CAI3034 – Autonomous Mobile Robotics Prepared by WS Ooi

Introduction to Control System

The terms, control and system are closely interrelated. Control is the process of forcing a system
output variable to conform to some desired value, called reference value.

In order to gain a better understanding of the task of control, a simple example is considered. Driving
a car is an excellent example of control system. The driver has to follow the given direction of a road.
He/she observes the actual path of the car and then forces the car, operating the steering wheel, to track
the desired path as closely as possible. The driver performs the following steps in detail:

 The driver uses his eyes as sensors for obtaining measurements, both of the car’s actual path and
the road course.
 Then he/she compares both directions and generates an error signal, which is used to decide in
which direction to move the steering wheel.
 The driver actuates the steering wheel according to his decision, making the car, the controlled
object, move to the desired direction.

Figure 1: Manual control of a car’s direction of travel

An animal or any hindrance on the road acts as a disturbance and should be avoided if possible.
After reaching such a disturbance, the driver must return the car to the desired direction. These three
steps of measuring, decision, and manipulation are characterizing the driver’s control action (Figure 1).

There are 2 basics form of control system: open-loop system and closed-loop system.

What is an open-loop control system?

Figure 2: A general open-loop control system

Those systems in which the output has no effect on the control action are called open-loop
control systems (Figure 2). In other words, in an open-loop control system the output is neither
measured nor fed back for comparison with the input. The advantages of an open-loop system are
simpler, cheaper and easy in maintenance.

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CAI3034 – Autonomous Mobile Robotics Prepared by WS Ooi

One practical example is a simple fan, where:

Plant/Process/System - refers to the system (simple fan) we want to control. It generally refers to a
physical process which we can either model or measure.

Reference input/Desired Output - Switch on the fan (that is, press the switch and 230 V is applied). So,
the reference input is the 230 V signal.

Controller - The electronic voltage controller (that is, turn the knob to the desired position). The effect is
to reduce/change the voltage to the appropriate value. We may have approximately 230 V (= full speed)
and 115 V (half-speed), and so on.

Once the speed is set there is nothing else that needs to be done. But suppose you have three fans.
Even if you give their knobs the same amount of turn, the speeds are likely to be slightly different. This
may happen due to inaccuracy in the settings, inconsistency in ball bearings performance, imperfect
setting of the fan blades causing different amount of drag on the blades, or maybe due to non-standard
performance of the electronic components.

So, essentially an open-loop system is one where there is no way to correct the error between the
desired output and the actual output.

What is a closed-loop control system?

Feedback control systems are often referred to as closed-loop control systems. In practice, the
terms feedback control and closed-loop control are used interchangeably.

Consider the same electronic fan control switch. Assume that you are looking at the fan blades to
make sure that the speed is right. If it isn’t, then you turn the knob continuously till the desired speed is
achieved. The block diagram in Figure 3 is not an exact representation of this, but it conveys the idea in
a broad sense. The measurement device or transducer is to convert the output signal to an equivalent
electrical system (e.g. from kinetic energy to electrical energy). This facilitates the comparison of the
output signal to the input.

Figure 3: A general closed-loop control system

Figure 4 shows an example of closed-loop control in mobile robotics. A sensor measurement is

compared to the desired measurement (called the set point), resulting in an error calculation. Some math
is performed on this error value (control calculations) to determine the output that goes to the actuator.
The actuator such as the motor has some effect on the system. The sensor is again checked to find out
the result of the actuators influence, and the whole loop is repeated.

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CAI3034 – Autonomous Mobile Robotics Prepared by WS Ooi

Figure 4: A closed-loop control in mobile robotics

Closed-loop systems have different characteristics when compared to open-loop systems. The
following summarizes the advantages and disadvantages of closed-loop system:

Advantages:
 Highly accurate as any error arising is corrected due to presence of feedback signal.
 They are less sensitive to disturbances.
 They are less sensitive to system characteristics/parameter variations.

Disadvantages:
 They have a tendency to oscillate.
 They are complicated to design.
 Required more maintenance.
 Stability is the major problem and more care is needed to design a stable closed loop system.

It is possible to use relatively inaccurate and inexpensive components to obtain the accurate control
of a given plant, whereas doing so is impossible in the open-loop case. From the stability point of view,
the open-loop control system is easier to build because system stability is not a major problem. On the
other hand, stability is a major problem in the closed-loop control system, which may tend to overcorrect
errors that can cause oscillations of constant or changing amplitude.

As control engineer we must be able to:

 model/measure the dynamic behaviour of the plant/system.
 choose an appropriate controller that allows the system output to meet a list of user designed criteria.

Explaining Open and Closed loop Systems in Robotics - Control System Engineering:
https://www.youtube.com/watch?v=f32SDx3C6sA

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CAI3034 – Autonomous Mobile Robotics Prepared by WS Ooi

Block Diagrams
 A robotic control system may consist of a number of components to show the functions performed by each
component. In robotic control engineering, we usually use a diagram called block diagram to represent the
components in a complex system.

 The transfer functions of the components are usually entered in the corresponding blocks which are connected by
arrows to indicate the direction of the signal flow.

 There are 2 basics form of control system: open-loop system and closed-loop system.

Open-loop system

Transfer
X(s) function, G(s) Y(s)

Y (s)
G( s) 
X (s)

Closed-loop system
E(s)
R(s) G(s) C(s)
+
−
B(s)
H(s)
C (s)
Determine the
R( s )

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CAI3034 – Autonomous Mobile Robotics Prepared by WS Ooi

Exercise: Determine the overall transfer function, C/R for each system.

(a) +
R G1 G2 C
–

H1 H2

(b)
G2

+
+ E +
R G1 C
+

H1

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CAI3034 – Autonomous Mobile Robotics Prepared by WS Ooi

(c)
G2

+
+ E +
R G1 C
+

H1

(d)
G2

–
R + + G3 C
P G1
–

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CAI3034 – Autonomous Mobile Robotics Prepared by WS Ooi

(e)
G4

+
+ E +
R G1 G2 G3 C
−

H1

(f)

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CAI3034 – Autonomous Mobile Robotics Prepared by WS Ooi

Transfer function
In engineering, a transfer function of an electronic or control system component is a mathematical function which
shows the relationship between the input and the output of a system.

Open-loop system

Transfer
X(s) function, G(s) Y(s)

Y (s)
G( s) 
X (s)

Example:
We want to design a cruise controller for a car that uses a simple proportional controller. The first stage is to model the
dynamics of the car.

Here we have an input force signal r(t) (supplied by the engine) and a frictional force. The output we are interested is the
velocity, v(t). The system parameters are the mass m and the friction coefficient b.

To get an ODE for the system we write down Newton's second law

We will assume 0 initial conditions for the output. By taking Laplace transform of the equation, the transfer function of
the system can be obtained as follows,

So lets say the car has a mass of 1000 Kg, the friction constant is 50 Ns/m and the output force of the engine is 500 N.
Then, what is the steady state velocity and what is step response of the system to this engine force?

First of all we can see that

Since we are interested in the step-response to a force of 500 N and assuming 0 initial conditions, the output Laplace
Transform is

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CAI3034 – Autonomous Mobile Robotics Prepared by WS Ooi

There are many ways to get the steady state velocity

We can see from the plot v(t) that it takes a long time for the car to reach the optimum speed. The rise time has various
definitions but we define it as the time taken for the output to rise from 10% to 90% for the final output value. In this
case, the rise time is approximately 44 seconds. It also takes approximately 100 seconds to reach the optimal speed.

More examples: