Integrated temperature and humidity controller with priority for humidity temperature control

Integrated temperature and humidity controller for priority order of humidity and temperature control

<p>12. . . Enclosed space</p><p>14. . . Humidity sensor</p><p>15. . . Temperature sensor</p><p>17. . . compressor</p><p>18. . . Amplifier coil</p><p>19. . . Air conditioning unit</p><p>20. . . hair dryer</p><p>twenty one. . . Heat exchanger space</p><p>twenty two. . . pipeline</p><p>twenty three. . . control element</p><p>25. . . Controller</p><p>26. . . path</p><p>27. . . Memory unit</p><p>28. . . Processor unit</p><p>29. . . switch</p><p>30. . . path</p><p>31. . . path</p><p>33. . . path</p><p>34. . . path</p><p>35. . . path</p><p>36. . . path</p><p>38. . . conductor</p><p>39. . . conductor</p><p>40. . . path</p><p>41. . . path</p><p>42. . . conductor</p><p>50. . . Laplace transform operation block</p><p>51. . . path</p><p>58. . . path</p><p>61. . . Function block</p><p>64. . . path</p><p>67. . . Calculation block</p><p>71. . . Total components</p><p>74. . . Calculation block</p><p>76. . . path</p><p>77. . . path</p><p>78. . . Sum cube</p><p>81. . . path</p><p>84. . . path</p><p> 86. . . ε=ε _DB</p><p>87. . . Decision box</p><p> 88. . . ε=ε _H</p><p>90. . . path</p><p>91. . . Gp</p><p>92. . . Gj/s</p><p> 93. . . G _d S </p><p>96. . . Sum cube</p><p>98. . . path</p><p>101. . . Sum cube</p><p>103. . . Hysteresis test block</p><p>105. . . path</p><p>108. . . Test block</p><p>113. . . Laplace transform cube</p><p>115. . . path</p>

Figure 1 shows a block diagram of a complete air conditioner installation using the present invention.

FIG. 2 is an operation diagram illustrating a preferred embodiment of the algorithm implemented by a controller of a climate control system.

Fig. 3 is a coordinate diagram showing the situation under a preferred embodiment implemented by a controller.

Field of invention

The present invention relates to thermostats and other temperature comfort controllers. The present invention particularly relates to controlling the operation of an air conditioner. The invention can basically be implemented in a mechanical cooling device, which uses a microcontroller in combination with a temperature sensor.

Background of the invention

The thermostats currently in use basically use the dry bulb temperature as a control variable to indicate the operation of the air conditioner. A typical controller is in the air-conditioning mode, when the temperature rises above the set temperature value, it will prompt the air conditioner to start operating. The air conditioner responds by injecting cold air into the enclosed space until the temperature in the enclosed space drops to a temperature lower than the set temperature value. A typical thermostat uses a predictive element to turn on the air conditioner before the actual set point is exceeded. In many cases, such control results in air temperatures that are more comfortable for people in enclosed spaces. It is well known that an air conditioner can remove moisture while cooling the air. The mechanism for removing moisture involves passing air through the air conditioner from the enclosed space or from the outside, reducing the temperature of the air to substantially below the comfortable range (for example, less than 74 degrees Fahrenheit).

In order to remove moisture from the air, the temperature of at least some of the cooling air must be lower or lower than the current dew point temperature, which is the temperature at which moisture will condense from the air. During this process, some water in the air will condense on the cooling coil of the air conditioner and drip from the coil into the pan below. Because the air will not release any moisture until it reaches 100% relative humidity, that is, its dew point temperature, it is necessary for the air at least adjacent to the cooling surface of the heat exchanger to reach this temperature. However, the overall air flow through the air conditioner cannot reach 100% relative humidity, because not all the air is cooled to its dew point. Therefore, the relatively cold and dry air-conditioned air is mixed with uncomfortable warm and humid air to achieve a more acceptable temperature of 40-60% relative humidity and a more comfortable temperature of 70-75 degrees Fahrenheit.

Usually this kind of procedure causes the humidity of the air in the enclosed space to be within the required comfort range. However, in some conditions, the humidity level is still too high, resulting in an uncomfortable closed space even if the temperature requirement has been met. In order to make the air reach a comfortable level of temperature and humidity at the same time, the size of an air conditioner is based on the expected load caused by the enclosed space, so when the set temperature value is reached, the humidity can be accepted. When the temperature is usually high or the air conditioner is capable of dehumidifying relative to the current environmental conditions, and the set temperature is reached, the air in the enclosed space may have excessive moisture.

