Jawaharlal Nehru Technological University Hyderabad B.Tech III PROCESS DYNAMICS AND CONTROL Previous Question Paper (March/April - 2021 - R16)

In process control, systems are classified based on how the output of one stage affects the input of the preceding stage. A non-interacting system consists of multiple stages where the output of one stage does not influence the dynamics of the previous stage. For example, in a series of liquid tanks where the flow from one tank to the next is determined solely by the head in the upstream tank (often achieved using a pump or a free-falling discharge), the time constant of each tank remains independent. The transfer function is simply the product of individual first-order transfer functions.

An interacting system occurs when the output of a downstream stage affects the input of an upstream stage. In a series of tanks where the flow between tanks depends on the difference in liquid levels, the level in the second tank exerts a back-pressure or reduces the head difference, thereby influencing the flow from the first tank. This coupling results in a higher-order system where the time constants are no longer independent, and the overall transfer function includes cross-coupling terms in the denominator, leading to a slower response compared to a non-interacting system of the same order.

Diagrammatic representation:

Real-time applications:

• Non-interacting systems: Used in cascade storage tanks where pumps are placed between stages to maintain unidirectional flow, such as in chemical feed systems or multi-stage water treatment units where independent control of each stage is required.
• Interacting systems: Commonly found in gravity-fed tank farms, heat exchanger networks where fluid temperatures influence upstream heat transfer rates, and multi-component distillation columns where the concentration profiles in different trays are inherently coupled.

A simple pressure process typically involves the storage of gas or vapor in a vessel. The dynamics are governed by the mass balance equation, where the rate of change of mass in the vessel equals the difference between the mass flow rate in and the mass flow rate out. For a gas at constant temperature, the pressure is directly proportional to the mass of gas stored. The transfer function of such a process is generally first-order, represented as:

where K is the process gain and τ is the time constant, defined as the product of resistance to flow and the capacitance of the vessel. An example is a pressurized air tank where a change in inlet valve position causes a first-order exponential rise or decay in tank pressure until a new steady state is reached.

A simple temperature process involves the heating or cooling of a fluid in a stirred tank. The dynamics are determined by the energy balance, where the rate of change of internal energy equals the net heat transfer rate. The process is characterized by a thermal time constant, which depends on the heat capacity of the fluid and the heat transfer coefficient of the vessel walls. The temperature response to a step change in heat input follows a first-order lag. An example is an electric heater in a jacketed vessel; the fluid temperature does not change instantaneously but follows an exponential curve determined by the thermal mass of the system and the resistance to heat transfer.

Both processes exhibit self-regulation, meaning they naturally return to a stable state after a disturbance, provided the system is not integrated. Their dynamic behavior is essential for designing controllers, as the time constant dictates how quickly the process responds to corrective actions.