CN105278359B - A controller that achieves multivariable control through a single variable control unit - Google Patents

Abstract

A controller that achieves multivariable control through a single variable control unit, comprising a control unit, at least one variable, a dynamic deviation factor unit and a compensation unit. The control unit obtains an output signal based on a measurement signal and a reference signal, and the output signal is sent to a program to make the measurement signal approach the reference signal. The variable is a signal in the program that can affect the measurement signal or be affected by the control unit. The dynamic deviation factor unit obtains a dynamic deviation factor of the variable based on a short-term average and a long-term average of the variable. The compensation unit compensates the dynamic deviation factor to the measurement signal, the reference signal or the output signal to obtain a corresponding compensation signal. The compensation signal replaces the corresponding measurement signal, the reference signal or the output signal to control the program.

Description

A controller that achieves multivariable control through a single variable control unit

technical field

The present invention relates to a controller, in particular to a controller that achieves multivariable control through a single variable control unit.

Background technique

FIG. 1 is a schematic diagram of a dynamic process (Dynamic Process, or process). In the dynamic program shown in Figure 1, there are three or more simulated process variables (Process Variable, PV), each process variable will change with time, and there will be different mutual influences between variables. At least one of them is an independent variable (IndependentVariable) and a dependent variable (Dependent Variable).

As shown in Figure 2, in order to control one of the dependent variables, it is defined as a controlled variable (ControlledVariable, CV) and a control unit 101 such as a single variable controller (Single-Input Single-Output, SISO) is added to form A control loop (Control Loop), so that the dynamic program also contains the control unit. The controlled variable can be controlled within the range of a specific reference value or set point (Reference or Setpoint, SP) through the influence of the independent variable (or Manipulated Variable (MV)) in the dynamic program on the controlled variable . In Fig. 2, the solid line represents the input and output signals and directions of the control unit, the thin dotted line represents the definite mutual influence relationship between variables, the thick dotted line represents the possible mutual influence relationship between variables, and the direction of the arrow represents the direction of the mutual influence relationship.

Due to the maturity of technology and the consideration of simple versatility and price, general industrial procedures use single-variable controllers. However, most general programs have two or more program variables, so in addition to the simple stand-alone single-variable control strategy, there are many different methods in the prior art to extend the single-variable controller to be suitable for In a multivariate environment, in order to achieve better control effect. For example, independent single-variable control strategy (Single LoopControl), cascaded single-variable control strategy (Cascade Control), feedforward single-variable control strategy (Feedforward Control) and multi-variable control strategy (Multi-Variable Control) Wait. The control strategy in the prior art usually needs to use multiple univariate controllers, and each univariate controller corresponds to a controlled variable (that is, the MV and CV of each univariate controller form a loop by itself), thus , can only provide a single control function, and cannot use the rest of the program variables to assist in the control.

Therefore, how to provide a controller that achieves multivariable control through a single variable control unit, especially how to achieve multivariable or multifunctional control performance with only a single variable controller, is one of the current important issues.

Contents of the invention

An object of the present invention is to provide a controller that achieves multivariable control through a single variable control unit. The controller can easily introduce program variables outside the control loop into the control loop of the dynamic program without modification or modification. By adjusting the control parameters, any single variable controller can be turned into a multivariable or multifunctional controller with superior performance.

To achieve the above purpose, the controller according to the present invention comprises a control unit, at least one variable, at least one dynamic deviation factor unit and a compensation unit. The control unit obtains an output signal according to a measurement signal and a reference signal, and the output signal is sent to the program to change the measurement signal. The variable is one of the signals in the program that can affect the measurement signal or be affected by the control unit. The at least one dynamic offshoot factor unit obtains a dynamic offshoot factor (Dynamic Offshoot Factor, DOF) of the variable according to a short-time mean value and a long-time mean value of the variable. The compensation unit compensates the dynamic deviation factor to one of the measurement signal, the reference signal and the output signal to obtain a corresponding compensation signal, and the compensation signal replaces the corresponding measurement signal, the reference signal or the output signal to control the control unit.

In one embodiment, the control unit is a single variable controller or a single variable control unit in a multivariable controller.

In one embodiment, each of the measurement signal, the reference signal, the output signal and the compensation signal is a value or a function.

In one embodiment, the variable is a program variable of the program, or a measurement signal, a reference signal or an output signal of another controller.

