Introduction to Systems and Control

Introduction to Systems and Control

The lecture introduces systems, basic ways to classify them, and the role of feedback in control engineering.

What Is a System?

A system is a collection of physical, biological, or abstract components that interact to perform an intended purpose. In control terms, a system receives an input or excitation and produces an output, also called its response. A system may consist of several connected subsystems.

Examples include:

• Motor: An electrical input produces a mechanical output, such as torque.
• Air conditioner: An electrical input affects room temperature.
• Human body: A drug is an input; its distribution and effects are outputs.
• Car: Control inputs produce motion, such as acceleration and displacement.

The lecture’s notation includes:

• (t): time
• (u(t)): input
• (y(t)): output
• (w(t)): time-varying disturbance
• (\Delta): a delay
• (f): a function

Main Classifications of Systems

Linear and Nonlinear

A linear system satisfies superposition and homogeneity: responses to inputs can be combined and scaled consistently.

A resistor illustrates linear behavior because its current is proportional to the applied voltage. An inductor also exhibits linear behavior under the usual linear model. A diode is nonlinear because its current–voltage relationship does not satisfy superposition or homogeneity.

Static and Dynamic

A static system is memoryless: its output depends only on the input at that instant. A resistor is an example.

A dynamic system has memory: its output depends on present and past inputs. An inductor stores energy, so after its voltage source is removed, its current decays rather than instantly becoming zero. The decay depends on circuit parameters such as resistance and inductance.

Time-Invariant and Time-Varying

A time-invariant system gives the same response to the same input regardless of when the input is applied. The key issue is whether the system’s parameters change over time—not whether its output changes with time.

A time-varying system has parameters that change over time. For example, an aircraft’s mass decreases as fuel is burned, so its response may differ at takeoff and landing.

Causal and Noncausal

A causal system depends only on present and past inputs; it does not anticipate future inputs. Most physical systems, such as motors and generators, are causal.

A noncausal system depends on future inputs. Forecasting and planning are examples of anticipatory processes: they use expectations about future conditions when making decisions in the present.

Control Systems and Feedback

A control system directs a plant or process toward a desired objective. The plant is the system being controlled, and a controller selects inputs based on a desired reference and, in feedback control, measured output.

Real systems are affected by disturbances—unwanted influences that change the output. Feedback helps address these effects:

1. Measure the plant’s output.
2. Compare it with the desired reference.
3. Use the difference between them to determine the controller’s action.
4. Apply a control input to move the output toward the desired value.
5. Continue monitoring and adjusting, including when disturbances occur.

For example, in a temperature-control system, the room is the plant, the desired temperature is the reference, and the air conditioner is the controller. If the room temperature changes because people enter or leave, feedback detects the difference and prompts corrective action. Feedback can therefore help maintain the desired performance despite disturbances.

Control-System Examples

Air Conditioner

• Plant: The room
• Reference: Desired room temperature
• Output: Measured room temperature
• Control action: Operating the air conditioner, such as switching it on or off
• Disturbances: Changes in ambient conditions or people entering or leaving
• Feedback: The measured temperature is compared with the desired temperature to guide the control action

Driving a Car

• Reference: Destination
• Plant: The car and its motion
• Control action: Steering and other driving inputs
• Output: Actual position
• Disturbances: Traffic, road conditions, and slopes
• Feedback: The driver checks the car’s position relative to the destination and adjusts accordingly

The lecture concludes by previewing a subsequent discussion of mathematical models, model types, and the steps involved in modeling systems.

Speakers and Sources

• Lecturer: Professor Ramkrishna Pasumarthy, Department of Electrical Engineering, IIT Madras, as identified in the video metadata.
• No other speakers or external sources are featured in the subtitles.