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Control systems play a crucial role in various industrial processes by ensuring stability, efficiency, and optimal performance. Among the myriad of control methods available, Model Predictive Control (MPC) vs Proportional-Integral-Derivative (PID) stand out as two competing strategies. In this article, we delve into the intricacies of each method, compare its strengths and weaknesses, explore applications, and provide insights on selecting the most suitable approach.

Model Predictive Control

Model Predictive Control is a sophisticated control strategy that leverages a predictive model of a system to make decisions about the control output. It calculates the optimal control action by minimizing a ‘cost function’, which can be likened to the ‘error’ in PID control. Because of the predictive nature of the MPC, it is ideal for systems with complex dynamics and varying operating conditions. The main features of MPC are the process model and optimization.

Process Model

This refers to the mathematical model that the system uses to predict future behavior. Often, it is derived from an algorithm unique to the system being controlled or from established first-principle equations. The model incorporates information about the system’s dynamics including past inputs, past outputs, and even future inputs in predicting an output to the controller. It keeps repeating this process until the desired output is achieved.

Optimization

The optimization feature of the MPC is targeted at finding the best control signal. After each time step or prediction from the process model, the optimizer takes into account the future errors, which is obtained by comparing the predicted output to the reference trajectory of the process. Moreover, the optimizer also considers the defined cost function and constraints as it solves the problem to produce future control outputs.

These outputs are still fed back to the process model and used in generating subsequent predicted outputs. This continuous exchange between the process model and optimizer enables the recalculation of the optimal control actions in real-time. As a result, the MPC adapts to changes in system dynamics and operating conditions, which makes it effective for systems with variable parameters or nonlinear behavior.

Benefits of MPC

The MPC provides several advantages including:

• Ability to control a system at both supervisory and local loop levels.
• Can cope with slow-moving processes with time delay. Also, it handles time-varying dynamics.
• It is the ideal control strategy for handling constraints and uncertainties due to its anticipatory control actions.
• Provides an easy method to integrate energy conservation strategies in the controller formulation.

Drawbacks of MPC

• The predictive nature of MPC involves solving optimization problems at each time step, thus, leading to higher computational demands.
• Implementing MPC requires a good understanding of system dynamics and model accuracy, which is difficult in certain applications.
• MPC often requires a large number of model coefficients to describe a response.

Applications of MPC Control

• Chemical Processes: The use of MPC is common in the control of chemical reactors and processes where precise control is crucial.
• Automotive Systems: Vehicle control systems, optimizing fuel consumption, and improving overall performance of automotive systems typically involves MPC deployment.

PID

As the most widely used control strategy, Proportional-Integral-Derivative control has proven to be a big advantage in industry. The basic idea of this control method is to adjust the output of a system based on the error, which is the difference between the setpoint and the measured output. Simply put, the PID uses the previous and current state of a system to determine an appropriate controller output. It achieves this using three parameters which are the proportional, integral, and derivative.

Basic Parameters of PID

• Proportional: The proportional parameter takes into consideration the current error in the system, which is the difference between the desired setpoint and the actual system output. Based on this current error, the controller in the system provides a response to minimize it.
• Integral: The function of the integral parameter is to accumulate the past errors over time, thus, eliminating steady-state errors. This covers up for the proportional parameter’s inability to account for long-term deviations from the setpoint.
• Derivative: The derivative term anticipates future errors by considering the rate of change of the error. As a result, it helps dampen the system’s response and improve stability. This is especially useful in systems that are prone to overshooting or oscillations.

With these three parameters working together in the system, the final control output, u(t), is a sum of the proportional, integral, and derivative terms. As the controller output is adjusted based on the current error, past errors, and the predicted future error trend.

Advantages of PID Control

PID control enjoys wide adoption in industry because of the following benefits:

• The implementation and tuning of PID control are straightforward, which makes it suitable for several applications.
• It offers good stability in many linear and near-linear systems.
• This control strategy is robust in dealing with uncertainties and variations in system parameters.

Disadvantages of PID Control

• PID controllers usually struggle when dealing with highly nonlinear systems and processes with significant changes in dynamics.
• Attaining optimal performance often requires careful tuning, which can be time-consuming.

