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Contents 1 Activation signals in Altair Activate 11 1.1 Introduction.......................................... 11 1.1.1 Simple queue..................................... 13 1.1.2 Traffic simulation.................................... 16 1.1.3 Re-initialization of continuous-time state....................... 19 1.1.4 Communication delay................................. 20 1.2 Types of activation signals.................................. 26 1.2.1 Programmed events.................................. 26 1.2.2 Zero-crossing events................................. 26 1.2.3 Continuous-time activation signal........................... 26 1.2.4 Initial-time activation signal.............................. 27 1.2.5 Periodic activation signals............................... 27 1.3 Activation inheritance..................................... 28 1.4 Synchronous vs. asynchronous activations......................... 29 1.4.1 Conditional blocks................................... 30 1.4.2 Sample and Resample Clock blocks......................... 30 2 Altair Activate Matrix Expression Block 35 2.1 Introduction.......................................... 35 2.2 Examples........................................... 36 2.2.1 Basic operators and functions............................ 36 2.2.2 Matrix construction, extraction and assignment................... 37 2.2.3 Use of OML functions................................. 38 2.3 Parser............................................. 39 2.4 Limitations........................................... 40 2.4.1 Fixed-sized matrix principle.............................. 40 2.4.2 All the branches of conditional expressions evaluated................ 40 2.4.3 No support for logical type.............................. 40 2.5 Data types........................................... 41 2.5.1 Supported data type.................................. 41 2.5.2 Unsupported data types................................ 41 2.5.3 Data coding...................................... 41 2.6 Supported operators..................................... 41 2.6.1 Arithmetic operators.................................. 41 2.6.2 Matrix construction and structuring.......................... 42 2.6.3 Relational and logical operators........................... 43 2.6.4 Conditional operators................................. 44 3 Extended Definitions Altair Activate 2019.4 Proprietary Information of Altair Engineering Inc. 2.7 Supported functions...................................... 44 2.7.1 Supported functions.................................. 45 2.7.2 Using OML functions................................. 46 3 C and OML Custom Blocks in Altair Activate 47 3.1 Activate block simulation function.............................. 48 3.2 Custom block parameter GUI................................. 48 3.3 Examples........................................... 50 3.3.1 Median block...................................... 50 3.3.2 Variable discrete delay................................ 54 3.3.3 Fluid flow........................................ 57 3.3.4 Simplified explicit automaton block.......................... 60 3.4 Non-inlined simulation functions............................... 65 4 Simulation restarts: implementing iterations 69 4.1 Nonlinear solver block..................................... 70 4.1.1 A reverse-communication solver........................... 70 4.1.2 Activate block implementation............................ 73 4.1.3 Examples....................................... 74 4.1.4 Solving nonlinear system without a specific block.................. 78 4.2 Repeating activations..................................... 81 4.2.1 Problem setup..................................... 82 4.2.2 System equations................................... 82 4.2.3 Implementation in Activate .............................. 83 5 Example: Implementation of an Extended Kalman Filter in Activate 87 5.1 Activate model........................................ 88 5.2 EKF model........................................... 89 5.3 Covariance prediction..................................... 90 5.4 State update.......................................... 91 5.5 Simulation........................................... 92 6 Optimization 97 6.1 Use of Optimization block in Activate ............................ 97 6.2 Example............................................ 98 6.3 GetFromeBase and AddToBase OML functions..................... 104 6.4 Script based optimization................................... 109 6.4.1 Direct scripting of optimization code in OML ..................... 109 6.4.2 Example........................................ 110 6.5 Activate Graphical optimization tool............................. 114 6.5.1 Example........................................ 115 6.6 Max-min/Min-max optimization problems.......................... 117 7 Linearization 123 7.1 Linearization function..................................... 123 7.1.1 Example: inverted pendulum............................. 124 7.1.2 Example: Cart on a beam............................... 129 7.2 Computation of the equilibrium point............................. 134 7.2.1 Use of infinite steady-state gain controller...................... 136 Altair Activate 2019.4 Extended Definitions 4 Proprietary Information of Altair Engineering Inc. 7.2.2 Equilibrium point for the inverted pendulum example................ 138 7.2.3 3D model of a spacecraft for take off and landing control.............. 143 7.3 Modeling in Activate ..................................... 145 7.4 State feedback control.................................... 146 8 Altair Activate Libraries 153 8.1 Library structure........................................ 153 8.2 Block structure......................................... 155 8.3 Palette............................................. 155 8.4 Library creation........................................ 156 8.4.1 Library Manager.................................... 156 8.4.2 OML functions..................................... 158 9 Altair Activate blocks 161 9.1 Block simulation function................................... 161 9.1.1 Simulation function implementation.......................... 163 9.1.2 Examples....................................... 169 9.1.3 Macros for accessing the block structure....................... 182 9.1.4 Macros for accessing the simulator structure.................... 187 9.2 Block builder.........................................