Presentation on theme: "Lecture 15: State Feedback Control: Part I"— Presentation transcript:
1Lecture 15: State Feedback Control: Part I Pole Placement for SISO SystemsIllustrative Examples
2Feedback Control Objective In most applications the objective of a control system is to regulate or track the system output by adjusting its input subject to physical limitations. There are two distinct ways by which this objective can be achieved: open-loop and closed-loop.
3Open-Loop vs. Closed-Loop Control Open-Loop ControlOutputDesiredOutputCommandInputControllerSystemClosed-Loop ControlOutputDesiredOutputControllerSystem-Sensor
4Closed-Loop Control Advantages Disadvantages automatically adjusts inputless sensitive to system variation and disturbancescan stabilize unstable systemsDisadvantagesComplexityInstability
6State-Feedback Control Objectives Regulation: Force state x to equilibrium state (usually 0) with a desirable dynamic response.Tracking: Force the output of the system y to tracks a given desired output yd with a desirable dynamic response.
20Flexible System Example Consider the linear mass-spring system shown below:x1x2Parameters:m1=m2=1Kg. K=50 N/mkum1m2Analyze PD controller based on a)x1, b)x2Design state feedback controller, place poles at
27Matlab Solution %Desired Close-Loop Poles pc=[-20;-20;-5*sqrt(2)*(1+j);-5*sqrt(2)*(1-j)];pd=exp(T*pc);% State Feedback ControllerK=acker(G,H,pd);%Closed-Loop Systemclsys=ss(G-H*K,H,C,0,T);gridstep(clsys,1)