15. LADDER LOGIC FUNCTIONS
15.1 INTRODUCTION
Ladder logic input contacts and output coils allow simple logical decisions. Functions extend basic ladder logic to allow other types of control. For example, the addition of timers and counters allowed event based control. A longer list of functions is shown in Figure 201 Basic PLC Function Categories. Combinatorial Logic and Event functions have already been covered. This chapter will discuss Data Handling and Numerical Logic. The next chapter will cover Lists and Program Control and some of the Input and Output functions. Remaining functions will be discussed in later chapters.
Most of the functions will use PLC memory locations to get values, store values and track function status. Most function will normally become active when the input is true. But, some functions, such as TOF timers, can remain active when the input is off. Other functions will only operate when the input goes from false to true, this is known as positive edge triggered. Consider a counter that only counts when the input goes from false to true, the length of time the input is true does not change the function behavior. A negative edge triggered function would be triggered when the input goes from true to false. Most functions are not edge triggered: unless stated assume functions are not edge triggered.
15.2 DATA HANDLING
15.2.1 Move Functions
There are two basic types of move functions;
MOV(value,destination) - moves a value to a memory location
MVM(value,mask,destination) - moves a value to a memory location, but with a mask to select specific bits.
The simple MOV will take a value from one location in memory and place it in another memory location. Examples of the basic MOV are given in Figure 202 Examples of the MOV Function. When A is true the MOV function moves a floating point number from the source to the destination address. The data in the source address is left unchanged. When B is true the floating point number in the source will be converted to an integer and stored in the destination address in integer memory. The floating point number will be rounded up or down to the nearest integer. When C is true the integer value of 123 will be placed in the integer file test_int.
A more complex example of move functions is given in Figure 203 Example of the MOV and MVM Statement with Binary Values. When A becomes true the first move statement will move the value of 130 into int_0. And, the second move statement will move the value of -9385 from int_1 to int_2. (Note: The number is shown as negative because we are using 2s compliment.) For the simple MOVs the binary values are not needed, but for the MVM statement the binary values are essential. The statement moves the binary bits from int_3 to int_5, but only those bits that are also on in the mask int_4, other bits in the destination will be left untouched. Notice that the first bit int_5.0 is true in the destination address before and after, but it is not true in the mask. The MVM function is very useful for applications where individual binary bits are to be manipulated, but they are less useful when dealing with actual number values.
15.2.2 Mathematical Functions
Mathematical functions will retrieve one or more values, perform an operation and store the result in memory. Figure 204 Arithmetic Functions shows an ADD function that will retrieve values from int_1 and real_1, convert them both to the type of the destination address, add the floating point numbers, and store the result in real_2. The function has two sources labelled source A and source B. In the case of ADD functions the sequence can change, but this is not true for other operations such as subtraction and division. A list of other simple arithmetic function follows. Some of the functions, such as the negative function are unary, so there is only one source.
An application of the arithmetic function is shown in Figure 205 Arithmetic Function Example. Most of the operations provide the results we would expect. The second ADD function retrieves a value from int_3, adds 1 and overwrites the source - this is normally known as an increment operation. The first DIV statement divides the integer 25 by 10, the result is rounded to the nearest integer, in this case 3, and the result is stored in int_6. The NEG instruction takes the new value of -10, not the original value of 0, from int_4 inverts the sign and stores it in int_7.
A list of more advanced functions are given in Figure 206 Advanced Mathematical Functions. This list includes basic trigonometry functions, exponents, logarithms and a square root function. The last function CPT will accept an expression and perform a complex calculation.
Figure 207 An Equation in Ladder Logic shows an example where an equation has been converted to ladder logic. The first step in the conversion is to convert the variables in the equation to unused memory locations in the PLC. The equation can then be converted using the most nested calculations in the equation, such as the LN function. In this case the results of the LN function are stored in another memory location, to be recalled later. The other operations are implemented in a similar manner. (Note: This equation could have been implemented in other forms, using fewer memory locations.)
The same equation in Figure 207 An Equation in Ladder Logic could have been implemented with a CPT function as shown in Figure 208 Calculations with a Compute Function. The equation uses the same memory locations chosen in Figure 207 An Equation in Ladder Logic. The expression is typed directly into the PLC programming software.
