Integrated Feedback Scheduling and Control Codesign for Motion Coordination of Networked Induction Motor Systems

Algorithm 1

Scheduling and control codesign.

(1) for a sampling interval [𝑘ℎ,(𝑘+1)ℎ] do

(2)  input: 𝑒_𝑖;

(3)  initialize the sampling periods ℎ_𝑖;          ⊳Optimal Bandwidth Allocation

(4)  initialize the upper delay bound 𝜏_𝑖;

(5)  for each control loop do

(6)   calculate the controller gain 𝐾^𝑃_𝑖 using Theorem 3;

(7)   calculate the sampling period ℎ_𝑖;

(8)   calculate the cost function 𝐽_𝑖(ℎ_𝑖);

(9)   end for

(10)  return  𝐾^𝑃_𝑖, ℎ_𝑖, and 𝐽_𝑖(ℎ_𝑖);

(11)  calculate the optimal ℎ_𝑖 to minimize 𝐽(ℎ_𝑖);

(12)  calculate the worst case blocking time 𝑐_𝑖;

(13)  verify the stability condition (22b);

(14)  verify the schedulability condition (22c);

(15)  for each control loop do            ⊳Networked Speed Control Law Update

(16)   calculate 𝜔(𝑘ℎ+𝜏_{𝑠𝑐,𝑘});

(17)   update 𝐾^𝑃_𝑖 and 𝐾^𝐼_𝑖;

(18)   calculate the speed tracking control law 𝑢^𝑇_𝑖;

(19)   end for

(20)  return  𝑢^𝑇_𝑖;

(21)  initialize the sensor priorities 𝑝_𝑖;           ⊳Online Priority Modification

(22)  for each control loop do

(23)   calculate the performance index 𝐽^′_𝑖;

(24)  end for

(25)  return  𝑝_𝑖;

(26)  sort the control loops with decreasing 𝐽^′_𝑖 values;

(27)  update 𝑝_𝑖 for sensors;

(28)  for each control loop do             ⊳Motion Coordination Operation

(29)   calculate the speed coupled error 𝑒^∗_𝑖;

(30)   end for

(31)  return  𝑒^∗_𝑖;

(32)  calculate the speed synchronization control law 𝑢^𝑆_𝑖;

(33) end for

(34) return  ℎ_𝑖, 𝑝_𝑖, 𝑢^𝑇_𝑖, and 𝑢^𝑆_𝑖;