Previous attempts to control the relative humidity in a closed space have been achieved by adding a relative humidity sensor to the thermostat, and then controlling the air conditioner to maintain the relative humidity within the selected set temperature range. The problem with these methods is that the relative humidity of the air in the enclosed space will actually rise when the air is cooled and dehumidified in the enclosed space. This is because the relative humidity is also a function of the amount of water vapor and its dry bulb temperature for a given air volume or mass. The relative humidity of any volume of air can be defined as the ratio of the partial pressure of water vapor in the air to the vapor pressure of saturated vapor at that temperature. Because the vapor pressure of the saturated vapor decreases rapidly at a temperature, a relatively small amount of water vapor and a volume of air at a lower temperature can cause a relative humidity of 100%. Therefore, it is possible to have a one-way situation in which the humidity control function in a thermostat will continue to call for further dehumidification, and when the temperature in the enclosed space drops, the relative humidity rises and causes the air conditioner Locked in the open state.

Subsequent attempts to solve the problem of high humidity include controlling the dew point temperature of the air in the enclosed space, regardless of the dry bulb temperature. See US Patent 4,105,063 by Bergt, and US Patent 4,889,280 by Grald and MacArthur. However, the disadvantages caused by these devices are that the temperature of the enclosed space reached is not always comfortable, and it is possible to over-circulate the cooling system. In addition, none of the reference materials listed above provide dehumidification after reaching the set point of the dry bulb temperature.

Other climate control systems have included the use of a humidity sensor and a dry bulb temperature sensor in the enclosed space. Please refer to US Patent Nos. 5,737,934 and 5,675,979. The humidity control using a reheating system reheats the cooled air to maintain the dry bulb temperature of an enclosed space at a specific set temperature, which is disclosed in US Patent No. 6,012,296. Another subject of the invention is temperature and humidity control, which has emphasized the use of the dry bulb and the relatively large error in the humidity temperature. An indoor climate control system that simultaneously adjusts the dry bulb temperature and the wet bulb or dew point temperature in a closed space is disclosed in US Patent No. 5,346,129, which is incorporated herein by reference.

From the above, it can be understood that there is a need to provide a more reliable and efficient system to control a climate correction device, such as an air conditioner, a heat pump, a fan unit, or the like, when there is an unusually high humidity. There is also a need to provide a climate control device that does not cause excessive circulation or lock the air conditioner in the open position.

Summary of the invention

In view of the above, the object of the present invention is to provide a control of an indoor climate correction device, such as an air conditioning unit, for maintaining the comfort of temperature for the user in the enclosed space. Another purpose is to control the operation of a mechanical cooling device, such as an air conditioner, a heat pump operating in a cooling mode, a fan unit operating in a cooling mode, or the like.

Another object of the present invention is to continuously monitor the difference between the dry bulb temperature and the humidity temperature.

Another object of the present invention is to provide a memory that can record the dry bulb temperature set point value and a humidity temperature set point value, and provide a set point signal to encode the dry bulb temperature set point value and the humidity temperature set point value.

Another object of the present invention is to provide a humidity temperature value, which can be used to generate an error signal in accordance with the dry bulb temperature, which is a function of the dry bulb or the humidity temperature value. This can allow the closed space temperature and the closed space humidity to be controlled at the same time without causing abnormal circulation of the climate control system.

Another object of the present invention is to provide an error value input to a temperature control algorithm used by a controller of the climate control system to determine the number of times to activate the climate control system to correct the temperature and humidity of the air in the enclosed space .

In an embodiment of the present invention, a controller continuously monitors the dry bulb temperature and humidity temperature error in the enclosed space, and controls the ON/OFF state of the cooling device based on the following conditions: a) If the humidity temperature error Less than or equal to 0, the dry bulb temperature error is used in a conventional PID (proportional, integral, derivative) control block to control the ON/OFF state of the cooling device, and to correct the temperature and humidity of the enclosed space; or b) if When the humidity temperature error is greater than 0, the dry bulb temperature error is ignored regardless of its magnitude, and the humidity temperature error is used in a conventional PID control block to control the ON/OFF state of the cooling device; or c) if The humidity temperature error and the dry bulb temperature error are both less than 0. When the humidity temperature error and the dry bulb temperature error are larger, it is used in a conventional PID control block to control the ON/OFF state of the cooling device. The humidity temperature error and the dry bulb temperature use the same PID control block and controller gain to prevent any equipment operation from time to time.