Math functions can result in status flags such as overflow, carry, etc. care must be taken to avoid problems such as overflows. These problems are less common when using floating point numbers. Integers are more prone to these problems because they are limited to the range.
15.2.3 Conversions
Ladder logic conversion functions are listed in Figure 209 Conversion Functions. The example function will retrieve a BCD number from the D type (BCD) memory and convert it to a floating point number that will be stored in F8:2. The other function will convert from 2s compliment binary to BCD, and between radians and degrees.
Examples of the conversion functions are given in Figure 210 Conversion Example. The functions load in a source value, do the conversion, and store the results. The TOD conversion to BCD could result in an overflow error.
15.2.4 Array Data Functions
Arrays allow us to store multiple data values. In a PLC this will be a sequential series of numbers in integer, floating point, or other memory. For example, assume we are measuring and storing the weight of a bag of chips in floating point memory starting at weight[0]. We could read a weight value every 10 minutes, and once every hour find the average of the six weights. This section will focus on techniques that manipulate groups of data organized in arrays, also called blocks in the manuals.
15.2.4.1 - Statistics
Functions are available that allow statistical calculations. These functions are listed in Figure 211 Statistic Functions. When A becomes true the average (AVE) conversion will start at memory location weight[0] and average a total of 4 values. The control word weight_control is used to keep track of the progress of the operation, and to determine when the operation is complete. This operation, and the others, are edge triggered. The operation may require multiple scans to be completed. When the operation is done the average will be stored in weight_avg and the weight_control.DN bit will be turned on.
Examples of the statistical functions are given in Figure 212 Statistical Calculations for an array of data that starts at weight[0] and is 4 values long. When done the average will be stored in weight_avg, and the standard deviation will be stored in weight_std. The set of values will also be sorted in ascending order from weight[0] to weight[3]. Each of the function should have their own control memory to prevent overlap. It is not a good idea to activate the sort and the other calculations at the same time, as the sort may move values during the calculation, resulting in incorrect calculations.
15.2.4.2 - Block Operations
A basic block function is shown in Figure 213 Block Operation Functions. This COP (copy) function will copy an array of 10 values starting at n[50] to n[40]. The FAL function will perform mathematical operations using an expression string, and the FSC function will allow two arrays to be compared using an expression. The FLL function will fill a block of memory with a single value.
Figure 214 File Algebra Example shows an example of the FAL function with different addressing modes. The first FAL function will do the following calculations n[5]=n[0]+5, n[6]=n[1]+5, n[7]=n[2]+5, n[7]=n[3]+5, n[9]=n[4]+5. The second FAL statement will be n[5]=n[0]+5, n[6]=n[0]+5, n[7]=n[0]+5, n[7]=n[0]+5, n[9]=n[0]+5. With a mode of 2 the instruction will do two of the calculations when there is a positive edge from B (i.e., a transition from false to true). The result of the last FAL statement will be n[5]=n[0]+5, n[5]=n[1]+5, n[5]=n[2]+5, n[5]=n[3]+5, n[5]=n[4]+5. The last operation would seem to be useless, but notice that the mode is incremental. This mode will do one calculation for each positive transition of C. The all mode will perform all five calculations in a single scan whenever there is a positive edge on the input. It is also possible to put in a number that will indicate the number of calculations per scan. The calculation time can be long for large arrays and trying to do all of the calculations in one scan may lead to a watchdog time-out fault.
15.3 LOGICAL FUNCTIONS
15.3.1 Comparison of Values
Comparison functions are shown in Figure 215 Comparison Functions. Previous function blocks were outputs, these replace input contacts. The example shows an EQU (equal) function that compares two floating point numbers. If the numbers are equal, the output bit light is true, otherwise it is false. Other types of equality functions are also listed.
The example in Figure 216 Comparison Function Examples shows the six basic comparison functions. To the right of the figure are examples of the comparison operations.
The ladder logic in Figure 216 Comparison Function Examples is recreated in Figure 217 Equivalent Statements Using CMP Statements with the CMP function that allows text expressions.
Expressions can also be used to do more complex comparisons, as shown in Figure 218 A More Complex Comparison Expression. The expression will determine if B is between A and C.
The LIM and MEQ functions are shown in Figure 219 Complex Comparison Functions. The first three functions will compare a test value to high and low limits. If the high limit is above the low limit and the test value is between or equal to one limit, then it will be true. If the low limit is above the high limit then the function is only true for test values outside the range. The masked equal will compare the bits of two numbers, but only those bits that are true in the mask.
Figure 220 A Number Line for the LIM Function shows a numberline that helps determine when the LIM function will be true.
File to file comparisons are also permitted using the FSC instruction shown in Figure 221 File Comparison Using Expressions. The instruction uses the control word c_0. It will interpret the expression 10 times, doing two comparisons per logic scan (the Mode is 2). The comparisons will be f[10]<f[0], f[11]<f[0] then f[12]<f[0], f[13]<f[0] then f[14]<f[0], f[15]<f[0] then f[16]<f[0], f[17]<f[0] then f[18]<f[0], f[19]<f[0]. The function will continue until a false statement is found, or the comparison completes. If the comparison completes with no false statements the output A will then be true. The mode could have also been All to execute all the comparisons in one scan, or Increment to update when the input to the function is true - in this case the input is a plain wire, so it will always be true.
15.3.2 Boolean Functions
Figure 222 Boolean Functions shows Boolean algebra functions. The function shown will obtain data words from bit memory, perform an and operation, and store the results in a new location in bit memory. These functions are all oriented to word level operations. The ability to perform Boolean operations allows logical operations on more than a single bit.
The use of the Boolean functions is shown in Figure 223 Boolean Function Example. The first three functions require two arguments, while the last function only requires one. The AND function will only turn on bits in the result that are true in both of the source words. The OR function will turn on a bit in the result word if either of the source word bits is on. The XOR function will only turn on a bit in the result word if the bit is on in only one of the source words. The NOT function reverses all of the bits in the source word.
15.4 DESIGN CASES
15.4.1 Simple Calculation
Problem: A switch will increment a counter on when engaged. This counter can be reset by a second switch. The value in the counter should be multiplied by 2, and then displayed as a BCD output using (O:0.0/0 - O:0.0/7)
15.4.2 For-Next
Problem: Design a for-next loop that is similar to ones found in traditional programming languages. When A is true the ladder logic should be active for 10 scans, and the scan number from 1 to 10 should be stored in n0.
As designed the program differs from traditional loops because it will only complete one 'loop' each time the logic is scanned.
15.4.3 Series Calculation
Problem: Create a ladder logic program that will start when input A is turned on and calculate the series below. The value of n will start at 1 and with each scan of the ladder logic n will increase until n=100. While the sequence is being incremented, any change in A will be ignored.
15.4.4 Flashing Lights
Problem: We are designing a movie theater marquee, and they want the traditional flashing lights. The lights have been connected to the outputs of the PLC from O[0] to O[17] - an INT. When the PLC is turned, every second light should be on. Every half second the lights should reverse. The result will be that in one second two lights side-by-side will be on half a second each.
15.5 SUMMARY
· Functions can get values from memory, do simple operations, and return the results to memory.
· Scientific and statistics math functions are available.
· Masked function allow operations that only change a few bits.
· Expressions can be used to perform more complex operations.
· Conversions are available for angles and BCD numbers.
· Array oriented file commands allow multiple operations in one scan.
· Values can be compared to make decisions.
15.6 PRACTICE PROBLEMS
(Note: Problem solutions are available at http://sites.google.com/site/automatedmanufacturingsystems/)
1. Do the calculation below with ladder logic,
2. Implement the following function,
3. A switch will increment a counter on when engaged. This counter can be reset by a second switch. The value in the counter should be multiplied by 5, and then displayed as a binary output using output integer 'O_lights'.
4. Create a ladder logic program that will start when input A is turned on and calculate the series below. The value of n will start at 0 and with each scan of the ladder logic n will increase by 2 until n=20. While the sequence is being incremented, any change in A will be ignored.
