Intelligent Crane Control. Part I: Planning and Controlling Motions

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1 Intelligent Crane Control. Part I: Planning and Controlling Motions Leonid Freidovich Department of Applied Physics and Electronics Umeå University, Sweden (http : //www.tfe.umu.se/forskning/control_systems/). DBT-course: Lecture 1 (September 14, 2007)

2 Outline Introduction Motion Planing Motion Control Plan for the other Lectures 1 Introduction 2 Motion Planing 3 Motion Control 4 Plan for the other Lectures Leonid Freidovich Intelligent Crane Control. Part I: Planning and Controlling Motions

3 Outline Introduction Motion Planing Motion Control Plan for the other Lectures 1 Introduction 2 Motion Planing 3 Motion Control 4 Plan for the other Lectures Leonid Freidovich Intelligent Crane Control. Part I: Planning and Controlling Motions

4 Consultants: Pedro La Hera (Hardware and sensors; dspace; Matlab/Simulink; Theory: motion planning, motion control), Uwe Mettin (Hardware and sensors; dspace; Matlab/Simulink; Theory: motion planning, motion control), Simon Westerberg (Visualization; Video Cameras; 3D Cameras, Ian Manchester (Video Cameras; Matlab/Simulink; Theory: motion planning, motion control), Leonid Freidovich (Matlab/Simulink; Theory: motion planning, motion control), Anton Shiriaev Short questions via are welcome, for more detailed discussions appointments are needed.

5 Structure of the system human-machine interface (HMI) local tasks global tasks turn 1st link motion planner desired motion actual motion error control system control action valve unit 2nd link telescope rotator gripper actual motion measurement devices...

6 Scenario? Split into small groups to solve more specific problems. For example: Planning a set of good motions (inverse/forward kinematics, defining a good motion, modeling,... ). Designing a Controller (tuning parameters of a standard PID, friction compensation, modeling,... ). Dealing with Sensors (available sensors, sensor fusion, signal processing, hardware,... ), Designing human-machine interface, and high-level decision making (visualization, signal processing, data transferring, software,... ).... Learn the available interface to the crane: Matlab / Simulink / dspace Interface (Control Desk)

7 Outline Introduction Motion Planing Motion Control Plan for the other Lectures 1 Introduction 2 Motion Planing 3 Motion Control 4 Plan for the other Lectures Leonid Freidovich Intelligent Crane Control. Part I: Planning and Controlling Motions

8 Crane geometry: picture

9 Crane geometry: scheme

10 Crane geometry: sets of coordinates Coordinates measured by encoders (controlled): d the position defining extension of the telescope, θ 2 the angle defined by the cylinder controlling the 1st link, θ 3 the angle defined by the cylinder controlling the 2nd link. Workspace coordinates: x horizontal position of the grip, z vertical position of the grip.

11 Crane geometry: kinematics Forward kinematics problem: Find the transformation from (d, θ 2, θ 3 ) to (x, z). There is only one solution. Possible usage: visualization, sensor fusion and fault detection (cameras and encoders), reachability analysis,... Inverse kinematics problem: Find a transformation from (x, z) to (d, θ 2, θ 3 ). There are infinitely many solutions. Possible usage: defining tasks for motion control, motion optimization and selection,...

12 Crane geometry: detailed scheme r 0 = , r 1 = , r 2 = , r 3 = , r 4 = , r 5 = , r 6 = , r 7 = ; d 1 = , d 2 = , d 3 = , d 4 = , d 5 = , d 6 =

13 Motion planning problem Motion planning problem: Define the desired trajectories for the controlled coordinates (d (t), θ 2 (t), θ 3 (t)) either on-line (interactively) or off-line (pre-planning). You might start as follows: Define a motion in the workspace coordinates: artificial: a simple curve like a circle, natural: record a useful motion done by a driver Derive an algorithm to connect two given points in the workspace with a nice trajectory. After that, use inverse kinematics to obtain the desired motion in controlled coordinates.

