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| 1 | +Finite-Control-Set Model Predictive Control (FCS-MPC) |
| 2 | +****************************************************** |
| 3 | + |
| 4 | +We apply a finite-control set (FCS) model predictive control (MPC) approach to realize |
| 5 | +current control of a permanent magnet synchronous motor (PMSM) and Synchronous Reluctance |
| 6 | +Motor (SRM) in rotor field-oriented coordinates. Unlike continuous-control set (CCS) MPC, |
| 7 | +FCS-MPC directly evaluates a finite set of switching states to optimize the control input |
| 8 | +based on a cost function over a prediction horizon. |
| 9 | + |
| 10 | +.. figure:: ../../plots/mpc_structure.png |
| 11 | + |
| 12 | + |
| 13 | +.. figure:: ../../plots/mpc_scheme.png |
| 14 | + |
| 15 | + |
| 16 | +With the help of the system model, the output variables are predicted for each possible |
| 17 | +switching state in the finite control set. The optimizer evaluates a cost function |
| 18 | +(typically the quadratic control error) for all possible switching combinations over |
| 19 | +the prediction horizon. The switching state that minimizes the cost function is |
| 20 | +selected and applied to the system in the next time step. |
| 21 | + |
| 22 | +Unlike CCS-MPC, FCS-MPC does not require an iterative numerical solver or barrier |
| 23 | +functions to handle constraints, as the voltage limits are inherently respected by |
| 24 | +evaluating only the physically realizable switching states of the converter. |
| 25 | +The computational efficiency of FCS-MPC comes from the direct enumeration and evaluation |
| 26 | +of the finite number of possible switching states, rather than solving an optimization |
| 27 | +problem with constraints. |
| 28 | + |
| 29 | + |
| 30 | +MPC Current Controller |
| 31 | +====================== |
| 32 | + |
| 33 | +.. autoclass:: gem_controllers.mpc_current_controller.MPCCurrentController |
| 34 | + :members: |
| 35 | + :undoc-members: |
| 36 | + :inherited-members: |
| 37 | + :show-inheritance: |
| 38 | + :member-order: groupwise |
| 39 | + |
| 40 | + |
| 41 | +Example Usage |
| 42 | +============= |
| 43 | + |
| 44 | +The following example demonstrates how to apply the :class:`MPCCurrentController` to |
| 45 | +control a permanent magnet synchronous motor (PMSM) using a finite-control-set MPC approach |
| 46 | +within the ``gym-electric-motor`` simulation environment. |
| 47 | + |
| 48 | +.. code-block:: python |
| 49 | +
|
| 50 | + import numpy as np |
| 51 | + import matplotlib |
| 52 | + matplotlib.use('Qt5Agg') |
| 53 | + from gem_controllers import GemController |
| 54 | + import gym_electric_motor as gem |
| 55 | + from gym_electric_motor.envs.motors import ActionType, ControlType, Motor, MotorType |
| 56 | + from gym_electric_motor.physical_systems import ConstantSpeedLoad |
| 57 | + from gym_electric_motor.reference_generators import ( |
| 58 | + MultipleReferenceGenerator, SwitchedReferenceGenerator, |
| 59 | + TriangularReferenceGenerator, SinusoidalReferenceGenerator, |
| 60 | + StepReferenceGenerator |
| 61 | + ) |
| 62 | + from gym_electric_motor.visualization.motor_dashboard import MotorDashboard |
| 63 | +
|
| 64 | + motor_parameter = dict(r_s=15e-3, l_d=0.37e-3, l_q=1.2e-3, psi_p=65.6e-3, p=3, j_rotor=0.06) |
| 65 | + limit_values = dict(i=160 * 1.41, omega=12000 * np.pi / 30, u=450) |
| 66 | + nominal_values = {key: 0.7 * limit for key, limit in limit_values.items()} |
| 67 | +
|
| 68 | + q_generator = SwitchedReferenceGenerator( |
| 69 | + sub_generators=[ |
| 70 | + SinusoidalReferenceGenerator(reference_state='i_sq', amplitude_range=(0, 0.3), offset_range=(0, 0.2)), |
| 71 | + StepReferenceGenerator(reference_state='i_sq', amplitude_range=(0, 0.5)), |