Applications of PID

• Temperature Control: PID controllers are popular in heating, ventilation, and air conditioning systems to maintain desired temperatures.
• Motion Control: Applications such as robotics and automation for precise motion and position control often deploy PID controllers.

Selecting the Best Control Method

Choosing between MPC vs PID depends on the specific characteristics of the system and control requirements. For systems with complex dynamics, varying operating conditions, and stringent performance requirements, MPC is the go-to option. Moreover, the MPC excels in systems with multiple disturbance variables, and multiple constraints. On the other hand, for simpler systems with well-defined dynamics and ease of implementation, PID control suffices.

Process control refers to the monitoring and adjusting process parameters to get a preset or desirable output. As industrial processes become larger and more complex, manual management becomes impractial. Thus, the deployment of automated process control systems delivers the following benefits:

• Energy Efficiency: Energy consumption is often a significant expense for industrial plants, so maximizing energy efficiency boosts profits. The presence of process control systems ensures that machinery can vary energy input according to the load requirements. Hence avoiding waste.
• Increase Automation and Throughput: Process control gives room to introduce automation to various aspects of operation. This increases throughput as well as eliminates human errors and redundancies.
• Quality Assurance: Process control facilitates repeatability, and the quality of products and services is predictable.
• Improved Safety: The level of safety increases due to eliminating human errors, precision in alteration of process variables, emergency shutdown functionality, etc.

Process Control in Manufacturing

Process control is an integral part of modern manufacturing due to the several benefits it offers. To adequately discuss process control in manufacturing, we have to review the four primary elements of a manufacturing process.

Process Control Elements in Manufacturing

Inputs

Process inputs refer to all raw materials, as well as factors such as electricity, water, etc, that help turn the raw materials into finished products. Most manufacturers have trusted suppliers that provide raw materials in line with certain specifications. In addition, the raw materials usually undergo some testing, especially at the batch level, to get approval for use. However, there will always be some form of difference between batches, whether it be variations in color, size, or chemical composition. To prevent this from going overboard, there should be a set tolerance where all variations must fall within.

Uncontrolled Variables

Uncontrolled variables are elements that influence the manufacturing process, but there is no way of altering them. Mostly, these include ambient conditions such as temperature, humidity, etc. Other factors that result in variations and cannot be controlled include shift changeovers and machines. Different shifts have different operators influencing the process differently, so the output will not be the same. Also, when using different machines to process the same product, the output will invariably not be identical. These variations in machine output could result from differences in maintenance, age, etc. 

Controlled Variables

These include variables such as temperature, flow rate, pressure, and other parameters that are influenced by machine settings. This is where the process control system gets involved. First, the system utilizes sensors, which monitor each control variable as well as the state of the end product. Then, a programmable logic system, software, or human operator decides which controlled variable to adjust and takes the necessary action using an actuator. More sophisticated systems automate this decision-making operation, utilizing artificial intelligence with increasing complexity of the operation. These adjustments to the controlled variable are a continuous occurrence for the duration of the manufacturing process to ensure process output is desirable.

Process Outputs

Outputs from a manufacturing process are not only the product that emerges but have other elements.

• Yield: Yield is the area of focus when dealing with process outputs. It refers to the ratio of products that conform to the specifications to the number of raw materials put in. It is a clear representation of the efficiency of the manufacturing process, as well as the process control system.
• Production Rate: This is the total number of goods produced over a given period or the time it takes to produce one item. 
• Waste: Waste includes scrap items and process inputs, such as energy and water, not utilized by the manufacturing process. A well-functional process control system aims to minimize waste.
• Downtime: Refers to periods when manufacture cannot continue due to machine failure or maintenance.

Process Control in Instrumentation

Process control in instrumentation performs the same function as it does in manufacturing. It manipulates a certain input to deliver a preset output. However, when describing process control in instrumentation, the elements that make up the system are not identical.

Process Control Elements in Instrumentation

The Method of Process

The process refers to a series of actions or operations that produce a set result. In instrumentation, this could be maintaining the water level in a tank, keeping a room at a particular temperature, etc. Generally, some disturbances/factors tend to disrupt the outcome/output of the process. So, controlling this outcome requires altering a single variable or, in complex scenarios, multiple variables.

