CN107479364A - A kind of fluid hybrid control system based on double closed-loop PID algorithm - Google Patents

Abstract

The invention discloses a fluid mixing control system based on a double-closed-loop PID algorithm, which includes a microcontroller module, a power management module, a management control module, an output drive module, and an output feedback module; the microcontroller modules are respectively connected to the power management module , a management control module, an output drive module, and an output feedback module. The fluid mixing control system based on the double-closed-loop PID algorithm of the present invention proposes a double-closed-loop PID algorithm, which can solve the problem that it is difficult to control the temperature of the indoor bathroom due to poor timeliness of algorithm feedback.

Description

A Fluid Mixing Control System Based on Double Closed-loop PID Algorithm

technical field

The invention relates to fluid mixing control, in particular to a fluid mixing control system based on a double-closed-loop PID algorithm.

Background technique

At present, the traditional bathroom control uses manual proportional mixing or measures the temperature of cold and hot water before mixing according to the temperature sensor and then performs proportional mixing. Afterwards, the water temperature is difficult to recover automatically and must be readjusted, which seriously affects the user experience.

The negative feedback hybrid control system based on the PID algorithm model is very significant in the field of industrial control, but due to the complexity of the algorithm model, the complexity of the algorithm model is high and the timeliness of feedback is poor, it cannot be applied to the field of home bathroom control.

And the traditional fluid temperature closed-loop PID algorithm only detects the temperature of the outflow fluid, compares the actual output temperature with the preset temperature, and then uses the PID algorithm for negative feedback adjustment. Due to the obvious delay when the fluid is mixed, the temperature time lag of the output is serious.

Contents of the invention

Aiming at the above problems, the present invention provides a fluid mixing control system based on a double-closed-loop PID algorithm, including a microcontroller module, a power management module, a management control module, an output drive module, and an output feedback module; the microcontroller modules are respectively Connect power management module, management control module, output driver module, output feedback module;

Power management module: It mainly provides power supplies of different specifications for the control circuit and drive circuit, among which the control module uses a 3.3V high-stable power supply, and the drive module provides a 12V high-power power supply;

Management control module: mainly used for the specific operation of the entire control module, including PID coefficient setting, start/stop operation of the drive module, and control data upload;

Microcontroller module: the core of the integrated system, mainly used to encapsulate the entire PID algorithm, control the entire drive processing, sensor signal processing and other functions;

Output drive module: mainly provides high-current drive control module, which is mainly used to control liquid flow rate devices such as solenoid valves and DC pumps;

Output feedback module: It mainly provides 3 sets of angular momentum sensors, 3 sets of single-bus type temperature sensor interfaces, and integrates the driver of the corresponding sensors in the MCU, and the user can directly use it;

The PID algorithm includes:

Closed loop one:

Use the temperature sensor to measure the actual temperature of the output water, use the PID algorithm for feedback adjustment, and then calculate the voltage value at both ends of the water temperature according to the water temperature required by the user, and use the temperature feedback to only revise a certain voltage, that is, use the temperature feedback Correct the effective value of the voltage across the water;

Closed loop two:

According to the data measured by the flow sensor, the flow through the water pump and the voltage across the pump are calculated, and then the actual value measured by the flow sensor is used for feedback, that is, the actual value of the output hot water flow is corrected.

Further, the PID algorithm is specifically:

Q ₁ T ₁ +Q ₂ T ₂ ＝QT

Mixed in proportions to get:

Among them, Q1 is the flow rate of hot water, T1 is the temperature of hot water, Q2 is the inflow flow of cold water, T2 is the temperature of cold water; Q is the outflow flow, and T is the outflow temperature;

which is:

Assume that the voltage across the pump is proportional to the flow through the pump, ie:

Where K is the proportional coefficient;

then there is which is: make M is a fixed value;

Then there is U(T ₁ ,T ₂ ,T)=MK(T ₁ ,T ₂ ,T), where so

It is known that the actual measured temperature is T _(t) , and the feedback value obtained according to the PID principle is: e(t)=T _r (t)-T(t)

After digitizing the fuzzy control of the above formula, we can get:

ΔT(k)=k _pt [e(k)-e(k-1)]+k _it e(k)+k _dt [e(k)-2e(k-1)+e(k-2)]

In the formula: k _it ＝k _pt /T _pt ; k _dt ＝k _pt /T _dt Among them, T is the sampling period, k is the serial number

The revised theoretical temperature value is then output as:

The theoretical voltage value calculated by deriving the theoretical temperature value is:

According to the same principle, the obtained flow rate of the actual control output is:

The actual output flow is Q ₁ (k) and The actual voltage value U _r is obtained as:

The deduced actual output control voltage is:

Advantages of the present invention:

The present invention has a small feedback time delay (small time lag) of the fluid outflow temperature.