These and other objectives not specifically enumerated here are believed to be handled by the present invention, which can be considered as a controller of a climate control system that can provide priority to humidity and temperature control.

Schematic description

Figure 1 shows a block diagram of a complete air conditioner installation using the present invention.

FIG. 2 is an operation diagram illustrating a preferred embodiment of the algorithm implemented by a controller of a climate control system.

Fig. 3 is a coordinate diagram showing the situation under a preferred embodiment implemented by a controller.

Detailed description of the invention:

The description contained herein relates to the specific structure of a controller of a climate control system, as currently considered. However, this description is only for description, and it does not limit the scope of the present invention. For example, when the present invention will be described in the context of a controller of an air conditioner, the present invention will also be applicable to various climate control systems.

In the figure, the same number represents the same element, which shows a controller of a climate control system according to the present invention. This drawing is architectural, and non-basic elements have been omitted.

As shown in Fig. 1, the present invention is implemented in a controller 25 installed in an air conditioner. However, the application of this invention can also be used to control the operation of other mechanical cooling devices, such as a heat pump operating in a cooling mode, a fan unit operating in a cooling mode, and the like.

An enclosed space 12 receives the cooled and dehumidified air from the air conditioning unit 19, which operates on an externally supplied AC power source provided by the conductor 42. A control element 23 switches power to a compressor 17 and a blower 20 on conductors 38 and 39, respectively, thereby providing the sequence required for its operation. The compressor 17 provides liquid refrigerant to the amplifier coil 18, which is located in a heat exchanger space 21 and the blower 20. The air conditioning unit 19 operates when a demand signal appears in the path 26. A demand signal on a path 26 turns off the switch 29, allowing a 24 VAC power supply to control current to flow on the path 40 to the air conditioning unit control element 23 on the path 41. When the air conditioning unit 19 is operating, the fan 20 causes the air to pass through the coil 18 to cool and dehumidify the air. The conditioned air flows into the enclosed space 12 through the duct 22 to reduce the temperature and humidity of the air in the enclosed space 12 at the same time. The demand signal on the path 26 is provided by a controller 25 whose function takes place in the electronic circuit.

The controller 25 includes a memory unit 27, which stores digital data, and a processor unit 28, which performs calculation and comparison operations on the data supplied to it from the memory 27 and from external sources, and includes a command memory element. Preferably, a microcontroller is used as the memory 27 and the processor 28. The controller 25 has a humidity sensor 14 located in the enclosed space 12, which provides a humidity signal on the path 30, which is shown to encode the relative humidity of the air in the enclosed space 12, but can additionally encode the relative humidity of the air The dew point temperature or the wet bulb temperature. A temperature sensor 15 is also located in the enclosed space 12, which similarly encodes the dry bulb temperature value in an air temperature signal on the path 31. The processor 28 receives these signals and converts them to digital values for internal operations. The code in the present invention can be a digital signal or an analog signal.

Paths 33-35 carry signals to memory 27 to encode the different pre-selected setpoint values required to implement the invention. The occupant in a closed space 12 can select the set point value by simply manipulating the controls outside the controller 25. The path 33 carries a humidity signal, which encodes a humidity set point value, which represents the relative humidity required in the enclosed space 12. The humidity set point value can be the actual required relative humidity, or the required dew point temperature, or even the required wet bulb temperature. The path 34 carries a signal to the memory 27, which encodes a minimum dry bulb temperature set point value, which is used as a limit value for the dry bulb temperature. Path 35 carries a signal to encode an air (dry bulb) temperature set point value. The memory 27 records these three set point values and encodes them on a path 36 to carry the set point signal to the processor 28. If the memory 27 and the processor 28 are formed by a microcontroller, the program of these set point values is provided to the processor 28 when needed, which is included in another circuit not shown, which provides this kind of micro-control One of the control functions of the overall operation of the device.

