle, any trajectory S _so ιι = f (t) and V _so n = f '(t) can be followed by dividing the trajectory into a large number of small segments, the end points (= bases) one after the other with the one described here Regulatory procedures can be started. As a result, the load has the correct position and speed at the support points, so that there is no significant path error S _Fe here = (V _lεt -V _S oiι) ^χ Δt between the support points and the course of the path is maintained with high accuracy.

A special case is the pure position control, in which the speed in the target position V _so n is not specified by the control system. In this case, the terminal velocity V can _thus n by rearranging Equation (3b) can be determined:

The value of V _{soll found in this way} is inserted into equation (4):

Damit ist V_soιι aus dem Regelungsalgorithmus eliminiert. Für k₂ können theoretisch beliebige Werte verwendet werden. Von besonderer praktischer Bedeutung sind zwei Fälle:

V is _thus eliminated from the control algorithm. In theory, any values can be used for k ₂ . Two cases are of particular practical importance:

a) k ₂ = 0. This results in an almost constant acceleration of the load, which then crosses the target position exactly when t _a expires. In this special case, equation (10) is simplified to:

The speed shows a linear course (Figure 13). This can be used to implement the triangular speed profile according to FIG. 3. Despite the unfavorable power loss (see above), this is advantageous if a high

Maximum speed is required in the middle of the movement or when smooth acceleration is desirable. For this purpose, regulation is carried out in the acceleration phase during the first part of the movement according to equation (11), the target S _being set to half the total distance and the arrival time t _a to half the total time _, for example. The equation (4) is then switched over to the braking phase and the total path S _so ιι and the rest of the total time for t _{a are} calculated. The division into an acceleration and braking phase has already been proposed in US Pat. No. 4,694,229, but an unfavorable control algorithm is used there, in which the arrival time cannot be predicted exactly.

b) k ₂ = -kι / t _a . The acceleration and the motor current that are set decrease linearly and disappear when t _a (a _load (t _a ) = 0, see equation (3)). The course is shown in FIG. 14. In this case, equation (10) is simplified to:

Applications arise when there is no acceleration force acting on the load at the time of arrival or when external disturbances can be expected shortly before the destination, the full engine torque of which should be available to regulate. In addition, a 25% lower energy loss is calculated compared to a regulation according to equation (11).

The application revealed a fast, highly accurate, energy-saving, simple, stable and robust control process. A test setup with a 1.3 KW servo motor confirms this. The two controlled variables S _actual and V _1Ξt are recorded with an incremental encoder (4000 pulses / revolution). An ordinary microcomputer takes over the entire signal processing of the controller. The control algorithm is repeated with a cycle time of 1 ms. In this structure, the motor passes over the target within ± 3μs the predetermined settling time t _a (at 30 U / s) and oscillates a maximum of 0.3 ° over the target position beyond _(to at V = 0).

Claims

claims 1. A numerical control method for controlling the position S and the speed V by a motor moving load as well as for other linear control processes, wherein an actual value _S, and its first time derivative of V _{is defined} as the time t = 0 the detected controlled variables as well as the Both associated target values S _aoll and V specified by a control system are _{to be processed} as the control variables corresponding to the control target at the time t = t _a into a control variable, characterized in that the control variable a _{load is} based on the relationship dLast {t) - kι + k ₂ xt with 0 <t <t _a and kι = 6 x ^Ssdl 7 ^{S> st} - 2 x ^{VsoU + 2 XV »} > ta t _a / c ₂ - 12 x - ₃ + 6 x ^ al _{a is} set, whereby variants of the function for a _load (t) can also be used if they also depend on the settling time t _a and the equations of motion ta V, st -r / a _La st {t) dt = V _so u {ta Sist - * - {V _ΪSt + / ÜLastit) dt) dt = S _so u 0 at least approximately meet. 2. The method according to claim 1, characterized in that always the current actual values of the controlled variables S _i8t and V _lst by repeated calculation based on the calculation rule a _load = 6 _x ^S "> u ^~ Si * _ _{2 χ} V ^ + 2 x V ^ ^ α t _a to the manipulated variable a _{load are} processed, where t _a indicates the settling time, at the expiration of which the control target

is achieved. 3. The method according to claim 1 or 2, characterized in that the manipulated variable a _La8t on the basis of the calculation rule _{O ^} ^s ° ^{11 ~} is _{0 s} „Vist k ₂ X t _a CLLast = 2 X 73 2 X tα t _a o is determined if the control system does not prescribe a specific value for V _soll and instead the value k _{2 is} known, which indicates the intended gradient of the manipulated variable, preferably by repeated calculation on the basis of the current actual values of the controlled variables. 4. The method according to claim 3, characterized in that k ₂ = 0 is set and the manipulated variable a _La6t thus on the basis of the calculation rule

is determined, as a result of which the manipulated variable assumes an almost constant value until the control target S _lst = S _{soll is reached} exactly with the settling time t _a . 5. The method according to claim 3, characterized in that k ₂ = -k ₁ / t _{a is} set and the manipulated variable a _load thus on the basis of the calculation rule aL «s _t = ϊ- x ( ^Ss °" ^{~ S} "'- V _i3t La V La is determined, as a result of which the manipulated variable decreases almost linearly until it disappears when the control target S _i8t = S _{target is reached} at the same time as the settling time t _a . 6. The method according to any one of claims 1 to 5, characterized in that a proportional to a _load Manipulated variable I motor = inertia x ai _ast is used, the inertia representing a system-specific proportionality constant that describes the relationship between the manipulated variable and the second time derivative of the controlled variable S _i8t [inertia = I _motor / (d ² S _lst / dt ² ) = I _motor / (dV _is / dt)]. 7. The method according to any one of claims 1 to 6, characterized in that the inertia is automatically determined by the controller. 8. A method according to any one of claims 1 to 7, characterized in that are that the need for the calculation of the manipulated variable setpoint variables S _should and V _8θU by scanning the management functions S _SOU = f (t) and V _80ll = f '(t) obtained. 9. The method according to any one of claims 1 to 8, characterized in that at least the initial value of the settling time t _a at the beginning of a control process is specified as part of the command variables by the control system. 10. The method according to any one of claims 1 to 9, characterized in that at least the initial value of the settling time t _a at the beginning of a control process is determined automatically by the controller by changing the control algorithm and resolving it to t _a and thus taking into account the system-specific Value range limits for the manipulated variable a value for the settling time t _{a is} determined, which ensures that the manipulated variable remains within the permissible actuating range. 11. The method according to any one of claims 1 to 10, characterized in that the controller holds the settling time t _a in a register, a variable or another storage device and updates it automatically by regularly reducing it by the elapsed time. 12. Regulator for applying the method according to one of claims 1 to 11, characterized in that a storage device is provided for holding the settling time t _a in a register or a variable in the regulator, and that the regulator is designed to automatically update the settling time t _a , preferably by regularly reducing it by the elapsed time.