1.7
Tuning of PID Controllers
Ziegler Nicholas Rules
Tuning is the process of selecting the controller parameters to meet given performance specifications.
Ziegler and Nicholas suggested rules for tuning PID controllers based on experimental step response

2.5
State Space Representation
State space method is based on the description of system equations in terms of n first-order difference
equations, which may be combined into a first-order vector matrix difference equation. The use of the
vector-matrix nota

2.4
Stability Analysis
2.4.1
Stability in the z-plane
Just as the transient analysis of continuous systems may be undertaken in the s-plane , stability and transient analysis
on discrete systems may be conducted in the z-plane It is possible to map from t

1.4
Derivative Control Action
The control signal u(t)is given by
d
u(t) = kd e(t)
dt
where kd is the derivative gain
when the slope of e(t) is large at the current time , the magnitude of u(t)will increase i.e the derivative
control law provides a large c

Integral Control
For integral control, the control signal u(t) is given by
u(t) = kie(t)dt
(1)
t
0
where ki is the integral gain constant
converting equation 1 to frequency domain
ki
U (s) = E (s)
s
Integral Control of type 0, first order system
Consider

Proportional Control of a type 1, second order system
Consider the system shown below
Figure 5: Proportional Control of type 1, second order system
The open loop transfer function is given by
kp
G(s) =
ks2 + cs
The closed loop transfer function is given b

Pulse Transfer Function
Pulse transfer function relates the Z transform of the output at the sampling instants to that of the sampled input
X0 (z) G(z) = U (z)
The ratio of the output X0 (z) and input U (z) is called the pulse transfer function of the dis

2.2.2
Inverse Z Transform
The inverse Z transform of X (z) yields the corresponding time sequence x(t)
The notation for the inverse Z transform is z1
1. Direct division method
We obtain the inverse Z-transform by expanding X (z) into an infinite power ser

Digital Control
Lecture Notes by A. M. Muhia
1
D
IGITAL
CONTROL
SYSTEMS
2.1
Sampled Data Systems
A sampled data system operates on discrete-time rather than continuous-time signals. A digital computer
is used as the controller in such a system. A D/A conv

2.8
Digital Controller Design
2.8.1
Controllability and Observability
Controllability is concerned with the problem of whether it is possible to steer a system from a given initial
state to an arbitrary state. A system is said to be controllable if it is

PID Controllers
Lecture Notes by A. M. Muhia
1
Process Control
1.1
Introduction
In a control system, the variable to be controlled is called the Process Variable or PV. In industrial process
control, the PV is measured by an instrument in the field and ac