5. The following program uses indirect addressing. Indicate what the new values in memory will be when button A is pushed after the first and second instructions.
6. A thumbwheel input card acquires a four digit BCD count. A sensor detects parts dropping down a chute. When the count matches the BCD value the chute is closed, and a light is turned on until a reset button is pushed. A start button must be pushed to start the part feeding. Develop the ladder logic for this controller. Use a structured design technique such as a state diagram.
7. Describe the difference between incremental, all and a number for file oriented instruction, such as FAL.
8. What is the maximum number of elements that moved with a file instruction? What might happen if too many are transferred in one scan?
9. Write a ladder logic program to do the following calculation. If the result is greater than 20.0, then the output 'solenoid' will be turned on.
10. Write ladder logic to reset an RTO counter (timer) without using the RES instruction.
11. Write a program that will use Boolean operations and comparison functions to determine if bits 9, 4 and 2 are set in the input word input_card. If they are set, turn on output bit match.
12. Explain how the mask works in the following MVM function. Develop a Boolean equation.
13. A machine is being designed for a foreign parts supplier. As part of the contractual agreement the logic will run until February 26, 2008. However, after that date the machine will enable a `contract_expired' value and no longer run. Write the ladder logic.
14. Use an FAL instruction to average the values in n[0] to n[20] and store them in 'n_avg'.
15. The input bits from 'input_card_A' are to be read and XORed with the inputs from 'input_card_B'. The result is to be written to the output card 'output_card'. If the binary pattern of the least 16 output bits is 1010 0101 0111 0110 then the output 'match_bell' will be set. Write the ladder logic.
16. Write some simple ladder logic to change the preset value of a counter 'cnt'. When the input `A' is active the preset should be 13, otherwise it will be 9.
17. A machine ejects parts into three chutes. Three optical sensors (A, B and C) are positioned in each of the slots to count the parts. The count should start when the reset (R) button is pushed. The count will stop, and an indicator light (L) turned on when the average number of parts counted is 100 or greater.
18. a) Write ladder logic to calculate and store the binary (geometric) sequence in 32 bit integer (DINT) memory starting at n[0] up to n[200] so that n[0] = 1, n[1] = 2, n[2] = 4, n[3] = 16, n[4] = 64, etc. b) Will the program operate as expected?
15.7 ASSIGNMENT PROBLEMS
1. Write a ladder logic program that will implement the function below, and if the result is greater than 100.5 then the output 'too_hot' will be turned on.
2. Write ladder logic to calculate the average of the values from thickness[0] to thickness[99]. The operation should start after a momentary contact push button A is pushed. The result should be stored in 'thickness_avg'. If button B is pushed, all operations should be complete in a single scan. Otherwise, only ten values will be calculated each scan. (Note: this means that it will take 10 scans to complete the calculation if A is pushed.)
3. Write a ladder logic program that will calculate the standard deviation of numbers in the locations f[0] to f[29] without using the STD function.
4. A program is to perform the following actions for a self-service security check. The device will allow bags to be inserted to the test chamber through an entrance door. If the bag passes the check it can be removed through an exit door, otherwise an alarm is sounded. Create a state diagram using the steps below.
1. The machine starts in an `idle' state. The `open_entry' output is activated to open the input door. The `open_exit' output is deactivated to close the output door.
2. When a bag is inserted the `bag_detected' input goes high. The `open_entry' input should be deactivated to close the door.
3. When the `entry_door_closed' and `exit_door_closed' inputs are active then a `test' output will be set high to start a scan of the bags.
4. When the scan of the bags is complete a `scan_done' input is set. The `test' output should be turned off.
5. The scan results in two real values `nitrates' and `mass'. The calculation below is performed. If the `risk' is below 0.3, or above 23.5, then the machine enters an alarm state (step 8), otherwise it continues to step 6.
6. The `open_exit' output is activated to open the exit door. The machine waits until the `bag_detected' input goes low.
7. The `open_exit' output is deactivated to close the door. The machine waits until the `exit_door_closed' input is high before returning to the `idle state.
8. In the alarm state an operator input `key' must be active to open the exit door. After this input is released the door will close and return to the `idle' state.