The temperature fluctuation range of the output fluid is small. Real-time measurement of the temperature of the hot and cold fluids has been completed before the fluid output, and the flow output according to the theoretical calculation, this design and the PID closed-loop feedback system of the flow rate is added at the flow inflow end, the problem of real-time output of the fluid is very close to the expected Set temperature.

The response speed is fast when the preset temperature is changed. When a preset temperature change is detected, the system can adjust the mixing ratio of hot and cold fluids in real time, and the corresponding speed is much higher than the traditional corresponding speed.

At the same time, the purpose of dual control output of fluid flow and temperature can be realized. According to the preset output flow and temperature, the system can adjust the size of the fluid flow (all fluid mixing chambers have a certain volume when the volume is large) while ensuring that the flow ratio of the inflow fluid remains unchanged, which can effectively control the size of the output fluid.

The fluid mixing control system based on the double-closed-loop PID algorithm of the present invention proposes a double-closed-loop PID algorithm, which can solve the problem that it is difficult to control the temperature of the indoor bathroom due to poor timeliness of algorithm feedback.

In addition to the objects, features and advantages described above, the present invention has other objects, features and advantages. Hereinafter, the present invention will be described in further detail with reference to the drawings.

Description of drawings

The accompanying drawings constituting a part of this application are used to provide further understanding of the present invention, and the schematic embodiments and descriptions of the present invention are used to explain the present invention, and do not constitute an improper limitation of the present invention.

Fig. 1 is a kind of fluid mixing control system block diagram based on double closed-loop PID algorithm of the present invention;

Fig. 2 is a PID control flow chart of a fluid mixing control system based on a double-closed-loop PID algorithm of the present invention.

Fig. 3 is a kind of management control module schematic diagram of the fluid mixing control system based on double closed-loop PID algorithm of the present invention;

Fig. 4 is a kind of output feedback module schematic diagram of the fluid mixing control system based on double closed-loop PID algorithm of the present invention;

Fig. 5 is a schematic diagram of an output drive module of a fluid mixing control system based on a double-closed-loop PID algorithm of the present invention;

Fig. 6 is a schematic diagram of a power management module of a fluid mixing control system based on a double closed-loop PID algorithm of the present invention;

Fig. 7 is a schematic diagram of a micro-controller module of a fluid mixing control system based on a double closed-loop PID algorithm of the present invention.

detailed description

In order to make the object, technical solution and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described here are only used to explain the present invention, not to limit the present invention.

With reference to Fig. 1, a kind of fluid mixing control system based on double closed-loop PID algorithm as shown in Fig. 1, comprises microcontroller module, power management module, management control module, output driver module, output feedback module; Described microcontroller The modules are respectively connected to the power management module, the management control module, the output driver module, and the output feedback module;

Referring to Figure 6, as shown in Figure 6, the power management module: mainly provides power supplies of different specifications for the control circuit and the drive circuit, wherein the control module uses a 3.3V high-stable power supply, and the drive module provides a 12V high-power power supply.

The power management module provides an external power supply interface, the control voltage supports 3.3V to 15V, and the driving voltage is 12V-36V; the control circuit adopts a wide voltage mode, and the internal voltage stabilization circuit eliminates the influence of circuit fluctuations on the control circuit; the drive circuit should be connected to Protection resistor; AMS1117-3.3 is selected as the voltage regulator chip, and a diode to prevent backflow should be added at the input end.

Referring to Figure 3, as shown in Figure 3, the management control module: mainly used for specific operations of the entire control module, such as PID coefficient setting, start/stop operation of the drive module, control data upload, etc.

It includes a minimum system working mode selection module, an extra expansion interface, and a data interface of the management control module. The SWDIO, SWCLK, NRST, BOOT0, USART1_RX, and USART1_TX ports are program download ports.

