Bachelor of Applied Technology
ETEC: 6419 – Control Engineering
Laboratory 3 weighting 6%,
Complete the following problems in Scilab, submit a word document containing
solutions with screen prints or cut and paste Scilab results (where Scilab has been
used).
1) A control system is shown in the following figure. The process Gp is a first
order with unity steady state gain and a 10 s time constant. The controller Gc is
a gain with value 10.
Using Scilab, model and simulate the system and determine the closed loop time
constant of the system (determined from a step input).
Compare the closed loop time constant determined from a Scilab simulation with one
computed analytically using block reduction tools and comment on the result.
2) The open loop transfer function of a system is given with ζ= 0.4, ωn= 0.5, k=1.
Using Scilab, determine the approximate values of peak overshoot, time to
peak, and settling time. Plot the approximate unit step response of the system.
3) A photocell with a 35 ms time constant is used to measure light flashes. How
long after a sudden dark to light flash before the cell output is 80 % of the final
value?
Using Scilab, simulate this system and plot the step response of this system.
Identify on the step response plot where 80% of the final value is?
4) A RC circuit has the following transfer function:
For a step input R(t) = 2V for t 0:
a) What is the steady-state response of the circuit?
b) What is the time taken for the output of the RC circuit to reach 95% of its steadystate response?
c) Check your result with a Scilab simulation of the system.
5) Consider the first-order system,
Obtain the unit-step response curves for T = 0.1, 0.5, 1.0, 5.0 and 10.0
respectively, with Scilab.
6) Consider the first-order system,
Obtain the unit-step response curves for k = 0.1, 0.5, 1.0, 5.0, and 10.0
respectively, with Scilab.
7) A second-order system is described by the differential equation:
a) Write down the transfer function Y(s)/U(s) of the system, where U(s) and Y(s) are
the Laplace transforms of u(t) and y(t), respectively.
b) Obtain the damping ratio and the natural frequency n of the system.
c) Calculate the rise time and percent overshoot of the system.
d) Evaluate y(t) for a unit-step input u(t).
e) Check your answers of the above with Scilab.
8) Consider the second-order system
Obtain the unit-impulse response curves for = 0.1, 0.3, 0.5, 0.7, 1.0, and 4.0
respectively, with Scilab.
9) Consider the second-order system
Assuming that n = 2, k = 2, obtain the unit-impulse response curves for = 0.1, 0.3,
0.5, 0.7, 1.0, and 4.0 respectively, with Scilab.