Measurement

Measurement is about converting the process variables into an analog or digital signal and transmitting it to a control system. A range of sensors such as pressure, temperature, force, or flow sensors can be used for measurement, depending on the variable under scrutiny.

Evaluation

The evaluation step involves assessing the value of the measured variable and comparing it to the ideal value or setpoint. In addition, this element determines the corrective action requirements and passes this information on to a controller. This evaluation step could be carried out by an operator or in more sophisticated facilities, software, artificial intelligence, etc.

Control

The control element or controller is a device that directly influences the variable according to the requirements from the evaluation stage. Common types of influence include electrical signals, pneumatic signals, etc. Typically, this is done manually by an operator or automatically by a programmable logic controller or an alternative software.

Examples

Process control has become the mainstay in several industries, with some examples as follows:

• Pharmaceutical Industry: Because of the sensitivity of their operations, process control is utilized with stringent measures to ensure products are of the highest quality. Process control ensures a high level of accuracy and precision in mixtures, human errors are eliminated, and contamination is avoided.

• Electronics Industry: Similar to pharmaceuticals, high levels of purity, repeatability, precision, and speed are critical in manufacturing microchips, semiconductors, etc. Process control ensures that batches of these components are produced with consistency.
• Petrochemical Industry: Consistency and continuous production is key in this industry. Also, the safety of personnel and equipment is vital, and process control systems enable the delivery of all these.

Despite a shift towards greener energy resources, natural gas provides a reliable and cost-effective energy source. As a result, manufacturers continually develop new technologies that improve the efficiency of gas turbines. In this article, we explore the concept of efficiency of gas turbines, how to calculate it, and ways to improve turbine efficiency.

What is Gas Turbine Efficiency?

Generally, the measurement of turbine efficiency relates to thermal efficiency and combustion efficiency. Thermal efficiency refers to the amount of energy in the gas that gets converted into useful work such as electricity. Combustion efficiency measures how well the gas burns in the combustion chamber.

Both efficiency values are typically expressed as a percentage and can vary depending on the specific turbine design and operating conditions. Even a particular turbine’s efficiency could change at different loads or power output. To properly understand why these variations occur, it is necessary to review the basic components that make up a gas turbine.

Basic Components of a Gas Turbine

Typically, all gas turbines have three main sections that enable them to function.

• Compressor: All gas turbines utilize a compressor, which intakes air, pressurizes it, and transmits it to the combustion chamber at high speeds. Most industrial setups utilize a series of compressors to satisfy pressure and flow rate requirements. The basic categories of compressors used are axial and centrifugal compressors, with the former usually delivering higher efficiency values.
• Combustion Chamber: This chamber contains multiple injectors that introduce fuel to mix with the air prior to combustion. Combustion occurs at temperatures greater than 2,000℉, producing high temperature, high-pressure gas stream that enters and expands through the turbine section.
• Turbine: This section houses an intricate array of blades on a shaft that rotate due to the stream of high-temperature, high-pressure gas. The torque from these blades then transmits via its shaft to a generator to produce electricity. Also, by rotating, the turbine blades draws more pressurized air into the combustion chamber.

Factors Affecting Efficiency

Some factors that influence the efficiency of turbines include:

• Compression Ratio: This refers to the ratio of the pressure at the compressor outlet to the pressure at the compressor inlet. The higher the compression ratio, the higher the efficiency, because it means that air is entering the combustion chamber at higher temperature and pressure.
• Pressure Drop and Airflow: The performance of the turbine and compressor is affected by the pressure drop and airflow across their components. If there are any losses or restrictions in pressure or airflow, then there will be a reduction in efficiency.
• Turbine Inlet Temperature: As the turbine inlet temperature gets higher, it makes for more efficient energy extraction from the combustion gas.
• Ambient Conditions: In warmer atmospheric conditions, air density decreases, thus resulting in the compressor doing more work. Also, this leads to a drop in the airflow rate. Because air constitutes over 90% of the air-fuel combustion mixture under normal conditions, this drop in airflow results in a drop in efficiency.
• Mechanical Losses: Reduction in efficiency can also be due to friction between components such as bearings, seals, etc. Usually, these are accounted for and minimized during the design stage.
• Fuel Properties: The type and quality of fuel in use impacts on the gas turbine efficiency. Factors such as calorific value, composition, and combustion characteristics of the fuel are important, so should be in line with specifications.
• Maintenance and Operating Conditions: Deploying a good maintenance strategy and utilizing the turbine in line with specifications are key to optimizing its efficiency.

