Control? Plot 1.Input distance to car suspension system from car going up curb (a step) over time. 2.Output distance of driver in the same time. Displacement Time

Why Use Control? Achieve the aims of your system efficiently and effectively –track reference –speed of response –avoid overshoots –avoid steady-state errors Autonomous operation Avoid disturbances Understand natural systems

What is a System? Environment System SystemSystem InputsOutputs Boundary Systems are built of signals (variables), constants and differential operators Systems are built of sub-systems!

Are Systems Perfect? 1. Open eyes: Extend your arms out at shoulder height Touch the tips of your little fingers in front of your nose! 2. Close eyes: Extend your arms out at shoulder height Touch the tips of your little fingers in front of your nose! 3. Strangeness: Make a circle with your right foot going in the clockwise position. While you are doing that, draw a six with your right hand.

Open v Closed loop Tutorial questions: 1. Explain the advantages and disadvantages of open loop control. 2. Explain the advantages and disadvantages of closed loop control (closed loop control is sometimes called feedback control)

Open v Closed loop 1.Open loop is simple to implement but does not know the actual value of the control variable so is vulnerable to changing the conditions. 2. Closed loop accounts for changes in conditions, but at the expense of increased complexity and can become unstable if care is not taken in its design.

Feedback The output signal is fed back to the input signal. InputsSystem Outputs

As an introduction, consider dynamic systems: these change with time As an example consider water system with two tanks Water will flow from first tank to second When will it stop following? Dynamic Systems I F L Stops when levels equal. Why stop then? Why flow at all? Plot time response of system….?

Level change – not instantaneous Initially: Large height difference  Large flow  L up a lot Then: Height difference less  Less flow  L increases, but by less Later: Height difference ‘lesser’  Less flow  L up, but by less, etc Graphically we can thus argue the variation of level L and flow F is: Dynamic Flow F t T T L t I

We have dynamic equation for L in terms of I: Put into ‘s’ domain to get output over input function: Add a unit step input for I: Integrate to determine variation of L As t gets larger, exponential term disappears, L tends to Input. Time Response

We have dynamic equation: Put into ‘s’ domain and rearrange: Add a unit step input for I: Integrate to determine variation of L As t gets larger, exponential term disappears, L tends to Input. Time Response

Laplace operator ‘s’ Reminder from ENGR201 Know how components behave in an instant of time Consider differential response Combine and simplify into standard forms Integration by lookup table determines long- term response t domain s domain

Systems An engineering system is a set of components connected together to accomplish a useful task When building up a model system: Components should be easily identifiable Components should have a simple and clearly defined interaction with other components Components numbers should be minimised

Systems In order to analyse a system: We identify an input signal [a variable] Using block diagram components [Basic block Summing junction Take-off point] We combine internal signals [modified variables] To produce the output signal [another variable]. The Input-Output relationship may then be determined

Car suspension model: Mechanical system Explain what happens when a car goes over a bump?

Car suspension model: Explain what happens when a car goes over a bump? x f input Simplify to single- input-single-output system Form individual component models Determine their relationships (use physical laws!) Combine (and simplify if possible) This gives us an instantaneous differential equation, but want a time response!

Spring Damper Mass Source Nise 2004 Car suspension model:

Tutorial question Determine the block diagram for each component? Source Nise 2004

Textbooks Martin Hargreaves, Engineering Systems - Modelling & Control, Longman Kevin Warwick, An Introduction To Control Systems, World Scientific N. Nise, Control Systems Engineering 6th Ed., J Wiley & Sons ISBN Ogato + Zak + Dorf and Bishop... Blackboard

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