Referring to Figure 7, as shown in Figure 7, microcontroller module: the core of the integrated system, mainly used to encapsulate the entire PID algorithm to control the entire drive processing, sensor signal processing and other functions.

Referring to Figure 5, as shown in Figure 5, the output drive module: mainly provides a large current drive control module, mainly used to control liquid flow rate devices such as solenoid valves and DC pumps.

The drive circuit and the MCU are isolated by optocouplers to prevent eddy current voltage from affecting the circuit; the drive circuit supports a voltage of up to 50V and can provide an output load of 50W; the output terminal uses 2510 terminals for direct operation by the user.

Referring to Figure 4, as shown in Figure 4, the output feedback module: mainly provides 3 sets of angular momentum sensors, 3 sets of single-bus type temperature sensor interfaces, and integrates the corresponding sensor drivers in the MCU, such as DS18B20, JR-A168 and other commonly used sensors Drivers and user access can be used directly.

P4, P5, P6 which ds18b20 temperature sensor interface is used to detect the temperature before and after liquid mixing; P7, P8, P9 are respectively used to detect the flow rate after liquid mixing; the temperature sensor adopts single bus protocol, angular momentum sensor The pulse mode is adopted; the interface uses 2510 terminal blocks, which is convenient for users to use.

With reference to Fig. 2, as shown in Fig. 2, described PID algorithm comprises:

Closed loop one:

Use the temperature sensor to measure the actual temperature of the output water, use the PID algorithm for feedback adjustment, and then calculate the voltage value at both ends of the water temperature according to the water temperature required by the user, and use the temperature feedback to only revise a certain voltage, that is, use the temperature feedback Correct the effective value of the voltage across the water;

Closed loop two:

According to the data measured by the flow sensor, the flow through the water pump and the voltage across the pump are calculated, and then the actual value measured by the flow sensor is used for feedback, that is, the actual value of the output hot water flow is corrected.

The PID algorithm is specifically:

Q ₁ T ₁ +Q ₂ T ₂ ＝QT

Mixed in proportions to get:

Among them, Q1 is the flow rate of hot water, T1 is the temperature of hot water, Q2 is the inflow flow of cold water, T2 is the temperature of cold water; Q is the outflow flow, and T is the outflow temperature;

which is:

Assume that the voltage across the pump is proportional to the flow through the pump, ie:

Where K is the proportional coefficient;

then there is which is: make M is a fixed value;

Then there is U(T ₁ ,T ₂ ,T)=MK(T ₁ ,T ₂ ,T), where so

It is known that the actual measured temperature is T _(t) , and the feedback value obtained according to the PID principle is: e(t)=T _r (t)-T(t)

After digitizing the fuzzy control of the above formula, we can get:

ΔT(k)=k _pt [e(k)-e(k-1)]+k _it e(k)+k _dt [e(k)-2e(k-1)+e(k-2)]

In the formula: k _it ＝k _pt /T _pt ; k _dt ＝k _pt /T _dt Among them, T is the sampling period, k is the serial number

The revised theoretical temperature value is then output as:

The theoretical voltage value calculated by deriving the theoretical temperature value is:

According to the same principle, the obtained flow rate of the actual control output is:

The actual output flow is Q ₁ (k) and The actual voltage value U _r is obtained as:

The deduced actual output control voltage is:

Fluid flow detection model analysis:

In this system, the flow sensor used is the JR-A168 flow sensor of Hall sensor, and its parameters are:

Working voltage: DC=12V; working current: I=300mA; the detection signal output is pulse voltage, its high level>=4.5V, low level<=0.5V; the duty cycle is 50%±10%; The pulse characteristic is F=(q*Q), (F is the output pulse frequency, Q is the flow rate), and the measurement range of the flow rate is 2-12L/min.

Within the measurable range of the flow sensor, the range of the pulse frequency of the flow sensor is 18HZ-108HZ, that is, the shortest time of each pulse cycle is 0.009s-0.0555s, that is, 9ms-55ms.

This control system is mainly based on the STM32F103 single-chip microcomputer as the core control unit, and according to the data interface of the angular momentum sensor (mainly used to test the flow of the fluid) and the temperature sensor (to measure the temperature of the fluid before and after mixing) to build a control circuit design control circuit module, using C language Build and implement the algorithm model, encapsulate the entire algorithm into a microcontroller, and provide algorithm adjustment parameters to the outside in the form of a serial port, which has achieved the goal of minimum realization.