Gas Turbine Efficiency Formula

Calculating the efficiency of a gas turbine is more complicated than a steam turbine, due to the dynamics that its vapor and vapor conditions present. To simplify it, a gas turbine’s operation is modeled after the Brayton Cycle with the following assumptions:

• The compression of air by the compressor is adiabatic.
• Combustion of the air-fuel mixture is isobaric.
• Also, the expansion of the air-fuel mixture at the turbine is adiabatic.
• The heat rejection stage that comes after the expansion of the gas stream is isobaric.

The efficiency expression for this cycle is as follows:

   

In this expression, the term η represents the thermal efficiency for an ideal Brayton Cycle, r_p is the pressure ratio from the compressor, while γ is the adiabatic index.

Typical Efficiency Values

Various OEMs are committed to improving turbine efficiency through research & development, aerodynamics, advancement in the type of materials, as well as combustion technologies. In 2018, a Guinness World Record of 63.08% efficiency was set, but gas turbines were not always this efficient. The first simple cycle turbine developed in 1939 was operating at 18% thermal efficiency with turbine inlet temperature less than 540℃ and exhaust temperature a little over 260℃. Over the years, this value has risen to 40% with inlet temperatures of 1500℃ and exhausts up to 630℃ on larger machines. Efficiency numbers even got higher in the 1990s as Combined Cycle Gas Turbines (CCGT) gaining traction in the market. This type of turbine emerged alongside better alloys, coatings, compressor ratios, advanced heat transfer technology, etc. Today CCGT are an industry as they are more efficient, albeit at a higher cost.

How to Improve Gas Turbine Efficiency

Improving the efficiency of gas turbines remains a high industry priority as OEMs continually invest in technological developments. This section reviews some common methods that improve turbine performance.

Inlet Air Cooling

One of the major deterrents to high turbine efficiency is a low compression ratio. A significant factor that contributes to the low compression ratio is the high air inlet temperature. Moreover, the higher the air inlet temperature, the less dense the air and the more difficult to compress. However, this can be overcome by cooling the inlet air before each compression stage. Some common methods of cooling include:

• Fogging: This entails reducing the inlet air temperature by injecting atomized water into the air inlet stream after filtration. It is one of the easiest and most economical methods to deploy. However, it requires a steady water supply, can cause erosion within the compressor, and is not effective when humidity is high.
• Evaporative Cooling: Similar to fogging, this method cools the air stream after filtration by passing it through a porous media, which is constantly wetted by one or more water pumps. As there are no water droplets introduced to the air stream, this method does not cause erosion. However, it still requires a constant water supply, a large space at the inlet to install the media, and is ineffective in high humidity.
• Inlet Chilling: This is the most effective way of cooling the inlet air as it deploys cooling tubes within the air filter system. Within these tubes, chilled water is continually pumped to ensure that the inlet air does not go above a certain temperature. Thus, the working principle is similar to a refrigerator.

Heat Recovery System

When it comes to the discharge air from the compressor, having a high temperature is beneficial to the system. This is why turbine manufacturers utilize heat recovery system generators (HRSG) to boost efficiency. The HRSG is positioned at the exhaust of the turbines where it captures the waste heat, and channels it to preheat air that is moving from the compressor to the combustion chamber.

Thermal Energy Storage

This entails using a system that stores the thermal energy generated by the turbine for later use. As a result, the turbine can generate energy during off-peak periods, which is then stored, and used during on-peak periods.

Despite a shift towards greener energy resources, natural gas still holds a significant market share as an energy source. As a result, manufacturers are continually developing new technologies that improve the efficiency of gas turbines. In this article, we explore the concept of efficiency of gas turbines, how to calculate it, and ways to improve turbine efficiency.