EMaSM Analysis of system response
Introduction: Analyse engineering system responses and corrective actions required to allow an engineering system to operate within its normal range.
Control principles Automatic control of systems relies on the accuracy of measurement of the variables which indicate the condition of the system. It uses this information to help keep the process or system operating within the specified limits.
List some examples of control systems.
Feedback Accurate information about the condition of its output is crucial for control of a system. In a closed loop system the data is fed back and compared with the set point or target of the system. Error is the term used for the result of the comparison and it is this error which is used as the input to the control element. The diagram, next slide, shows the general arrangement for control systems.
Error (e = SP- FB) Set Point SP Comparator Feed Back FB Control Element Feedback Element System Output General Block Diagramof a Control System
Control solution This is the term used to describe, mathematically, the actions of the control element. It is an equation which shows how the error is processed so as to bring the system s output to match the set point. Transfer function is a more general term used to show the actions of the parts of the system.
The corrective action of the element will depend on the system, for example on a ship or aircraft it may be a change in direction to take into account the effects of tidal or wind conditions. If the temperature is too low in a building then the heating system will be turned on until the temperature is correct.
From your study of associated Units, you will recall that although many different engineering systems exist, there are sufficient common features in many types to allow their analysis to be easily adapted to match shared characteristics and so modify standard control solutions.
System Response
The graph, on the previous slide, is typical of the response of many systems to a step change in the input or set point, or some disturbance such as a fall in the available power. The general mathematics involved for systems is identifiable for both mechanical and electrical systems as both commonly have energy storage elements in them, for example springs and capacitors.
Analysis of such systems can be performed by physical means or by utilising suitable software to perform simulations. It will not prove possible to investigate systems which are too complex, but we can compare the actions of simple mechanical and electrical systems. Carried out carefully, we should be able to identify the similarities in response of the two types.
R voltage source L When the switch closes, current will flow from the source and we can write a differential equation which describes the system action as follows: C RLC System
The spring mass damper system shown above has the following differential equation: where M is the mass (kg) D is the damper resistance (Ns/m) S is the spring constant (m/n) x is the displacement (m) F is the applied force (N)
Inspection of the two differential equations shows that their format is identical. Which element in the mechanical system performs a similar function to the capacitor in the RLC circuit? Which element in the electrical system performs a similar function to the damper in the spring mass damper system?
System Damping Think of the shock absorbers or McPherson struts on a car. These are the damping systems used on a car to make sure that either -the passenger comfort is good, if the dampers are set to smooth out the bounce of the car Or -if it s a boy racer perhaps he has hardened up the springs in order that the car does not dig into a bend when cornering fast.
System Damping Graph B shows an over damped system. It takes too long to reach a steady state. Graph D shows a critically damped control system. It reaches a steady state in the shortest possible time without overshooting. Graph A shows an under damped system. This one overshoots before eventually settling down. Often the critically damped case is the best choice. Graph A, under damped, can be better if the goal is to get the control system to within, say, 20% of the target as fast as possible and some overshoot and oscillation can be tolerated. Graph C is the worst. In this case it overshoots and never settles. This is called hunting.
PV = change in Process Variable, max usually the set point Rise time = time taken to reach the set point Settling time = the time taken to get within 5% of set point