The fluid mixing control system based on the double-closed-loop PID algorithm of the present invention proposes a double-closed-loop PID algorithm, which can solve the problem that it is difficult to control the temperature of the indoor bathroom due to poor timeliness of algorithm feedback.

The present invention has a small feedback time delay (small time lag) of the fluid outflow temperature.

The temperature fluctuation range of the output fluid is small. Real-time measurement of the temperature of the hot and cold fluids has been completed before the fluid output, and the flow output according to the theoretical calculation, this design and the PID closed-loop feedback system of the flow rate is added at the flow inflow end, the problem of real-time output of the fluid is very close to the expected Set temperature.

The response speed is fast when the preset temperature is changed. When a preset temperature change is detected, the system can adjust the mixing ratio of hot and cold fluids in real time, and the corresponding speed is much higher than the traditional corresponding speed.

At the same time, the purpose of dual control output of fluid flow and temperature can be realized. According to the preset output flow and temperature, the system can adjust the size of the fluid flow (all fluid mixing chambers have a certain volume when the volume is large) while ensuring that the flow ratio of the inflow fluid remains unchanged, which can effectively control the size of the output fluid.

The fluid mixing control system based on the double-closed-loop PID algorithm of the present invention proposes a double-closed-loop PID algorithm, which can solve the problem that it is difficult to control the temperature of the indoor bathroom due to poor timeliness of algorithm feedback.

The above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included in the protection of the present invention. within range.

Claims (2)