The processor unit 28 has an internal memory in which instructions are stored and executed by the processor unit 28. The execution of these instructions causes the processor unit 28 to perform the functions shown, the details of which are shown in the functional block diagram of FIG. 2. Fig. 2 represents a modification to the hardware shown broadly in Fig. 1, wherein the modification allows the processor unit 28 to implement the present invention. As shown, each element of FIG. 2 has an actual physical embodiment within the processor unit 28. The execution of each instruction, when the instruction is executed, causes the processor unit 28 to actually become a part of the element shown in FIG. 2. The memory in the processor unit 28 also forms a part of each functional block in FIG. 2, which essentially stores and supplies the instructions that cause the functional block to be generated.

At the same time, the arithmetic operation register in the processor unit 28 temporarily stores the result of the operation. These can be regarded as forming part of the memory 27, even though it may actually be located in the processor unit part of the microcontroller.

As shown in Figure 2, signal transmission is represented by a line starting from one functional block and ending at another, as shown by the arrow. This means that the signal formed by one functional element is supplied to another functional element for its use. This is when the execution of a series of instructions causes the microcontroller to include a functional element, it occurs in a microcontroller, and actually generates a digital value, which is then transmitted to the microcontroller on its signal path. This circuit is used to execute instructions from other functional elements. The same actual signal path in a microcontroller can carry different signals, and each path is shown in Figure 2 individually.

The following description defines the value of each code in the signal, as shown in Figures 2 and 3:

<tables><img file="TW554154B_D0001.tif" /></tables>

Please refer to FIG. 2, the individual function block has an internal mark, which describes the individual function represented. Each rectangular square represents some form of mathematics or arithmetic operation encoded in the value of the signal supplied to the square. For example, the signal on path 58 encodes the average room temperature T _AV , Which is shown supplied to the function block 61 to form a T _AV The Laplace conversion operation device. Other functional blocks represent decision-making operations, calculations of other mathematical functions, such as products, and other different forms of Laplace transformation operations. The circle supplying two or more signals represents a sum or difference calculation represented by the adjacent plus or minus sign. Therefore, the plus and minus signs adjacent to the junction of paths 35 and 64 have a summing element 71, which represents the value coded on path 64 minus the value coded on path 35.

Preferably, the different calculations, operations and decisions represented in FIG. 2 are executed in a sequence represented by appropriate intervals, which is every minute or continuously. If the calculation continues, it is necessary to determine the time it takes from one completion to the next to determine the rate of change of different values, which is very important for operation. Because the temperature and humidity in a closed space 12 usually change very slowly, the calculation once per minute basically provides sufficient control accuracy.

Block 61 receives the signal on path 58, whose code represents the air temperature T in the enclosed space 12 _Av The value of the weighted average. Box 61 represents for T _Av The Laplacian conversion operation is to compensate for the sensors lagging response and generate a signal code T on the path 64 _DBSN . T on path 35 _DBSP The value is used to self-encode the T in the signal on path 64 _DBSN Value to produce the error value of the dry bulb temperature <img file="TW554154B_D0002.tif" />_DB , Which is a customary error used to control air conditioners and stoves. <img file="TW554154B_D0003.tif" />_DB It is encoded in the signal on path 84.

Humidity is another variable used to calculate the error, which is used in the control operation of the air conditioning unit 19 (see FIG. 1). The present invention uses a relative humidity value Φ, which is encoded in the signal supplied on the path 30 from the sensor 14 (see FIG. 1). The value of Φ is supplied to a Laplace conversion operation block 50, which compensates for the lag and instability of the sensor 14, and provides a converted relative humidity value Φ on the path 51 _sN 。

It usually determines the wet bulb and dew point temperature from a given dry bulb temperature and a given relative humidity value (which are collectively referred to as a humidity temperature in the following). This is only the equivalent of digits or calculations that manually query a value in a standard air humidity table. Operation block 67 receives Φ _sN And T _DBSN , And calculate the sensed humidity temperature T _HSN The approximate value of, and encode this value in the signal on path 76.

