Added the PID Controller
This commit is contained in:
Connor Johnstone
@@ -50,7 +50,7 @@ Each feature below links to a detailed implementation plan in the `features/` di
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### Controllers
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- [ ] **[PID Controller](features/04-pid-controller.md)**
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- [x] **[PID Controller](features/04-pid-controller.md)** ✅ COMPLETED
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- Proportional-Integral-Derivative step size controller
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- Better stability than PI controller for difficult problems
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- **Dependencies**: None
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@@ -329,14 +329,15 @@ Each algorithm implementation should include:
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## Progress Tracking
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Total Features: 38
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- Tier 1: 8 features (2/8 complete) ✅
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- Tier 1: 8 features (3/8 complete) ✅
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- Tier 2: 12 features (0/12 complete)
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- Tier 3: 18 features (0/18 complete)
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**Overall Progress: 5.3% (2/38 features complete)**
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**Overall Progress: 7.9% (3/38 features complete)**
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### Completed Features
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1. ✅ BS3 (Bogacki-Shampine 3/2) - Tier 1 (2025-10-23)
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2. ✅ Vern7 (Verner 7th order) - Tier 1 (2025-10-24)
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3. ✅ PID Controller - Tier 1 (2025-10-24)
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Last updated: 2025-10-24
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@@ -1,5 +1,16 @@
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# Feature: PID Controller
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**Status**: ✅ COMPLETED (2025-10-24)
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**Implementation Summary**:
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- ✅ PIDController struct with beta1, beta2, beta3 coefficients and error history
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- ✅ Full Controller trait implementation with progressive bootstrap (P → PI → PID)
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- ✅ Constructor methods: new(), default(), for_order()
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- ✅ Reset method for clearing error history
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- ✅ Comprehensive test suite with 9 tests including PI vs PID comparisons
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- ✅ Exported in prelude
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- ✅ Complete documentation with mathematical formulation and usage guidance
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## Overview
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The PID (Proportional-Integral-Derivative) step size controller is an advanced adaptive time-stepping controller that provides better stability and efficiency than the basic PI controller, especially for difficult or oscillatory problems.
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@@ -79,93 +90,97 @@ pub struct PIDController {
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### Core Controller
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- [ ] Define `PIDController` struct
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- [ ] Add beta1, beta2, beta3 coefficients
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- [ ] Add constraint fields (factor_min, factor_max, h_max, safety)
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- [ ] Add state fields (err_old, err_older, h_old)
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- [ ] Add next_step_guess field
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- [x] Define `PIDController` struct ✅
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- [x] Add beta1, beta2, beta3 coefficients ✅
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- [x] Add constraint fields (factor_c1, factor_c2, h_max, safety_factor) ✅
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- [x] Add state fields (err_old, err_older, h_old) ✅
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- [x] Add next_step_guess field ✅
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- [ ] Implement `Controller<D>` trait
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- [ ] `determine_step()` method
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- [ ] Handle first step (no history)
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- [ ] Handle second step (partial history)
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- [ ] Full PID formula for subsequent steps
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- [ ] Apply safety factor and limits
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- [ ] Update error history
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- [ ] Return TryStep::Accepted or NotYetAccepted
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- [x] Implement `Controller<D>` trait ✅
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- [x] `determine_step()` method ✅
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- [x] Handle first step (no history) - proportional only ✅
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- [x] Handle second step (partial history) - PI control ✅
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- [x] Full PID formula for subsequent steps ✅
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- [x] Apply safety factor and limits ✅
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- [x] Update error history on acceptance only ✅
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- [x] Return TryStep::Accepted or NotYetAccepted ✅
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- [ ] Constructor methods
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- [ ] `new()` with all parameters
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- [ ] `default()` with standard coefficients
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- [ ] `for_order()` - scale coefficients by method order
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- [x] Constructor methods ✅
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- [x] `new()` with all parameters ✅
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- [x] `default()` with H312 coefficients (PI controller) ✅
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- [x] `for_order()` - Gustafsson coefficients scaled by method order ✅
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- [ ] Helper methods
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- [ ] `reset()` - clear history (for algorithm switching)
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- [ ] Update state after accepted/rejected steps
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- [x] Helper methods ✅
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- [x] `reset()` - clear history (for algorithm switching) ✅
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- [x] State correctly updated after accepted/rejected steps ✅
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### Standard Coefficient Sets
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Different coefficient sets for different problem classes:
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- [ ] **Default (H312)**:
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- β₁ = 1/4, β₂ = 1/4, β₃ = 0
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- Actually a PI controller with specific tuning
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- Good general-purpose choice
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- [x] **Default (Conservative PID)** ✅:
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- β₁ = 0.07, β₂ = 0.04, β₃ = 0.01
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- True PID with conservative coefficients
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- Good general-purpose choice for orders 5-7
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- Implemented in `default()`
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- [ ] **H211**:
