Building a Programmable Logic Controller Model

Building a Programmable Logic Controller Model

The primary functions of a Programmable Logic Controller (PLC) are reading sensors, executing sequence control programs, and updating actuators. PLCs interact generally with target plants by a time driven approach. That is, PLC captures the state change of the target plants and drives the actuators by acyclic scan. The period of the cyclic scan is called generally by a scan time (T).

PLCs are composed commonly of execution subsystems (ESs) and I/O subsystems (I/OSs). While I/OSs are interconnected over a system area bus in small scale PLCs, they are interconnected over a LAN (Local Area Network) in large scale PLCs. To provide enough bandwidth and low latency for data communication, the ES contains of a PEU (Program Execution Unit) and DTU (Data Transmission Unit) powered by separate processors.

The PEU refers to data in the IODM (I/O Data Memory) that consists mirror images of the actual values of the actuators and the sensors. The DTUs keep data coherency between the IODM in the ES and actuators or sensors in the IOSs. The PEU executes the program and the DTUs transmit the data with the period, T. the execution order of the I/O instructions of the sequence control program is not the same as the transmission order of the corresponding I/O data because the I/O data is packetized by the location of the IOSs and the data type. The execution time of the task and the data transmission time of the task should be counted independently. The execution time of the task and the data transmission time of the task should be counted independently in computing the PLC processing delay of a task. The data transfer delay between the DTU in the ES and the DTU in the IOS must be bounded. Currently, field bus networks have become suitable solutions for this purpose.

Since the PLC synchronous operates to the periodic time tick but handles asynchronous event of a plant, a shorter T enables PLCs to accommodate higher speed plant dynamics. Although the allowable minimum T often has accounted for a performance measure of PLCs, R indicates the performance more accurately. Generally, the state of the plant may change by both internal events and external stimuli. Sensing the plant state,

The PLC computes the suitable command to send to the plant within D. it does not respond to the command immediately after the plant receives the controller command. There is a delay on the change of the plant state. We denote the largest plant delay by P, L is the minimum control idle time, which is the minimum latency of a PLC from the control update to the next input sensing.

PLC often form the feedback control loops with the plant; it checks how the previous actuation influences the plant and determines the next value of actuation. The proper feedback control can be accomplished provided that P < L. P is a given constant that depends on the plant dynamics. L is a design parameter that depends on the scheduling. Let us assume that the control rules are increase the output for one degree if the plant state is less than the desired state, and decrease the output for one degree it he plant state is greater than the desired state.

The PLC senses the plant state at the beginning. The PLC actuates the output to make the plant state increase by one degree according to the control rule within the time bound D. the plant state increases following the PLC actuation of P. The plant state comes to the desired state fast. However, the plant becomes marginally unstable due to L < P that is caused by the short T. the PLC can not control the plant to be stationary at the desired value because it computes the actuation value from the plant state that has not reflected yet the previous PLC actuation.

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