Discrete Controller Design Thanh Vo-Duy Department of Industrial Automation thanh.voduy@hust.edu.vn... Prior to LectureDiscrete-time System with analog reference input Discrete-time Syst
Trang 1Discrete Controller
Design
Thanh Vo-Duy Department of Industrial Automation
thanh.voduy@hust.edu.vn
Trang 3Prior to Lecture
Discrete-time System with analog reference input
Discrete-time System with digital reference input
Trang 4Digital Controllers
• Consider the Discrete-time System as
• 𝑅 𝑧 - Reference Input
• 𝐸 𝑧 - Error signal
• 𝑈 𝑧 - Output of the Controller
• 𝑌 𝑧 - Output of the System
• 𝐻𝐺 𝑧 - Digitized plant with Zero-order hold
Trang 6Digital Controllers
Dead-Beat Controller
• Dead-Beat Controller: brings system to steady state
in the smallest number of time steps
Trang 81 − 𝑧−𝑘
Trang 111 − 𝑧−1 1 − 𝑒−
𝑇
𝑞 𝑧−1
Trang 121 − 𝑧 −1 1 − 𝑒−
𝑇
𝑞 𝑧 −1
1 − 𝑧−11
→ 𝑇 𝑧 = 𝑧
−𝑘−1 1 − 𝑒−
𝑇 𝑞
Trang 13Design a Dahlin digital controller for the system
(let’s choose 𝑞 = 10note: 𝑒−0.1 = 0.904)
Trang 16Digital Controllers
Dahlin Controller
• Solution (cont.)
Trang 17• Use Time Shifting property of z-Transform
Trang 21Digital Controllers
PID Controller
• PID – Proportional – Integral – Derivative controller
• Proportional - 𝐾𝑝 (or 𝑃): error is multiplied by 𝐾𝑝
• High 𝐾𝑝 causes instability, Low gain causes drifting away
• Integral - 𝐾𝑖 (or 𝐼): integral of error and multiplied
Trang 22Digital Controllers
PID Controller
Trang 23𝑇𝑖 and 𝐾𝑑 = 𝐾𝑝𝑇𝑑
Trang 24𝑒 𝑘 + 𝑢0
Trang 25𝑇 𝑒 𝑘 − 2𝑒 𝑘 − 1 − 𝑒 𝑘 − 2
Trang 27Digital Controllers
PID Controller
• Problems with PID controller
• Saturation and Integral Wind-up
• Causes by physical constraints
• Results in long period overshoot
• Solution: fix the limits of integral, use velocity form of PID….
• Derivative kick
• Causes by sharply change in setpoint
• Results in damage of system
Trang 28Digital Controllers
PID Controller
• PID Tuning – Ziegler-Nichols tuning algorithm
A system can be approximated as:
𝐺 𝑠 = 𝐾𝑒
−𝑠𝑇𝐷
1 + 𝑠𝑇1
where
𝑇𝐷: System time delay
𝑇1: Time constant of system
Trang 30Digital Controllers
PID Controller
• Close-loop Tuning
1 Leave the controller only Proportional control
2 Carry out a step input of system
3 Increase/decrease controller gain until stable oscillation This gain is called 𝐾𝑢 (ultimate gain)
4 Read the period 𝑃𝑢
5 Calculate controller parameters:
PI: 𝐾𝑝 = 0.45𝐾𝑢 and 𝑇𝑖 = 𝑃𝑢/1.2
PID: 𝐾𝑝 = 0.6𝐾𝑢, 𝑇𝑖 = 𝑃𝑢/2, 𝑇𝑑 = 𝑃𝑢/8
Trang 322 Explain the difference between Positional and
Velocity form of PID controller
3 The open-loop unit step response of a system is shown as figure below Obtain the transfer function
of the system and use Ziegler-Nicholes algorithm to design:
- A Proportional Controller
- A PI Controller
- A PID Controller
Trang 335 The continuous-time PI Controller has transfer