Advanced Control PROJECT 2 Motor Drive with Flexible Shaft Introduction This control problem can occur in manufacturing processes. Basically, one has a motor driving a load via a shaft which can twist. The same equations cover the case where a motor drives a load via a belt drive which can stretch — this is perhaps more realistic. The load may be anything – it is easier perhaps to imagine a simple conveyor. The aim is to control the (generally variable) speed of the load. One has a speed sensor to measure the speed and one can place this at the load or at the motor. If you can only measure the speed of the motor, you can imagine the difficulty of trying to control the load speed if you have a stretching belt between them! Fig. 1 The symbols and values are the same as before except that: Jm Moment of Inertia of Motor = 0.2kgm2 JL Moment of Inertia of Load = 0.2kgm2 Bm Friction coefficient of Motor = 0.1Nrn/rads-I BL Friction coefficient of Load = 0.582Nm/rads-1 K Twisting coefficient of shaft = 91Nrn/rad i.e. torque to twist to shaft = 91(0n,-8L) θm instantaneous motor angle θL instantaneous load angle ωm instantaneous motor speed ωL instantaneous load speed θ = (θm- θL) actual twist angle Exercise 1 The aim is to control the speed of the LOAD – ωL If we assume that the current loop is very fast we can assume that i = i*, i.e. the transfer function between current and its demand is unity. Then we can model the above system with = [ ] and = [ ] . With this defmition and = , show that: Enter the system into Simulink and check the eigenvalues. Augment the system with integral of ωL as this is the controlled variable. Decide on a set of closed loop eige
nvalues such that the ωL step response has a 2% settling between 0.5 and 1s. Get the feedback matrix and implement the gains. Verify the design by looking at the closed-loop eigenvalues and the transient response (of any variables you think interesting) to step load speed demands. What is i* during the transients Take appropriate action. Exercise 2 The design of Exercise 1 assumes that ωm, ωL and θ are both measurable. It is wasteful to measure two speeds (or two positions to get θ). Let us measure ωL alone. Design a full-order or reduced-order observer to observe the other states. Implement the observer together with the feedback control law to produce a combined controller-observer closed loop system. Verify the design through simulation. Note that to test the observer dynamic response, you can plot and together. You can set different initial conditions on these variables by implementing the observer with integrators/gains etc. How does the combined controller-observer behave if the system is subject to load disturbances Does it work OK when the current demand is limited Simulate if you are not sure! Report guidelines Structure your report around the 2 exercises. It should be illustrated with Simulink diagrams and Matlab plots of time simulations. For each exercise, explain the design methodology used, discuss eigenvalue selections and try to answer as many of the points and problems raised as you can. Try and be inventive and show that you understand what is going on. Report must not exceed 15 pages. Please use Microsoft Word or an equivalent software to write it, including equations. Do not put hand-written parts. Also schematic and diagram have to be drawn with a software of your choice.