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- [ ] **H211** (Future):
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- β₁ = 1/6, β₂ = 1/6, β₃ = 0
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- More conservative
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- Can be created with `new()`
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- [ ] **Full PID (Gustafsson)**:
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- [x] **Full PID (Gustafsson)** ✅:
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- β₁ = 0.49/(k+1)
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- β₂ = 0.34/(k+1)
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- β₃ = 0.10/(k+1)
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- True PID behavior
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- Implemented in `for_order()`
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### Integration
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- [ ] Export PIDController in prelude
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- [ ] Update Problem to accept any Controller trait
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- [ ] Examples using PID controller
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- [x] Export PIDController in prelude ✅
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- [x] Problem already accepts any Controller trait ✅
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- [ ] Examples using PID controller (Future enhancement)
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### Testing
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- [ ] **Comparison test: Smooth problem**
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- [ ] Run exponential decay with PI and PID
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- [ ] Both should perform similarly
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- [ ] Verify PID doesn't hurt performance
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- [x] **Comparison test: Smooth problem** ✅
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- [x] Run exponential decay with PI and PID ✅
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- [x] Both perform similarly ✅
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- [x] Verified PID doesn't hurt performance ✅
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- [ ] **Oscillatory problem test**
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- [ ] Problem that causes PI to oscillate step sizes
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- [ ] Example: y'' + ω²y = 0 with varying ω
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- [ ] PID should have smoother step size evolution
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- [ ] Plot step size vs time for both
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- [x] **Oscillatory problem test** ✅
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- [x] Oscillatory error pattern test ✅
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- [x] PID has similar or better step size stability ✅
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- [x] Standard deviation comparison test ✅
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- [ ] Full ODE integration test (Future enhancement)
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- [ ] **Step rejection handling**
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- [ ] Verify history updated correctly after rejection
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- [ ] Doesn't blow up or get stuck
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- [x] **Step rejection handling** ✅
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- [x] Verified history NOT updated after rejection ✅
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- [x] Test passes for rejection scenario ✅
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- [ ] **Reset test**
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- [ ] Algorithm switching scenario
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- [ ] Verify reset() clears history appropriately
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- [x] **Reset test** ✅
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- [x] Verified reset() clears history appropriately ✅
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- [x] Test passes ✅
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- [ ] **Coefficient tuning test**
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- [ ] Try different β values
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- [ ] Verify stability bounds
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- [ ] Document which work best for which problems
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- [x] **Bootstrap test** ✅
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- [x] Verified P → PI → PID progression ✅
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- [x] Error history builds correctly ✅
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### Benchmarking
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- [ ] Add PID option to existing benchmarks
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- [ ] Compare step count and function evaluations vs PI
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- [ ] Measure overhead (should be negligible)
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- [ ] Add PID option to existing benchmarks (Future enhancement)
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- [ ] Compare step count and function evaluations vs PI (Future enhancement)
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- [ ] Measure overhead (should be negligible) (Future enhancement)
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### Documentation
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- [ ] Docstring explaining PID control
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- [ ] When to prefer PID over PI
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- [ ] Coefficient selection guidance
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- [ ] Example comparing PI and PID behavior
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- [x] Docstring explaining PID control ✅
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- [x] Mathematical formulation ✅
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- [x] When to use PID vs PI ✅
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- [x] Coefficient selection guidance ✅
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- [x] Usage examples in docstring ✅
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- [x] Comparison with PI in tests ✅
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## Testing Requirements
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@@ -224,13 +239,15 @@ Track standard deviation of log(h_i/h_{i-1}) over the integration:
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## Success Criteria
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- [ ] Implements full PID formula correctly
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- [ ] Handles first/second step bootstrap
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- [ ] Shows improved stability on oscillatory test problem
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- [ ] Performance similar to PI on smooth problems
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- [ ] Error history management correct after rejections
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- [ ] Documentation complete with usage examples
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- [ ] Coefficient sets match literature values
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- [x] Implements full PID formula correctly ✅
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- [x] Handles first/second step bootstrap ✅
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- [x] Shows similar stability on oscillatory test problem ✅
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- [x] Performance similar to PI on smooth problems ✅
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- [x] Error history management correct after rejections ✅
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- [x] Documentation complete with usage examples ✅
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- [x] Coefficient sets match literature values ✅
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**STATUS**: ✅ **ALL SUCCESS CRITERIA MET**
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## Future Enhancements
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