| 72 | + TriangularReferenceGenerator(reference_state='i_sq', amplitude_range=(0, 0.3), offset_range=(0, 0.2)) |
| 73 | + ], |
| 74 | + super_episode_length=(500, 1000) |
| 75 | + ) |
| 76 | +
|
| 77 | + d_generator = SwitchedReferenceGenerator( |
| 78 | + sub_generators=[ |
| 79 | + SinusoidalReferenceGenerator(reference_state='i_sd', amplitude_range=(0, 0.3), offset_range=(0, 0.2)), |
| 80 | + StepReferenceGenerator(reference_state='i_sd', amplitude_range=(0, 0.5)), |
| 81 | + TriangularReferenceGenerator(reference_state='i_sd', amplitude_range=(0, 0.3), offset_range=(0, 0.2)) |
| 82 | + ], |
| 83 | + super_episode_length=(500, 1000) |
| 84 | + ) |
| 85 | +
|
| 86 | + reference_generator = MultipleReferenceGenerator([d_generator, q_generator]) |
| 87 | +
|
| 88 | + visu = MotorDashboard(state_plots=['i_sq', 'i_sd', 'u_sq', 'u_sd'], update_interval=10) |
| 89 | +
|
| 90 | + motor = Motor( |
| 91 | + MotorType.PermanentMagnetSynchronousMotor, |
| 92 | + ControlType.CurrentControl, |
| 93 | + ActionType.Finite |
| 94 | + ) |
| 95 | +
|
| 96 | + #physical_system_wrapper = [DeadTimeProcessor(steps=1)] # Dead time processor with 1 step delay |
| 97 | + #uncomment the above line to activate the DeadTimeProcessor |
| 98 | + env = gem.make( |
| 99 | + motor.env_id(), |
| 100 | + visualization=visu, |
| 101 | + load=ConstantSpeedLoad(omega_fixed=1000 * np.pi / 30), |
| 102 | + reference_generator=reference_generator, |
| 103 | + reward_function=dict( |
| 104 | + reward_weights={'i_sq': 1, 'i_sd': 1}, |
| 105 | + reward_power=0.5, |
| 106 | + ), |
| 107 | + supply=dict(u_nominal=400), |
| 108 | + motor=dict( |
| 109 | + motor_parameter=motor_parameter, |
| 110 | + limit_values=limit_values, |
| 111 | + nominal_values=nominal_values |
| 112 | + ), |
| 113 | + #physical_system_wrappers=physical_system_wrapper, |
| 114 | + #uncomment the above line to activate the DeadTimeProcessor |
| 115 | + ) |
| 116 | +
|
| 117 | + visu.initialize() |
| 118 | +
|
| 119 | + controller = GemController.make( |
| 120 | + env=env, |
| 121 | + env_id=motor.env_id(), |
| 122 | + base_current_controller="MPC", |
| 123 | + block_diagram=False, |
| 124 | + prediction_horizon=1, |
| 125 | + w_d=0.5, |
| 126 | + w_q=2.0 |
| 127 | + ) |
| 128 | +
|
| 129 | + (state, reference), _ = env.reset() |
| 130 | + cum_rew = 0 |
| 131 | +
|
| 132 | + for i in range(10000): |
| 133 | + env.render() |
| 134 | + action = controller.control(state, reference) |
| 135 | + (state, reference), reward, terminated, truncated, _ = env.step(action) |
| 136 | + cum_rew += reward |
| 137 | + if terminated: |
| 138 | + (state, reference), _ = env.reset() |
| 139 | + controller.reset() |
| 140 | +
|
| 141 | + print('Reward =', cum_rew) |
| 142 | + env.close() |
| 143 | +
|
| 144 | +Simulation Results |
| 145 | +================== |
| 146 | + |
| 147 | +The following figures illustrate the performance of the FCS-MPC controller in current control of the PMSM under varying reference trajectories. |
| 148 | +The controller accurately tracks both the d- and q-axis current references while ensuring smooth control actions. |
| 149 | + |
| 150 | +.. figure:: ../../plots/MPC_Time_Plots.png |
| 151 | + |
| 152 | + FCS-MPC current tracking of *i<sub>d</sub>* and *i<sub>q</sub>*. |
| 153 | + |
| 154 | +The results show that the finite-control-set MPC effectively minimizes the current tracking error within each sampling period while satisfying the converter switching |
| 155 | +constraints. Compared to conventional PI controllers, the FCS-MPC achieves faster dynamic response and improved steady-state performance without overshoot. |
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