In one embodiment, the dynamic deviation factor is related to the degree to which the short-term mean value or current measured value deviates from the long-term mean value.

In one embodiment, the short-time mean value is the signal value measured under one measurement interval (Sampling Interval), or the average value of the signal measured under S measurement intervals, or the signal of the variable The signal value after passing through a low-pass filter, the settling time of the filter is equivalent to S measurement intervals, and the S is greater than or equal to 1; the long-term mean value is the signal value measured under a measurement interval after passing through The signal value after a low-pass filter, or the average value of the signal measured under L measurement time intervals, the settling time of the filter is equivalent to the L measurement time intervals, and the value of L is greater than that of S value.

In one embodiment, the compensation unit compensates the dynamic deviation factor to one of the measurement signal, the reference signal and the output signal in an additive or percentage manner.

In one embodiment, when the short-time mean value is substantially equal to the long-term mean value, the dynamic deviation factor of the variable is substantially zero, or when the short-time mean value is close to the long-term mean value, the value of the dynamic deviation factor is close to Zero and can be ignored.

In one embodiment, the formula for calculating the dynamic deviation factor is as follows:

Among them, β is the dynamic deviation factor, is the short-term average, is the long-term average value, α is zero or an adjustable constant, which can avoid the denominator from being zero or can be used to adjust β. Furthermore, the dynamic deviation factor can be processed to obtain a compensation amount and then compensated to at least one of the measurement signal, the reference signal and the output signal.

Other objectives, advantages and features of the present invention will be described in detail by the following preferred embodiments and accompanying drawings.

Description of drawings

Figure 1 is a schematic diagram of a dynamic program.

Figure 2 is a schematic diagram of a dynamic program with a single variable controller.

FIG. 3 is a schematic diagram of a controller according to an embodiment of the present invention.

FIG. 4 is a schematic diagram of a dynamic deviation factor unit according to an embodiment of the present invention.

FIG. 5 is a schematic diagram of curves of short-time mean value, long-time mean value and dynamic deviation factor according to an embodiment of the present invention.

Fig. 6 is a schematic diagram of a controller according to another embodiment of the present invention.

FIG. 7 is a schematic diagram of a controller of the present invention having a feed-forward control characteristic.

Fig. 8 is a schematic diagram showing that the controller of the present invention has the characteristics of many-to-one control and multi-function control.

FIG. 9 is a schematic diagram of the controller of the present invention having many-to-many control characteristics.

Fig. 10 is a schematic diagram of the controller of the present invention applied to a heating furnace.

Symbol Description:

2: Controller

2a～2e: Control loop

100: heating furnace

101: Feed flow controller

102: Air flow controller

103: Fuel gas flow controller

104: Outlet temperature controller

105: Peroxygen controller

106: Fuel gas heat indicator

107: Fuel gas flow indicator

201: Control unit

202: variable

203: Dynamic Deviation Factor Unit

204: compensation unit

205: Measurement signal

206: Reference signal

207: output signal

208: Short-term mean

209: Long-term mean

210: Dynamic deviation factor

211: Compensation amount

212: Compensation signal

213: Original signal

Detailed ways

3 and 4 show a controller 2 according to an embodiment of the present invention. The controller 2 is used to control a program, and includes a control unit 201, at least one variable 202, at least one dynamic deviation factor unit 203 and a compensation Unit 204.

The control unit 201 of this embodiment takes a single variable controller as an example, wherein the control unit 201 does not directly compare the original measurement signal 205 and the reference signal 206 to obtain the output signal 207 (the output signal 207 is sent to the program to make the measurement signal 205 change. approaching the reference signal 206 ), because the measurement signal 205 will be replaced by the compensated compensation signal 212 (detailed below). In other embodiments, the control unit may be a multivariable controller.

The variable 202 is one of the signals in the program that can affect the measurement signal 205 or be affected by the control unit 201 . There can be one variable 202 or more than one variable. This embodiment takes multiple variables 202 as an example. The variable 202 can be a program variable of a program, or a measurement signal, a reference signal or an output signal of another controller. Here, a program variable is taken as an example for illustration.