1. A kind of fluid mixing control system based on double closed-loop PID algorithm, it is characterized in that, comprise microcontroller module, power management module, management control module, output drive module, output feedback module; Described microcontroller module connects power supply respectively Management module, management control module, output drive module, output feedback module; Power management module: It mainly provides power supplies of different specifications for the control circuit and drive circuit, among which the control module uses a 3.3V high-stable power supply, and the drive module provides a 12V high-power power supply; Management control module: mainly used for the specific operation of the entire control module, including PID coefficient setting, start/stop operation of the drive module, and control data upload; Microcontroller module: the core of the integrated system, mainly used to encapsulate the entire PID algorithm, control the entire drive processing, sensor signal processing and other functions; Output drive module: mainly provides high-current drive control module, which is mainly used to control liquid flow rate devices such as solenoid valves and DC pumps; Output feedback module: mainly provides 3 sets of angular momentum sensors, 3 sets of single-bus type temperature sensor interfaces, and integrates the corresponding sensor driver in the MCU, and the user can directly use it; The PID algorithm includes: Closed loop one: Use the temperature sensor to measure the actual temperature of the output water, use the PID algorithm for feedback adjustment, and then calculate the voltage value at both ends of the water temperature according to the water temperature required by the user, and use the temperature feedback to only revise a certain voltage, that is, use the temperature feedback Correct the effective value of the voltage across the water; Closed loop two: According to the data measured by the flow sensor, the flow through the water pump and the voltage across the pump are calculated, and then the actual value measured by the flow sensor is used for feedback, that is, the actual value of the output hot water flow is corrected. 2. the fluid mixing control system based on double closed-loop PID algorithm according to claim 1, is characterized in that, described PID algorithm is specifically: Q ₁ T ₁ +Q ₂ T ₂ ＝QT Mixed in proportions to get: Among them, Q1 is the flow rate of hot water, T1 is the temperature of hot water, Q2 is the inflow flow of cold water, T2 is the temperature of cold water; Q is the outflow flow, and T is the outflow temperature; which is: <mfenced open=""close=""><mtable><mtr><mtd><mrow><msub><mi>Q</mi><mn>1</mn></msub><msub><mi>T</mi><mn>1</mn></msub><mo>+</mo><mrow><mo>(</mo><mi>Q</mi><mo>-</mo><msub><mi>Q</mi><mn>1</mn></msub><mo>)</mo></mrow><msub><mi>T</mi><mn>2</mn></msub><mo>=</mo><mi>Q</mi><mi>T</mi></mrow></mtd></mtr><mtr><mtd><mo>&amp;DoubleDownArrow;</mo></mtd></mtr><mtr><mtd><mrow><msub><mi>Q</mi><mn>1</mn></msub><mrow><mo>(</mo><msub><mi>T</mi><mn>1</mn></msub><mo>-</mo><msub><mi>T</mi><mn>2</mn></msub><mo>)</mo></mrow><mo>=</mo><mi>Q</mi><mrow><mo>(</mo><mi>T</mi><mo>-</mo><msub><mi>T</mi><mn>2</mn></msub><mo>)</mo></mrow></mrow></mtd></mtr><mtr><mtd><mo>&amp;DoubleDownArrow;</mo></mtd></mtr><mtr><mtd><mrow><msub><mi>Q</mi><mn>1</mn></msub><mo>=</mo><mfrac><mrow><mo>(</mo><mi>T</mi><mo>-</mo><msub><mi>T</mi><mn>2</mn></msub><mo>)</mo></mrow><mrow><msub><mi>T</mi><mn>1</mn></msub><mo>-</mo><mi>T</mi></mrow></mfrac><msub><mi>Q</mi><mn>2</mn></msub></mrow></mtd></mtr></mtable></mfenced> Assume that the voltage across the pump is proportional to the flow through the pump, ie: Q ₁ =K _u U Among them, K is the proportional coefficient; then there is which is: make M is a fixed value; Then there is U(T ₁ ,T ₂ ,T)=MK(T ₁ ,T ₂ ,T), where so It is known that the actual measured temperature is T _(t) , and the feedback obtained according to the PID principle is: e(t)=T _r (t)-T(t) <mrow><msub><mi>k</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></msub><mo>=</mo><msub><mi>K</mi><mrow><mi>T</mi><mi>P</mi></mrow></msub><msub><mi>e</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></msub><mo>+</mo><msub><mi>K</mi><mrow><mi>T</mi><mi>I</mi></mrow></msub><mrow><mo>&amp;Integral;</mo><mrow><msub><mi>e</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></msub><mi>d</mi><mi>t</mi></mrow></mrow><mo>+</mo><msub><mi>K</mi><mrow><mi>T</mi><mi>D</mi></mrow></msub><mfrac><mrow><mi>d</mi><mi>e</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mrow> After digitizing the fuzzy control of the above formula, we can get: <mrow><msub><mi>T</mi><mi>r</mi></msub><msup><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow><mo>&amp;prime;</mo></msup><mo>=</mo><msub><mi>K</mi><mrow><mi>T</mi><mi>P</mi></mrow></msub><mi>e</mi><msub><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow><mi>t</mi></msub><mo>+</mo><msub><mi>K</mi><mrow><mi>T</mi><mi>I</mi></mrow></msub><munderover><mo>&amp;Sigma;</mo><mrow><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>k</mi><mo>=</mo><mfrac><mi>t</mi><mrow><mi>&amp;Delta;</mi><mi>t</mi></mrow></mfrac></mrow></munderover><mi>e</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow><mi>T</mi><mo>+</mo><msub><mi>K</mi><mrow><mi>T</mi><mi>D</mi></mrow></msub><mfrac><mrow><mi>e</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow><mo>-</mo><mi>e</mi><mrow><mo>(</mo><mi>k</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><mi>T</mi></mfrac></mrow> ΔT(k)=k _pt [e(k)-e(k-1)]+k _it e(k)+k _dt [e(k)-2e(k-1)+e(k-2)] In the formula: k _it ＝k _pt /T _pt ; k _dt ＝k _pt /T _dt Among them, T is the sampling period, k is the serial number The revised theoretical temperature value is then output as: <mfenced open=""close=""><mtable><mtr><mtd><mrow><msub><mi>T</mi><mi>r</mi></msub><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow><mo>=</mo><msup><msub><mi>T</mi><mi>r</mi></msub><mo>&amp;prime;</mo></msup><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow><mo>+</mo><mi>&amp;Delta;</mi><mi>T</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow><mo>&amp;DoubleRightArrow;</mo><msub><mi>T</mi><mi>r</mi></msub><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow><mo>=</mo></mrow></mtd></mtr><mtr><mtd><mrow><msubsup><mi>T</mi><mi>r</mi><mo>&amp;prime;</mo></msubsup><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow><mo>=</mo><msub><mi>k</mi><mrow><mi>p</mi><mi>t</mi></mrow></msub><mo>&amp;lsqb;</mo><mi>e</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow><mo>-</mo><mi>e</mi><mrow><mo>(</mo><mi>k</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mo>&amp;rsqb;</mo><mo>+</mo>mo><msub><mi>k</mi><mrow><mi>i</mi><mi>t</mi></mrow></msub><mi>e</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow><mo>+</mo><msub><mi>k</mi><mrow><mi>d</mi><mi>t</mi></mrow></msub><mo>&amp;lsqb;</mo><mi>e</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow><mo>-</mo><mn>2</mn><mi>e</mi><mrow><mo>(</mo><mi>k</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mo>+</mo><mi>e</mi><mrow><mo>(</mo><mi>k</mi><mo>-</mo><mn>2</mn><mo>)</mo></mrow><mo>&amp;rsqb;</mo></mrow></mtd></mtr></mtable></mfenced> The theoretical voltage value calculated by deriving the theoretical temperature value is: <mrow><msub><mi>Q</mi><mrow><mn>1</mn><mi>r</mi></mrow></msub><msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>&amp;prime;</mo></msup><mo>=</mo><msub><mi>Q</mi><mn>2</mn></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>&amp;CenterDot;</mo><mfrac><mrow><msup><msub><mi>T</mi><mi>r</mi></msub><mo>&amp;prime;</mo></msup><mo>-</mo><msub><mi>T</mi><mrow><mn>2</mn><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></msub></mrow><mrow><msub><mi>T</mi><mrow><mn>1</mn><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></msub><mo>-</mo><msup><msub><mi>T</mi><mi>r</mi></msub><mo>&amp;prime;</mo></msup></mrow></mfrac><mo>&amp;DoubleRightArrow;</mo><msub><mi>Q</mi><mrow><mn>1</mn><mi>r</mi></mrow></msub><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow><mo>=</mo><msub><mi>Q</mi><mn>2</mn></msub><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow><mo>&amp;CenterDot;</mo><mfrac><mrow><msub><mi>T</mi><mi>r</mi></msub><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow><mo>-</mo><msub><mi>T</mi><mn>2</mn></msub><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></mrow><mrow><msub><mi>T</mi><mn>1</mn></msub><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow><mo>-</mo><msub><mi>T</mi><mi>r</mi></msub><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></mrow></mfrac></mrow> According to the same principle, the obtained flow rate of the actual control output is: The actual output flow is Q ₁ (k) and The actual voltage value U _r is obtained as: The deduced actual output control voltage is: <mrow><mtable><mtr><mtd><mrow><mi>U</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mn>1</mn><msub><mi>K</mi><mi>u</mi></msub></mfrac><mo>&amp;CenterDot;</mo><mo>&amp;lsqb;</mo><msub><mi>Q</mi><mn>2</mn></msub><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow><mo>&amp;CenterDot;</mo><mfrac><mrow><msub><mi>T</mi><mi>r</mi></msub><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow><mo>-</mo><msub><mi>T</mi><mn>2</mn></msub><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></mrow><mrow><msub><mi>T</mi><mn>1</mn></msub><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow><mo>-</mo><msub><mi>T</mi><mi>r</mi></msub><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></mrow></mfrac><mo>+</mo><msub><mi>k</mi><mrow><mi>p</mi><mi>q</mi></mrow></msub><mo>&amp;lsqb;</mo><mi>e</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow><mo>-</mo><mi>e</mi><mrow><mo>(</mo><mi>k</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mo>&amp;rsqb;</mo></mrow></mtd></mtr><mtr><mtd><mrow><mo>+</mo><msub><mi>k</mi><mrow><mi>i</mi><mi>q</mi></mrow></msub><mi>e</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow><mo>+</mo><msub><mi>k</mi><mrow><mi>d</mi><mi>q</mi></mrow></msub><mo>&amp;lsqb;</mo><mi>e</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow><mo>-</mo><mn>2</mn><mi>e</mi><mrow><mo>(</mo><mi>k</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mo>+</mo><mi>e</mi><mrow><mo>(</mo><mi>k</mi><mo>-</mo><mn>2</mn><mo>)</mo></mrow><mo>&amp;rsqb;</mo></mrow></mtd></mtr></mtable><mo>.</mo></mrow> 2