Operation block 74 performs a similar operation to obtain the dry bulb temperature set point T _DBSP And the relative humidity set point Φ _SP Humidity and temperature set point T _HSP The approximate value. The same instructions in the processor memory 28 can be used to perform two operations at different times. These instructions form a program, which is called at an appropriate time and supplies the relative humidity value and dry bulb temperature value. . Block 74 receives T on path 35 _DBSP Value, and Φ on path 33 _SN Value, and encode the corresponding set point humidity temperature T in the previous signal on path 77 _HSP value. Block 74 can be regarded as including a memory element that temporarily stores T at the end of the calculation _HSP . The summing block 78 receives the T on paths 77 and 76, respectively _HSP And T _HSN Value and form the humidity temperature error value <img file="TW554154B_D0004.tif" />_H =T _HSN -T _HSP , Which is encoded in the signal carried on path 81. Encode on paths 81 and 84 <img file="TW554154B_D0005.tif" /> H and <img file="TW554154B_D0006.tif" />_DB The individual signal of is used to calculate the initial error signal in decision block 87.

The development provided by the present invention is the use of a decision block 87. Decision box 87 Use dry bulb temperature error <img file="TW554154B_D0007.tif" />_DB And humidity temperature error <img file="TW554154B_D0008.tif" />_H To get a second-level or composite error value <img file="TW554154B_D0009.tif" /> , Which is included in the signal carried on the path 90. There are a few different algorithms to get this composite error value. Preferably, the algorithm is only a decision block, which sets the error e to be equal to the dry bulb temperature error <img file="TW554154B_D0010.tif" />_DB Or the humidity temperature error <img file="TW554154B_D0011.tif" />_H . The determined error value controls the ON/OFF state of the cooling device. The decision block calculation is based on the following conditions: (a) If the humidity temperature error <img file="TW554154B_D0012.tif" /> H is less than or equal to 0 (see reference number 85), the dry bulb temperature can use the composite error value <img file="TW554154B_D0013.tif" /> equal <img file="TW554154B_D0014.tif" />_DB 86 to calculate the composite error; or (b) if the humidity temperature error is greater than 0 (see reference number 85), the dry bulb temperature error <img file="TW554154B_D0015.tif" />_DB Regardless of its size, it is ignored, and the humidity temperature error <img file="TW554154B_D0016.tif" />_DB As the error value <img file="TW554154B_D0017.tif" /> 88; or (c) If the humidity temperature error <img file="TW554154B_D0018.tif" />_H And the dry bulb temperature error <img file="TW554154B_D0019.tif" />_DB Are less than 0, the composite error e is equal to the humidity temperature error <img file="TW554154B_D0020.tif" /> H and the dry bulb temperature error <img file="TW554154B_D0021.tif" />_DB The larger the median value.

It is not recommended to directly use the composite error value e to obtain a demand signal. Instead, it provides e to the conventional PID (proportional, integral, derivative) control function, which contains G _p ,G _i /s and G _d s blocks 91-93, the output values are then summed by a summing block 96 (also part of the PID control function) to produce a final error value <img file="TW554154B_D0022.tif" />_f , And encoded in a final error signal on path 98.

The final error signal carried on path 98 <img file="TW554154B_D0023.tif" />_f The demand signal is converted to the path 26. <img file="TW554154B_D0024.tif" />_f Through some conventional calculation stages, it is modified to insert an expected function to obtain the final demand signal on the path 26. The demand signal calculation at each stage generates a signal with a logic 1 voltage level, which can be regarded as corresponding to the ON state of the air conditioning unit 19. The signal voltage on the path 26 has a level corresponding to a logic 0 when the demand signal does not exist. When a logic 1 appears in the path 26, the switch 29 (see FIG. 1) is closed, and current flows to the air conditioning unit 19. When the path 26 carries a logic 0 value, the shutoff 29 is opened, and the unit 19 does not operate.

The expectation function is implemented by the summing block 101 and the functional blocks 103 and 113 in a conventional manner. The block 113 performs a Laplacian conversion operation θ/(τS+1) on the signal carried on the path 26, and shifts its logic 0 and 1 in real time. Hysteresis test block 103 provides the first stage demand signal on path 105, and its logic 1 section will ignore T _DBSN And T _DBMN Relative size. If the Laplace transforms the block 113 back to the value 0 on the path 115 to the sum block 111, then the final error value ε on the path 98 _f The hysteresis test block 103 is used to determine the time and length of the first phase of the demand signal on the path 105. If the block 113 returns a value different from 0 to the summing block 101, the error value of 98 on the path of the test block 103 is supplied <img file="TW554154B_D0025.tif" /> f is lowered by the summing block 101, which will delay the start of the demand signal and shorten the segment length, thereby delaying the start, and speeding up the shutdown time of the air conditioning unit 19.