The dynamic deviation factor unit 203 obtains a dynamic deviation factor 210 of the variable 202 according to a short-term mean value and a long-term mean value of the variable 202 . FIG. 4 is a schematic diagram of the dynamic deviation factor unit 203 according to an embodiment of the present invention. The dynamic deviation factor unit 203 obtains a short-term mean value 208 and a long-term mean value 209 according to the variable 202 . The short-time mean value 208 is the signal value measured under a measurement interval (Sampling Interval), or the signal average value measured under S measurement intervals, or the signal of the variable is subjected to a low-pass filter The signal value after the device. Here, taking the average value of the signal measured at S measurement time intervals as an example, if a low-pass filter is used, the settling time of the filter is equivalent to S measurement time intervals (S greater than or equal to 1). The long-term average value 209 is the signal value after the signal value measured under one measurement time interval passes through a low-pass filter, or the signal average value measured under L measurement time intervals. Here, taking the average value of the signal measured at L measurement time intervals as an example, if a low-pass filter is used in the example, the settling time of the filter is equivalent to L measurement time intervals (the value of L is greater than the S).

The formula for calculating the dynamic deviation factor is as follows:

(Formula 1)

(Formula 2)

(Formula 3)

(Formula 4)

Among them, the mean value estimator F(T, x(t)) estimates the mean value of the signal based on a program variable x(t) and the signal value measured under T measurement intervals (samplingInterVal), or It is the value of a signal measured according to the program variable after passing through the Low Pass Filter. λ _i and γ _i are coefficients determined according to the average time length (T measurement time intervals) and filter settling time (equivalent to T measurement time intervals), and N represents the order of the filter (Order) so that The settling time of the filter is equivalent to T; α is zero or an adjustable constant, which can avoid the denominator from being zero or can be used to adjust β; is the short-term average; is the long-term average value; β is the dynamic deviation factor.

FIG. 5 is a graph of the short-time mean value, the long-term mean value and the dynamic deviation factor according to an embodiment of the present invention, wherein the dynamic deviation factor is about the degree to which the short-time mean value deviates from the long-term mean value. Furthermore, the dynamic deviation factor has the following properties:

1. The initial value of the dynamic deviation factor is equal to zero.

2. When there is no significant difference between the long-term mean value and the short-term mean value of the variable, or when it reaches a steady state (SteadyState), the dynamic deviation factor is equal to zero, or its value is close to zero and can be ignored.

3. When the variable remains near the same value for a long time, the dynamic deviation factor (DOF) is equal to zero or close to zero and can be ignored.

The signal value of a variable may be an original electronic signal or a signal that has been converted to represent a physical meaning. Therefore, the signal of a variable can be converted first and then estimated the average value, or first estimated the average value and then converted. In addition, the dynamic deviation factor 210 of the variable 202 can be further processed to obtain a compensation value 211 (as shown by the g function in FIG. 4 ), such as limiting directivity with a sign or adjusting its strength with a gain ratio.

As shown in FIG. 3, the compensation unit 204 is used to compensate the dynamic deviation factor 210 to the measurement signal 205, the reference signal 206 or the output signal 207 to obtain a corresponding compensation signal 212 (the compensation signal 212 can be a value or a function) , the compensation signal 212 replaces the measurement signal 205 , the reference signal 206 or the output signal 207 for the control unit 201 to control the procedure. The original signal (z(t)) 213 shown in FIG. 4 may represent one of the measurement signal 205, the reference signal 206 and the output signal 207, and represents its corresponding compensation signal 212 . In the embodiment of FIG. 3 , the variable 202 is a signal that affects the measurement signal 205 , and the compensation signal 212 replaces the original measurement signal 205 as the input measurement signal of the control unit 201 .

The compensation unit 204 can add or compensate the dynamic deviation factor 210 to at least one of the measurement signal 205 , the reference signal 206 and the output signal 207 by percentage. Here, the method of compensating the dynamic deviation factor 210 to the measurement signal 205 in an additive manner is taken as an example for illustration. In other embodiments, the compensation unit 204 can compensate the dynamic deviation factor 210 in other ways, for example, in a function way.

