Introduction to digital control system, Lecture notes of Advanced Control Systems

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Data Acquisition and Control Systems

Engr. Dr. Sufyan Ali Memon

Assistant Professor Mehran University of Engineering & Technology Jamshoro, Pakistan

Lecture-12-

Introduction to digital control systems

1

What is control? What is control? Control is whenever some quantity, such as temperature, altitude, or speed must be made to behave in some desirable way over time. In other words, control makes some object (called plant or process) behave in some desirable manner. What is a control system? A control system consists of subsystems and a process, assembled for the purpose of controlling the output of the process. For example, an electric furnace produces heat as a result of electricity.

What is a control system? Objective : To make the system OUTPUT and the desired REFERENCE as close as possible, i.e., to make the ERROR as small as possible. Key Issues : 1) How to describe the system to be controlled? (Modeling)

2. How to design the controller? (Control)

What is an output in a control system? TYPICALLY, the output variable is

• Temperature in thermal systems
• Position and velocity in mechanical systems
• Voltage, current, charge, or frequency in electrical systems

What is automatic control?

• Operator has been replaced by a machine, usually an electronic circuit
• Control is now automatic : it is accomplished without human intervention

Why do you need control (or a control system)? We build control systems for five primary reasons:

1. Power amplification
2. Precision
3. Remote control
4. Convenience of input form
5. Compensation for disturbances With control systems, elevators carry us quickly to our destination, automatically stopped at the right floor. We alone could not provide the power required for the load and the speed; motors provide the power ( power amplification) and controllers regulate the position and speed (precision). Control systems are useful in remote or dangerous locations. A remote-controlled robot arm can be used to pick up material in a radioactive environment ( remote control). In a temperature control systems (like a thermostat), the input is a position on the thermostat while the output is heat. A convenient position input yields a desired thermal output ( convenience of input form). An antenna that points in a commanded direction can be subjected to wind (disturbance) forcing the antenna rotates from its commanded direction. A feedback controller must detect the disturbance and correct the antenna position ( compensation for disturbances).

Examples of open-loop control systems Example 1: Toaster The output of a toaster is the color of the toast. The device is designed with the assumption that the toast will be darker the longer it is subjected to heat. The toaster does not measure the color of the toast; it does not correct for the fact that the toast is rye or white, nor does it correct for the fact that toast comes in different thicknesses. Example 2: Examination system Assume that you calculate the amount of time you need to study for examination that covers three chapters to get an A. If we add a fourth chapter - a disturbance - you are an open-loop system if you do not detect the disturbance and add study time to that previously calculated. The result of this oversight would be a lower grade than you expected.

Closed-loop control ( feedback control ) Measurements of the

output variable are fed back to the process through the controller.

The disadvantage of open-loop systems that are sensitive to disturbances and thus not able to correct for these disturbances may be now overcome in closed-loop systems. However, closed-loop systems are more complex and expensive than open-loop systems.

A typical control system

Terminology

• Plant or Process: System to be controlled
• Inputs: Excitations/stimulus and disturbances (known, unknown) to

the system

• Disturbances: Unwanted inputs to the system
• Outputs: Responses of the system
• Sensors: They measure system variables (excitations, responses,

etc.)

• Actuators: They drive various parts of the system.
• Controller: Device that generates control signal
• Control Law: Relation or scheme according to which the control

signal is generated

• Control System: Plant + controller, (can include sensors,

actuators, signal conditioning, etc.)

• Feedback Control: Control signal is determined according to plant

response

• Feedforward Control: No feedback of plant response to controller

Control system analysis and design objectives Elevator example Summary: A control system is dynamic; It responds to an input by undergoing a transient response before reaching a steady-state response that generally resembles to the input. Transient response is important. a slow response makes elevator passengers impatient, whereas an excessively rapid response makes them uncomfortable. If the elevator oscillates about the arrival floor for more than a second, a disconcerting feeling can result. Transient response is also important for structural reason: Too fast a transient response could cause a permanent physical damage. Thus, we analyze the elevator for its transient response and (if needed) we adjust parameters or design components to yield desired transient response. The steady-state response of the elevator is its location reached near the fourth floor. An elevator must be level enough with the floor for the passengers to exit. Thus, the elevator’s steady-state error should be analyzed and (if needed) design corrective action to reduce the steady- state error should be taken.

Control system analysis and design objectives Elevator example STATEMENT: Discussion of transient response and steady-state error is moot if the system does not have stability. Actually, the total response of a system is Total response = Natural response + Forced response For a control system to be stable, the natural response must eventually approach zero, thus leaving only the forced response, which is an approximation of the input. BE CAREFUL: If the natural response grows without bound the system is no longer controlled or unstable. Instability could lead to self-destruction of the physical device if limit stops are not part of the design. In our example, the elevator would crash through the floor or exit through the ceiling. Thus, a control system must be analyzed and designed to be stable. NOTICE THAT: The transient response is the sum of natural and forced responses when the natural response is large, while the steady-state response is the sum of the natural and forced responses when the natural response is small.

Brief view of control techniques:

There are tons of research published in the literature on how to design control laws for various control purposes. These can be roughly classified into the following techniques:

• Classical control: Proportional-integral-derivative (PID) control, developed in 1940s and used for control of industrial processes. Examples: chemical plants, commercial aero planes.
• Optimal control: Linear quadratic Gaussian control (LQG), Kalman filter, H2 control, developed in 1960s to optimize a certain ‘cost index’ and boomed by NASA Apollo Project.
• Adaptive control: Uses online identification of the process parameters, thereby obtaining strong robustness properties. Adaptive control was applied for the first time in the aerospace industry in the 1950s.
• Robust control: H 2 control, developed in 1980s & 90s to achieve robust performance and/or stability in the presence of small modeling errors. Example: military systems.
• Nonlinear control: Currently hot research topics, developed to handle nonlinear systems with high performances. Examples: military systems such as aircraft, missiles.
• Intelligent control: Predictive control, neural networks, fuzzy logic, machine learning, evolutionary computation and genetic algorithms, researched heavily in 1990s, developed to handle systems with unknown models. Examples: economic systems, social systems, human systems.

Other considerations in control system analysis and design

• Factors affecting hardware selection motor sizing to fulfill the power requirements  (^) choice of sensors for accuracy
• Design economic impact budget allocation competitive pricing