Prof. Wahied Gharieb Ali Abdelaal Faculty of Engineering Computer and Systems Engineering Department Master and Diploma Students CSE 502: Control Systems (1) Topic# 9 Digital Control Design (PID)

2 Outline  Introduction  Indirect Control Design  Digital PID control design  Design Examples  Direct Control Design  Direct Design using Root Locus  Deadbeat Control Design

3 Introduction

4 Indirect control Design

5 Indirect Control Design

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7 Approximations to Integration Indirect Control Design

8 Euler’s Approximation Indirect Control Design

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10 Indirect Control Design

11 Indirect Control Design

12 Indirect Control Design

13 Indirect Control Design

14 Indirect Control Design

15 Digital PID Control Design  A proportional controller (P) reduces error responses to disturbances, but still allows a steady-state error.  When the controller includes a term proportional to the integral of the error (I), then the steady state error to a constant input is eliminated, although typically at the cost of deterioration in the dynamic response.  A derivative control typically makes the system better damped and more stable. Controller Effects

16 Digital PID Control Design Rise timeMaximum overshoot Settling time Steady- state error PDecreaseIncreaseSmall change Decrease I Increase Eliminate DSmall change Decrease Small change  Note that these correlations may not be exactly accurate, because P, I and D gains are dependent of each other. Closed-loop Response

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18 Digital PID Control Design PID controller with integral anti-windup

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26 Discrete time equivalent of analog controller using Euler’s forward method (sampling period =T) Example Design Examples

27 Discrete-time controllers when T = 0.4 s, which is relatively large as compared to the continuous-time controller’s fastest mode e−2t, the discrete-time controller approximation deviates significantly from the continuous-time controller. As the sampling interval is decreased, the step responses of the analog and discrete-time controllers are the same. Design Examples

28 If we use the trapezoidal method, the transfer function of the digital controller becomes Design Examples

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44 Direct Control Design

45 Direct Control Design

46 Direct Design using Root Locus

47 Direct Design using Root Locus

48 Direct Design using Root Locus

49 Direct Design using Root Locus

50 Direct Design using Root Locus

51 Direct Design using Root Locus

52 Direct Design using Root Locus

53 Direct Design using Root Locus

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55 Direct Design using Root Locus

56 Direct Design using Root Locus N= Number of samples per oscillation

57 Direct Design using Root Locus

58 Deadbeat Control Design One difference between a continuous-data control system and a discrete-data control system is that the latter is capable of exhibiting a deadbeat response. A deadbeat response is one that reaches the desired reference trajectory in a minimum amount of time without error. In contrast, a continuous-data system reaches the final steady- state trajectory or value theoretically only when time reaches infinity. The switching operation of sampling allows the discrete-data systems to have a finite transient period.. The output response reaches the desired steady state with zero error in a minimum number of sampling periods without inter sampling oscillations. Design with Deadbeat Response

59 Deadbeat Control Design For the sampled system with ZOH

60 Example: Consider the forward-path transfer function of the uncompensated system is given by Deadbeat Control Design

61 Deadbeat Control Design Closed loop poles at the origin, so it is so fast Steady state after two samples without error

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64 Deadbeat Control Design The output is delayed one sample than the input Explain

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