The present invention also provides a control method for achieving multivariable control through a single variable control unit, the control method comprising the following steps:

1. Select a program variable x(t) outside the control loop. This variable must have an interactive relationship with the signal z(t) of the control unit in the loop, that is, the change of x(t) will affect y(t) ), or z(t) changes will affect x(t);

2. Use a mean estimator to calculate the short-term mean of x(t)

3. Use a mean estimator to calculate the long-term mean of x(t)

4. Using the results of steps 2 and 3, calculate the dynamic deviation factor β;

5. Use β to calculate the compensation amount Δz(t) of the signal;

6. Import the compensation amount Δz(t) into z(t), so that the original signal of the control unit can be changed into a compensation signal

7. If it is necessary to add other program variables, repeat steps 1 to 6.

Where z(t) represents the measurement signal y(t), reference signal r(t), or output signal u(t) of the control unit in the control loop, or any combination of the three (as shown in Figure 6) .

In Fig. 6, it is shown that the controller 2 of the present invention can be applied to the measurement signal 205, the reference signal 206, the output signal 207 of the control unit 201 or any combination of the three; The output signals 207 have a mutual influence relationship. If necessary, one or more dynamic deviation factor units 203 can be selected to obtain the corresponding dynamic deviation factors 210 of individual variables according to the corresponding program variables 202 . The compensation unit 204 compensates the corresponding dynamic deviation factor 210 to the measurement signal 205 , the reference signal 206 or the output signal 207 to obtain a corresponding compensation signal 212 . In this way, the single-variable control unit 201 can achieve a multi-variable control function.

The following examples illustrate the characteristics of a controller 2 of the present invention.

(1) Features of feed-forward control: Since the dynamic deviation factor has no unit (Dimensionless), it can be applied to multiple control loops by utilizing the mutual influence relationship between program variables. As shown in Fig. 7, when a program variable 202 outside the control loop 2a has mutual influence on the measurement signal 205 (controlled variable CV) in the loop, through the conversion of the dynamic deviation factor unit 203, x ₁ (t ) into the control loop 2a, so that the effect similar to feedforward control can be produced. In FIG. 7, z(t) may be one of a measurement signal, a reference signal, and an output signal of the control unit.

(2) Features of many-to-one control and multi-function control: as shown in Figure 8, when the control loop 2b has an obvious mutual influence on the measurement signal 205 in the control loop 2c, the measurement signal 205 can be dynamically deviated The conversion of the factor unit 203 is compensated in the control loop 2b, so that two single variable controllers can control the measurement signal 205 at the same time, thereby producing the effect of many-to-one control. z ₁ (t) in FIG. 8 may be one of the measurement signal, reference signal, and output signal of the control unit 201 of the control loop 2b. As far as the control loop 2b is concerned, in addition to its own control function, when the measurement signal 205 deviates too much, it can also take into account the function of controlling the measurement signal 205 to achieve a multi-functional effect.

(3) Features of many-to-many control: as shown in Figure 9, when the control loop 2d has an obvious mutual influence on the control loop 2e, the output signals or reference signals of the two loops can pass through the dynamic deviation factor unit 203 The conversion of the control unit 201 is compensated in the other's control loop, so that the two control units 201 can control each other, that is, the effect of many-to-many control is generated. z ₁ (t) or z ₂ (t) in FIG. 9 may be one of the measurement signal, reference signal, and output signal of the control unit 201 of the control loop 2 b. The embodiment in FIG. 9 is presented with two variables (y ₁ , y ₂ ), however, it can be extended to configurations with more than two variables according to requirements.

The controller 2 of the present invention can be applied to control in various fields, and the application to a heating furnace is used as an example for illustration below.

FIG. 10 is a schematic diagram of a control loop in which the controller 2 is applied to the heating furnace 100 according to an embodiment of the present invention. In this application, air and fuel gas are introduced into the heating furnace 100 separately, so that when the feed material is in the heating furnace 100, a combustion reaction can occur, and then a discharge material can be produced. The heating furnace 100 is a typical multi-variable control program. In order to make the heating furnace 100 operate stably, it must be confirmed that the feed material and the incoming air and fuel gas meet the operating goals. Therefore, the control of the heating furnace 100 basically has a feed flow controller 101 , an air flow controller 102 and a fuel gas flow controller (FIC-FG) 103 . In addition, in order to make the heating furnace 100 operate at a default output temperature (TI-OUT), a furnace tube outlet temperature controller 104 is added to control the fuel gas flow rate. The control circuit also includes an oxygen peroxide controller 105 for controlling the peroxygen, a fuel gas heat content indicator (AI-FG) 106 and a fuel gas flow indicator (FI-FG) 107 .

