Low Level Control
Control System Components

The main components of a control system are

The plant, or the process that is being controlled

The controller, which controls the plant

The measurement system, which is needed for
feedback control
Control



Aim of control: making the plant respond to
inputs in a desired manner.
In a regulator-type control system the objective is
to maintain the output at a desired (constant)
value.
In a servomechanism-type control system the
objective is for the output to follow a desired
trajectory.
Types of Feedback Control
Systems

Linear versus Nonlinear Control

Time-Invariant vs Time-Varying

Continuous vs Discrete
Open Loop Control


If the plant is stable and is completely and
accurately known, and if the inputs to the plant
from the controller can be generated and applied
accurately, accurate control will be possible even
without feedback control.
In this case the measurement system is not
needed (or at least not needed for feedback) and
thus we have an open-loop control system
Control System Specifications
Attribute
Desired
value
Purpose
Specifications
Stability
High
The response does not grow without limit Percentage overshoot, settling time,
and decays to the desired value
pole (eigenvalue) locations, time
constants, phase and gain margins,
damping ratios
Speed of
response
Fast
The plant responds quickly to inputs
Rise time, peak time, delay time,
natural frequencies, resonant
frequencies, bandwidth
Steady-state Low
error
The offset from the desired response is
negligible
Error tolerance for a step input
Robustness
High
Accurate response under uncertain
Input noise tolerance, measurement
conditions (signal noise, model error, etc.) error tolerance, model error tolerance
and under parameter variation
Dynamic
interaction
Low
One input affects only one output
Cross-sensitivity, cross-output
transfer functions
Performance Parameters
Conventional Control Methods

Proportional Integral Derivative Control

Nonlinear Feedback Control

Adaptive Control

Sliding Mode Control

Linear Quadratic Control

H-Infinity Control
Proportional (P) Control


Using both the direction and the magnitude of the
error allows the control system to respond in
proportion to the error, and thus compensate for it
more effectively.
A proportional controller has an output o
proportional to its input e:
o = Kp * e

where Kp is a proportionality constant.
Gains



Incorrect gain values will cause the system to
undershoot or overshoot, i.e., not reach or go
beyond the desired state.
If a system cannot correct its gain incrementally,
and it overshoots, it will do so repeatedly,
resulting in oscillations.
We use the term damping for systematically
decreasing oscillations. A system is properly
damped if it does not oscillate out of control
Derivative (D) Control




Setting gains is difficult, and simply increasing the
proportional gain does not remove oscillatory problems
in a control system.
While at low values this may work, as the gain increases,
the system's oscillations increase.
The basic problem has to do with the distance from the
set point/desired state: when the system is close to the
desired state, it needs to be controlled differently than
when it is far from it.
A derivative controller has an output o proportional to
the derivative of its input e:
o = Kd * de/dt

where Kd is a proportionality constant.
Integral (I) Control




This type of a system observes repeatable fixed
steady state errors.
It integrates them over time, and when they reach
a threshold, moves the system in a direction to
compensate for the errors.
An integral controller has an output o
proportional to the integral of its input e:
o = Ki *
e(t)dt
∫
where Ki is a proportionality constant.
Proportional-Integral-Derivative
Servo Control
Characteristics of PID Control
Controller Description
Parameter
Functions
Undesirable side effects
Kp
Proportional
gain
Speeds up the response.
System can become less stable
Reduces offset. Reduces cross- (overshoot, oscillations, etc.)
coupling
Ki
Integral time
constant
Reduces offset. Reduces noise
Can slow down the system. Has a
destabilizing effect. Introduces a
phase lag
Kd
Derivative
time constant
Stabilizes the response
(damping). Speeds up the
system. Provides a phase lead
(anticipatory effect)
Enhances high frequency noise.
Difficult to physically implement.
Nonlinear Feedback Control



Simple linear servo control is inadequate for
transient and high speed operation of complex
plants.
Nonlinearities and dynamic coupling must be
compensated faster than the control bandwidth.
One method is feedback linearization.
Model-Based Nonlinear Feedback
Control System
Adaptive Control

A feedback control system in which the values of
some or all of the control parameters are modified
(adapted) during system operation on the basis of
some performance measure when the output
requirements are not satisfied.
Model Reference Adaptive Control




The same reference input applied
to the plant is applied to the
model.
The difference between the
response of the physical system
and the output from the model is
the error.
The ideal objective is to make this
error zero at all times.
The reference model is an
idealized model which generates
a desired response at least in an
asymptotic manner.
Sliding Mode Control
Linear Quadratic Gaussian Control

An optimal control technique intended for linear
systems with random input disturbances and output
(measurement) noise
H-Infinity Control
Evaluation of Conventional Control
Methods

Advantages



When the values of the controller parameters are known,
the control signals are generated exactly.
When the underlying assumptions are satisfied, many of
these methods provide good stability, robustness to model
uncertainties and disturbances, and speed of response.
Disadvantages:

The control algorithms are ''hard'' or “inflexible'' and
cannot generally handle "soft'' intelligent control which
may involve reasoning and inference making using
incomplete, vague, not-crisp, and qualitative information,
and learning and self-organization through past
experience and knowledge.