Another feature of the present invention is a test block 108 that receives the first stage of the demand signal on the path 105. In some rare cases of air conditioning units with relatively high humidity or different sizes, or choose a relatively low Φ _SP Value, when the humidity temperature error <img file="TW554154B_D0026.tif" />_H When the level has been lowered to a value of ε on the path 90, it may cause an induced dry bulb temperature T _DBSN This is an uncomfortable low value, but allows the air conditioning unit 19 to be turned on and operated for an extended period of time. To deal with this problem, test block 108 receives T on path 64 _DBSN Value, and T on path 34 _DBMN value. T _DBMN It is used to limit the dry bulb temperature to stop the operation of the air conditioning unit. If it reaches T _DBMN &gt;T _DBSN Condition, regardless of the actual humidity in the enclosed space 12, the final demand signal on the path 26 is ignored, thereby causing the air conditioning unit 19 to be turned off, which is due to the humidity temperature error <img file="TW554154B_D0027.tif" />_H Reduced to produce one <img file="TW554154B_D0028.tif" /> The level of the value, which usually causes this situation.

Figure 3 shows a graph of possible dry bulb temperature error and humidity temperature error. In a thermally stable condition, the goal is always to achieve zero error. The invention can efficiently handle humidity and temperature errors <img file="TW554154B_D0029.tif" />_H Positive condition, but less than the error of dry bulb temperature <img file="TW554154B_D0030.tif" />_DB . The area marked P on the map has a positive humidity and temperature error <img file="TW554154B_D0031.tif" />_H , The humidity temperature error <img file="TW554154B_D0032.tif" />_H Will have priority higher than the dry bulb temperature error until the humidity temperature error <img file="TW554154B_D0033.tif" />_H Is zero or non-positive. This represents the control error <img file="TW554154B_D0034.tif" /> Will be equal to the positive humidity temperature error <img file="TW554154B_D0035.tif" />_H . Once the humidity temperature error <img file="TW554154B_D0036.tif" />_H Is a non-positive value, the dry bulb temperature error <img file="TW554154B_D0037.tif" />_DB That is control. When the dry bulb temperature error and the humidity temperature error are both lower than 0, the thermostat will be turned off.

In addition, a dehumidification system (not shown) may be added to the present invention, or to the cooling system, in which the thermostat does not remove enough moisture from the air. Additional functions can be added to change the speed of the fan 20 and/or to change the speed of the compressor 17 to remove moisture in the enclosed space 12. For example, the speed of the fan 20 can be reduced to allow more time for the air to come into contact with the cooling coil 18, and/or the speed of the compressor 17 can be increased to increase the cooling capacity of the air conditioning unit 19 .

Although the present invention has been illustrated with specific specific embodiments and applications, those skilled in the art can be inspired by the principles to produce additional specific embodiments and modifications without departing from the spirit of the claimed invention and beyond its scope. Therefore, it must be understood that the drawings and descriptions herein are used to explain the present invention through examples, and should not be regarded as a limitation of the present invention.

Symbol description of main components

12. . . Enclosed space

14. . . Humidity sensor

15. . . Temperature sensor

17. . . compressor

18. . . Amplifier coil

19. . . Air conditioning unit

20. . . hair dryer

twenty one. . . Heat exchanger space

twenty two. . . pipeline

twenty three. . . control element

25. . . Controller

26. . . path

27. . . Memory unit

28. . . Processor unit

29. . . switch

30. . . path

31. . . path

33. . . path

34. . . path

35. . . path

36. . . path

38. . . conductor

39. . . conductor

40. . . path

41. . . path

42. . . conductor

50. . . Laplace transform operation block

51. . . path

58. . . path

61. . . Function block

64. . . path

67. . . Calculation block

71. . . Total components

74. . . Calculation block

76. . . path

77. . . path

78. . . Sum cube

81. . . path

84. . . path

86. . . ε=ε _DB

87. . . Decision box

88. . . ε=ε _H

90. . . path

91. . . Gp

92. . . Gj/s

93. . . G _d S

96. . . Sum cube

98. . . path

101. . . Sum cube

103. . . Hysteresis test block

105. . . path

108. . . Test block

113. . . Laplace transform cube

115. . . path