In the operation of the heating furnace 100, when the calorific value of the fuel gas (the fuel gas flow rate multiplied by the unit calorific value of the fuel gas) is unstable, the amount of overoxygen will of course be very difficult to control. When the air is insufficient, it will lead to incomplete combustion. The most direct The consequence is black smoke, and of course the generation of other harmful gases, causing environmental pollution. When there is too much air, it will cause waste of energy and also cause environmental pollution. In fact, the oxygen peroxide (AI-02) is not only affected by the change of the air flow, but also the calorific value of the fuel gas has an even greater impact on the peroxygen. In order to improve the control performance, you can consider using the fuel gas flow rate to control the amount of oxygen. However, the fuel gas flow has been used to control the furnace outlet temperature and forms its own control loop, whereas a single variable controller can only control one variable at a time. However, through the setting of the dynamic deviation factor unit 203 of the present invention, the dynamic deviation factor β of the measurement signal y(t) of the peroxygen controller can be calculated first, as follows:

(Formula 5)

And the dynamic deviation factor is subtracted from the fuel gas flow F _FG (t). Thus, the resulting fuel gas flow Can be compensated by changes in peroxygen levels.

(Formula 6)

For example, when the peroxygen level is lower than its long-term average value, its dynamic deviation factor 210 is negative. Multiplied by a negative value of k, the compensated fuel gas flow will be greater than F _FG (t). When the input signal of the fuel gas flow controller 103 is adjusted, the fuel gas flow controller 103 can work according to the predetermined design. With no change in its reference signal, The amount higher than the actual fuel gas flow rate ΔF _FG (t). As a result, as its input signal goes high, the fuel gas flow controller will reduce its output to reduce the actual fuel gas flow. In the case that other settings of the controller 103 are not changed, it can be estimated that the final fuel gas flow rate will decrease by ΔF _FG (t).

Through the application of the present invention, when the oxygen peroxide is too low, not only the peroxygen controller 105 will increase the air flow, but also the fuel gas flow will be affected by the fuel gas flow controller 103 due to the dynamic deviation factor of the peroxygen was indirectly reduced. Therefore, when the overoxygen level of the heating furnace is too low and black smoke is about to be generated, the fuel gas flow controller 103 can be prompted to reduce the fuel gas flow rate by using the dynamic deviation factor 210β of the overoxygen level. The value of k in the dynamic deviation factor of peroxygen can be calculated as follows:

(Formula 7)

Wherein, α is a positive constant, and b is the minimum permissible amount of excess oxygen under the condition that the fuel gas flow rate is not reduced and the heating furnace does not emit black smoke. In this case, the fuel gas flow will only be adjusted if the oxygen excess is below b. Conversely, when the excess oxygen is higher than b, the fuel gas flow will not be adjusted. In this way, the fuel gas flow controller 103 only controls the outlet temperature of the heating furnace. Only when the heating furnace is about to emit black smoke, the fuel gas flow controller 103 first meets the urgent environmental requirements and reduces the fuel gas flow. When the long-term mean is close to the short-term mean, the dynamic deviation factor will gradually approach zero. The effect of DOF will not appear throughout.

When the oxygen peroxide is very close to its moving average value, the dynamic deviation factor (DOF) is also close to zero, that is, the fuel gas compensation flow and the fuel gas flow will be very close, so the fuel gas flow controller (FIC-FG) 103 It works fine. When the oxygen peroxide becomes low in a short time, generally speaking, the fuel air flow controller 103 will not be able to act on the air baffle in time. Through the present invention, through the application of the dynamic deviation factor (DOF), the fuel gas valve can be turned down first to avoid black smoke. The principle is that when the oxygen peroxide becomes low in a short period of time, the dynamic deviation factor is a negative value, and the compensation flow of fuel gas will increase after compensation. Under the normal operation of the fuel gas flow controller 103, when the controlled variable CV (that is, the measurement signal of the fuel gas flow rate) increases due to compensation, the fuel gas flow controller 103 will act to close the control valve until the compensation flow rate approaches its set point (ie, the reference signal), so the fuel gas flow rate The actual flow rate will be reduced, and at the same time, the function of increasing the peroxygen amount will be achieved. The furnace tube outlet temperature controller 104 still adjusts the set point (ie, the reference signal) of the fuel gas flow controller 103 according to the measured value of the output temperature (TI-OUT). Therefore, the flue gas peroxygen can also be controlled by the fuel gas flow controller 103 except that the peroxygen controller (AIC-02) 105 is controlled through the air flow controller (FIC-AIR) 102, and A two-to-one control effect is achieved, so the control effect will be greatly improved.

