M1A1 Textbook Activity: Operation of Feedback Control Systems
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Solve the following problems:
- Sketch a block diagram of an air-conditioning system in a car where the driver sets the desired interior temperature on a dashboard panel. Identify the function of each element.
- The student-teacher learning process is inherently a feedback process intended to reduce the system error to minimum. Construct a feedback model, similar to Figure 1.3 (Below) in the textbook, of the learning process and identify each block of the system.Discussion Question:
- Using a specific control system as an example (position control, temperature control, pressure control, flow control, etc.), describe how you would apply the four design steps to meet the design criteria.
Background and topic information:
In this module, we use the example of a DC motor speed control system to introduce the concepts of a control system, control system design criteria, and the design steps.
A control system is made up of interconnected components forming a system configuration that provides a desired system output (response). There are two types of control systems: open-loop control and closed-loop control. An open-loop control system has the following block diagram:
Figure 1. Block diagram of an open-loop control system (Dorf & Bishop, 2011).
Notice that there is no feedback loop in the diagram, and as a result, the actual output cannot be compared to the desired output. On the other hand, a typical closed-loop control system has the following block diagram:
Figure 2. Block diagram of a closed-loop control system (Dorf & Bishop, 2011).
The major difference here is that the actual output is fed back and compared to the desired output, and any error can be dealt with by the controller. Let’s consider our DC motor speed control example. The input is the desired speed and the output is the actual speed. The actuator is a power amplifier, the process is the DC motor, the sensor is a tachometer, and the controller consists of op-amps and RLC components.
Suppose the input voltage is 10 V, representing an output speed of 1000 rpm, and the sensor ratio is 0.01. If the actual output is 1000 rpm, the feedback voltage is 1000*0.01 = 10 V, and the error is 0, so no action is needed from the controller. If, for some reason (like a sudden load increase), the actual rpm drops to 900, and the feedback voltage is now 9 V, then the error signal will be 10 – 9 = 1 V and is sent to the controller. The controller will send a signal to the actuator to increase its output to the process (motor) so as to increase the speed. This example shows that closed-loop (feedback) control in general works better than open-loop control because automatic speed control is achieved.
There are a few general criteria to follow when designing a control system:
- Stability (absolute and relative): The system must be stable with a certain stability margin. This will be discussed more in Modules 5 and 7.
- Steady-state error: This is the difference between the desired output and actual output at steady state. This value should be as small as possible. This will be covered more in Modules 3 and 4.
- Transient response: This includes rise time, maximum overshoot, peak time, and settling time. These parameters must meet the requirements. We will cover this more in Module 4.
- Sensitivity to parameter changes and disturbances: These values should be as small as possible and must meet the requirements. This will be discussed further in Module 3.
There are a few steps to follow in the design process in order to meet these design criteria:
- Choose the sensors and actuators. Note that these are system dependent. For example, you will need a transducer, instead of a tachometer, as a sensor for a temperature control system.
- Develop the process, sensor, and actuator mathematical models. Note that this is not an easy task in general and may require people with different areas of expertise. For example, a mechanical engineer is needed to develop a flow control model, while an electrical engineer is needed to develop a DC motor speed control model. The models can be in the forms of differential equations or transfer functions. This is covered further in Chapter 2 of the textbook.
- Based on the models from step 2, design the controller to meet the control criteria. The controller is the only component in the block diagram whose mathematical model can be changed (or designed) at will. Therefore, the design of the controller is critical in meeting the criteria. We’ll see more on this in Chapter 10 of the textbook.
- Evaluate the design analytically, by simulation, and by actual system tests. Since actual system tests can be costly, they should be the last step of the design process.