14 Example of a planed motion: a circle 2 autonomous motion circle 1 z position [m] x position [m]

15 Example of a planed motion: a circle (cont d) MOVIE: circle_0.25radps_optimized.avi

16 Outline Introduction Motion Planing Motion Control Plan for the other Lectures 1 Introduction 2 Motion Planing 3 Motion Control 4 Plan for the other Lectures Leonid Freidovich Intelligent Crane Control. Part I: Planning and Controlling Motions

17 How to realize the motion? After the motion planning problem is solved, one has a desired (reference) trajectory for each controlled angle. The cylinder must be activated to force following this trajectory via assignment of current (control input). How do we influence the system? Current is generated = Valve opens = Oil flows in = Piston moves = Force is applied = Torque is created However, until certain level of current is reached, nothing is happening! Why? What is wrong?

18 Compensating Coulomb friction Typical force due to Coulomb friction is a function of relative velocity between moving surfaces and look like so: A certain level of current must be generated to overcome this friction force. Experiments must be designed (planned) to identify the required values for each of three cylinders: To initiate moving up when the measured coordinate is smaller than the desired one. To initiate moving down when the measured coordinate is bigger than the desired one.

19 Compensating friction What does the level of current, needed to overcome friction, depend on? Is it enough to compute it around one value of each coordinate? Do we need to know only the desired direction of motion or an estimate for velocity is required to compensate the Coulomb friction as well? If yes, it can be computed using the Euler difference formula or a differentiating block of Simulink: θ(t) θ(t) θ(t ε) ε, θ(t) s 1 + ε s θ(t), where ε > 0 is small. Remark: it is better to saturate the estimates at reasonable levels and to filter out noises. It might be better to compensate viscous friction (proportional to the velocity) as well. In this case, it should be identified experimentally.

20 Compensating gravitational forces When the valve is open and friction is compensated, gravitational torques influence the motion of links. It might be better or not to counteract the gravity directly using forces produced by hydraulic cylinders. It possible to compute the gravitational forces from the geometry and knowledge of mass-length distributions? Is it reasonable to assume that the current is proportional to the force, produced by the cylinder? Is the compensation based on such calculations reliable? The gravitational force at every cylinder is defined by the values of all three measured coordinates. A series of experiments must be designed either: to compute the current, needed to compensate gravity, as a function of the measured coordinates; to compute the coefficient of proportionality between the force and the current, and to validate the efficiency of the analytically computed gravitational force.

21 ε > 0 is small (typically, 0.1 T d < ε < 0.2 T d ). The controller must be realized in Simulink. The integral part (1/s) should be restricted and reseted (see help for the integrator block). Total control signal To control the crane, for each cylinder we generate the current input as follows: i = i coulomb + i }{{ viscous + i } gravity + i }{{}} main {{} friction compensation necessary? to be tuned There main part of the controller might often be taken in the following form ( ) i main = C... (s) θ(t) θ (t) where C... (s) is one of the following ( PI is recommended) ( C P (s) = K p, C PID (s) = K p T r s + T d s εs+1 ( ) ( ) C PI (s) = K p T r, C s PD (s) = K p 1 + T d s εs+1 ),

22 Tuning parameters of the main controller The following empiric procedures to tune coefficients of the last part of the controller might work when the desired velocities and desired accelerations are sufficiently small. The range of applicability must be verified experimentally. One of the procedures is Ziegler-Nichols Oscillation Method. Set the plant under C P (s) with a small gain. Increase the gain until oscillations are observed. They should be detected at the controller output. Record the controller critical gain K c and the period of oscillation T at the controller output. Adjust the controller parameters according to the table: P K p T r T d 0.5K c PI 0.45K c T/1.2 PID 0.6K c T/2 T/8

23 Outline Introduction Motion Planing Motion Control Plan for the other Lectures 1 Introduction 2 Motion Planing 3 Motion Control 4 Plan for the other Lectures Leonid Freidovich Intelligent Crane Control. Part I: Planning and Controlling Motions

24 The other two Lectures Questions / suggestions / requests? What are your background / knowledge / interests? Are you familiar with: Matlab, Simulink, Mechanics, Physics, Control Theory, Differential Equations, Mathematical Analysis, Mechanical Design / Engineering, Sensors, Signal Processing, Networking, Programming, Visualization Techniques, System Engineering? We plan the following two lectures. September 17: Camera sensors, Visualizations,..., (suggestions / requests?) by Ian Manchester and Simon Westerberg September 27: Matlab / Simulink, dspace, available hardware and software,..., (suggestions / requests?) by Pedro La Hera and Uwe Mettin

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