The controller 2 of the present invention first calculates the dynamic deviation factor 210 of the program variable, and compensates it to the measurement signal, reference signal or output signal, and obtains a corresponding compensation signal, and replaces the measurement signal, reference signal or output signal with the compensation signal The signal is used for the control unit to control the program. In this way, the present invention can turn any single-variable controller into a multi-variable or multi-functional controller with superior performance, and has real control over the program to improve the control performance.

The foregoing are examples only, not limitations. Any equivalent modification or change made without departing from the spirit and scope of the present invention shall be included in the scope of the appended patent application. If the control unit is set to manual operation, or the control unit is ignored or omitted, the compensation signal after DOF compensation of the measurement signal can still provide an early warning function for the operator. Controllers can be hardware or software or a combination of both.

Claims (8)

1. A controller that achieves multivariable control by a single variable control unit, is characterized in that it is used to control a program, and includes: a control unit to obtain an output signal according to a measurement signal and a reference signal, the output signal is sent to the program to change the measurement signal; at least one variable, which is one of the signals in the program that can affect the measurement signal or be affected by the control unit; At least one dynamic deviation factor unit for obtaining a dynamic deviation factor of the variable according to a short-term mean value and a long-term mean value of the variable; and a compensation unit, which compensates the dynamic deviation factor to one of the measurement signal, the reference signal and the output signal to obtain a corresponding compensation signal, and the compensation signal replaces the corresponding measurement signal, the reference signal or the output signal to control the control unit, The dynamic deviation factor is the degree to which the signal value of the variable measured under a measurement time interval deviates from the long-term mean value of the variable. The short-time mean value is the signal value measured under a measurement time interval, or The average value of the signal measured under S measurement time intervals, or the signal value of the variable signal after passing through a low-pass filter. The settling time of the filter is equivalent to S measurement time intervals. The S is greater than or equal to 1; the long-term mean value is the signal value measured under a measurement time interval after passing through a low-pass filter, or the average value of the signal measured under L measurement time intervals, the filter The settling time of is equivalent to the L measurement time intervals, and the value of L is greater than the value of S. 2. The controller according to claim 1, wherein the control unit is a single variable control unit in a single variable controller or a multivariable controller. 3. The controller according to claim 1, wherein the measurement signal, the reference signal, the output signal, and the compensation signal are each a value or a function. 4. The controller of claim 1, wherein the variable is a program variable of the program, or a measurement signal, a reference signal or an output signal of another controller. 5 . The controller according to claim 1 , wherein the compensation unit compensates the dynamic deviation factor to one of the measurement signal, the reference signal and the output signal by addition or percentage. 6. The controller according to claim 1, wherein when the short-time mean value is substantially equal to the long-time mean value, the dynamic deviation factor of the variable is substantially zero, or the short-time mean value and the long-term mean value When , the value of the dynamic deviation factor is close to zero and is ignored. 7. A controller that achieves multivariable control through a single variable control unit, characterized in that it is used to control a program and includes: a control unit to obtain an output signal according to a measurement signal and a reference signal, the output signal is sent to the program to change the measurement signal; at least one variable, which is one of the signals in the program that can affect the measurement signal or be affected by the control unit; At least one dynamic deviation factor unit for obtaining a dynamic deviation factor of the variable according to a short-term mean value and a long-term mean value of the variable; and a compensation unit, which compensates the dynamic deviation factor to one of the measurement signal, the reference signal and the output signal to obtain a corresponding compensation signal, and the compensation signal replaces the corresponding measurement signal, the reference signal or the output signal to control the control unit, The formula for calculating the dynamic deviation factor is as follows: Among them, β is the dynamic deviation factor, is the short-term average, is the long-term mean, α is zero or an adjustment constant, used to avoid zero denominator or for adjustment. 8 . The controller according to claim 7 , wherein the dynamic deviation factor is processed to obtain a compensation amount and then compensated to one of the measurement signal, the reference signal and the output signal.