Control Systems: Linear, Non-Linear, Analog, Digital

• A control system manages, commands, directs, or regulates the behavior of other devices or systems to achieve desired results
• Modern control engineering deals with Multiple Input - Multiple Output (MIMO) systems

Types of Control Systems

• Linear control systems adhere to the principle of superposition
• Homogeneity means if the input is multiplied by a constant (A), the output is multiplied by the same constant (A)
• Additivity means:
  • Input a1 gives output b1
  • Input a2 gives output b2
  • Input (a1 + a2) gives output (b1 + b2)
• Non-linear control systems do not follow the principle of homogeneity; most systems are non-linear in practice
• An example of a non-linear system is the no-load curve of a DC machine, showing the relationship between air gap flux and field winding mmf
• Analog (or continuous) systems use a continuous signal as input
• Digital or discrete systems use a discrete signal (e.g., pulse) as input
• Digital control systems can convert continuous input signals into a discrete form using a switch
• Advantages of digital control systems:
  • They handle non-linear control systems better than analog systems
  • They have lower power requirements compared to analog systems
  • They are more accurate and can perform complex computations easily
  • They are more reliable, smaller, and more compact than analog systems
  • They work with logical operations, increasing accuracy
  • They generally have lower losses compared to analog systems
• Single Input Single Output (SISO) systems have a single input for a single output; examples include temperature and position controllers
• Multiple Input Multiple Output (MIMO) systems have multiple inputs for multiple outputs; examples include PLC controllers
• ON/OFF control systems have control elements that are either fully closed or fully open, without intermediate positions
• In ON/OFF control, when a process variable crosses a preset level, the output valve fully opens to give 100% output
• When the process variable changes and crosses a predetermined level in the reverse direction, the output valve immediately closes to 0%
• An example of ON/OFF control is a fan for a transformer cooling system, which turns on when the temperature rises and off when it decreases

Requirements of a Good Control System

• Accuracy is the measurement tolerance of the instrument and can be improved with feedback elements and an error detector
• Sensitivity refers to how much the parameters of a control system change due to surrounding conditions or internal disturbances; a good system should be insensitive to such parameters but sensitive to input signals
• Noise is an undesired input signal that a good control system should be able to reduce
• Stability means that for a ranged input signal, the output must be ranged, and if the input is zero, the output must also be zero
• Bandwidth is determined by the operating frequency range; a good control system should have a large bandwidth for suitable frequency response
• Speed is the time taken by a control system to achieve its stable output; a good system has high speed and a very small transient period
• Oscillation refers to small or constant oscillations of output that aid in the system being stable

Types of Control Systems

• Manual control systems involve manual intervention to achieve the desired output (e.g., manually switching a heating element on/off to control room temperature)
• Automatic control systems use automatic mechanisms, such as timer switches or sensors with feedback, to control the output (e.g., a timer switching a heating element or a sensor controlling a heating element based on temperature)
• Open-loop control systems have control actions that are independent of the system's output (e.g., a bread toaster or a timer-based clothes dryer)
• Open-loop systems are simple, economical, and easy to maintain
• Open-loop systems are inaccurate, unreliable, and cannot automatically correct changes in output
• Closed-loop control systems have output that affects the input quantity, allowing the input quantity to adjust itself based on the output (e.g., an automatic electric iron or a water level controller)
• Closed-loop systems are more accurate, have a large bandwidth, and can facilitate automation
• Closed-loop systems are costlier, complicated to design, require more maintenance, and can lead to oscillatory response
• A feedback loop compares the feedback signal with a reference input to generate an error signal, which is then applied to the controller to correct the output
• A positive feedback system adds the reference input signal and the feedback signal
• A negative feedback system subtracts the feedback signal from the reference input signal to get the error signal
• Block diagrams represent control systems in diagrammatic form, simplifying complex systems by representing each element with a block
• Take-off points apply an input to more than one block without dividing the input signal
• Cascade blocks connect systems or control blocks in a cascaded manner, with the transfer function of the entire system being the product of the transfer functions of individual blocks
• Summing points represent the summation of input signals, where the resultant input signal is the sum of all applied input signals

Open and Closed Loop Theory

• Open-loop systems (non-feedback systems) have output with no influence on the input signal's control action
• Open-loop systems are expected to faithfully follow their input command or set point, but cannot self-correct any errors (e.g., a clothes dryer)
• Open-loop systems are poorly equipped to handle disturbances or changes in conditions
• Feed forward control anticipates potential open-loop disturbances and compensates for them manually before the controlled variable deviates too far from the original set point
• Open-loop control is suitable for systems where changes in load occur slowly and infrequent changes to control action are needed
• In open-loop motor control, the motor's rotation speed depends on the voltage supplied by the potentiometer, and the system is susceptible to variations or disturbances
• Closed-loop control systems use feedback to base control on the difference between actual and desired values
• The feedback signal measures the output, and the control system uses feedback signals to control and adjust itself
• Closed-loop systems generate an error signal, which is the difference between the output and the reference input
• Closed-loop systems can reduce a system's sensitivity to external disturbances by compensating through the controller
• Characteristics of closed-loop control:
  • Reducing errors by automatically adjusting the system's input
  • Improving stability of an unstable system
  • Increasing or reducing the system's sensitivity
  • Enhancing robustness against external disturbances
  • Producing reliable and repeatable performance
• Closed-loop systems must be more complex by having one or more feedback paths
• A summing point (comparison element) determines the error between the actual and desired output
• A plus (+) symbol in the summing point indicates a "summer" used for positive feedback, while a minus (-) symbol indicates a "comparator" used for negative feedback
• In closed-loop motor control, external disturbances create a difference between the actual motor speed and the set point, producing an error signal that the controller responds to by adjusting the motor's speed