ME 132 Summary –Intro and motivation of Feedback Control Following a reference (lectures, sec 1, pp1-3, sec 5) Rejecting a disturbance (lectures, sec 1, pp1-3, sec 5) Increasing the speed-of-response (lectures, sec 1, pp1-3, sec 5) Doing all of the above robustly to process variations (lectures, sec 1, pp1-3, sec 5) Effect of sensor noise on process (lectures, sec 1, pp1-3, sec 5) Block diagrams (sec 2, pg 9) and Simulink (sec 3 and lecture) P and PI controller for simplified cruise-control (sec 5, sec 8) & simplified stick-balancing (sec 2, page 10-12)

ME 132 Summary –Systems governed by ODEs (1 st order and higher), PPT file Input/output (sec 6, sec 7) Definition of stability (sec 7, pg 59) Theorems of stability, location of roots, 1 st, 2 nd, 3 rd, 4 th order tests (sec 7, pg 62-64) Characterizing homogeneous solutions (sec 7.3) Step responses and sinusoidal steady-state responses (sec 7.5, sec 11, complex number identities) Effect of right-hand-side of ODE on the response to inputs (sec 9 and 10)

ME 132 Summary –Transfer function representation of systems governed by ODEs (sec12) Algebraic manipulations (derived by considering LDOs as fundamental) Characterizing stability, steady-state gain, frequency- response, etc., in terms of the transfer function (lectures, Sec 13) class (HW in Sec 12) Basic properties of and (lectures, HW in sec 11 and 12)

ME 132 Summary –Robustness Margins of Feedback Systems Gain margin Time delay margin Percentage-variation margin (“small-gain” theorem), (lectures) Phase Margin (lectures) Deriving L effective for general problem (handout, HW 6 in Section 14) –Controlling the position of an inertia using PI control with velocity feedback (PID control) (sec 23) –Saturation and Anti-Windup Logic in controllers with Integral action (sec 15, HW #7 in sec 18)

ME 132 Summary –Systems governed by state-space models General form of state-equations (sec 3, sec 17, first 2 pages of sec 19) Rules for picking state variables in a few classes of systems (sec 16 and 17) Transfer function and Stability of a linear system of the form –Linearizing a nonlinear system about an equilibrium point (sec 18) Equilibrium points Deriving the linearization Regulating a system near an equilibrium point with a feedback controller (hw #7 and #8 in sec 18)

ME 132 Summary –Intro and motivation of Feedback Control Following a reference (lectures, sec 1, pp1-3, sec 5) Rejecting a disturbance (lectures, sec 1, pp1-3, sec 5) Increasing the speed-of-response (lectures, sec 1, pp1-3, sec 5) Doing all of the above robustly to process variations (lectures, sec 1, pp1-3, sec 5) Effect of sensor noise on process (lectures, sec 1, pp1-3, sec 5) Block diagrams(sec 2, pg 9) and Simulink (sec 3 and lecture) P and PI controller for simplified cruise-control (sec 5, sec 8) & simplified stick-balancing (sec 2, page 10-12) –Systems governed by ODEs (1 st order and higher), PPT file Input/output (sec 6, sec 7) Definition of stability (sec 7, pg 59) Theorems of stability, location of roots, 1 st, 2 nd, 3 rd, 4 th order tests (sec 7, pg 62-64) Characterizing homogeneous solutions (sec 7.3) Step responses and sinusoidal steady-state responses (sec 7.5, sec 11, complex number identities) Effect of right-hand-side of ODE on the response to inputs (sec 9 and 10) –Transfer function representation of systems governed by ODEs (sec12) Algebraic manipulations (derived by considering LDOs as fundamental) Characterizing stability, steady-state gain, frequency-response, etc., in terms of the transfer function (lectures, Sec 13) class (HW in Sec 12) Basic properties of and (lectures, HW in section 12) –Robustness Margins of Feedback Systems Gain margin Time delay margin Percentage-variation margin (“small-gain” theorem), (lectures) Phase Margin (lectures) Deriving L effective for general problem (handout, HW 6 in Section 14) –Controlling the position of an inertia using PI control with velocity feedback (PID control) (sec 23) –Saturation and Anti-Windup Logic in controllers with Integral action (sec 15, HW #7 in sec 18) –Systems governed by state-space models General form of state-equations (sec 3, sec 17, first 2 pages of sec 19) Rules for picking state variables in a few classes of systems (sec 16 and 17) Transfer function and Stability of a linear system of the form –Linearizing a nonlinear system about an equilibrium point (sec 18) Equilibrium points Deriving the linearization Regulating a system near an equilibrium point with a feedback controller (hw #7 and #8 in sec 18)