PD controller

A proportional/derivative controller where both the proportional and derivative actions are taken from input signals.

JCS Network Configuration

structure.yaml Configuration


type	proc_pd

Signals - From Process

Signal name	Type	Required	Description
u	float32	required	Controller output Signal name can be renamed by the user

Signals - To Process

Signal name	Type	Required	Description
p_setpoint	float32	required	Proportional term command input
p_feedback	float32	required	Proportional term feedback input
d_setpoint	float32	optional	Derivative term command input
d_feedback	float32	optional	Derivative term feedback input
feedforward	float32	optional	Feed forward input
kp	float32	optional	Proportional term gain If not connected, then must be set by parameter `proc_pd_kp`
kd	float32	optional	Derivative term gain If not connected, then must be set by parameter `proc_pd_kd`
output_limit	float32	optional	Output and integrator limit Defines both output limit high and low

Note: The PD controller breaks out the gains as optional signals. If they are not connected as signals the gains can be set via parameter.

Configuration Parameters

Parameter name	Type	Required	Description
`proc_pd_kp`	float32	optional	Proportional gain term Ignored if signal `kp` is connected
`proc_pd_kd`	float32	optional	Derivative gain term Ignored if signal `kd` is connected
`proc_pd_kff`	float32	optional	Feedforward gain term
`proc_pd_limit_out_h`	float32	optional	Controller output limit - high (output_units)
`proc_pd_limit_out_l`	float32	optional	Controller output limit - low (output_units)
`proc_pd_rate_limit_rising`	float32	optional	Controller output rising rate limiter (output_units/s)
`proc_pd_rate_limit_falling`	float32	optional	Controller output falling rate limiter (output_units/s)
`proc_pd_startup_rate_limit`	float32	optional	Startup output limits rate limiter (output_units/s/s)
`proc_pd_p_is_rotational_error`	boolean	optional	True: wraps the computed proportional error term \(e[k]\) to the interval \([-\pi, \pi]\) Default value: false
`proc_pd_d_is_rotational_error`	boolean	optional	True: wraps the computed derivative error term \(e[k]\) to the interval \([-\pi, \pi]\) Default value: false

Operation

The PD controller is implemented in parallel form as the following difference equations:

If the parameter option proc_pd_p_is_rotational_error is set to false, then the proportional term is computed as:

\[ p[k] = k_p (r_{p}[k] - y_{p}[k]) \]

If the parameter option proc_pd_p_is_rotational_error is set to true, then the proportional term is computed as:

\[ p[k] = k_p wrap(r_{p}[k] - y_{p}[k], -\pi, \pi) \]

Here, \(r_{p}\) is the p_setpoint signal and \(y_{p}\) is the p_feedback signal.

If the parameter option proc_pd_d_is_rotational_error is set to false, then the derivative term is computed as:

\[ d[k] = k_d (r_{d}[k] - y_{d}[k]) \]

If the parameter option proc_pd_d_is_rotational_error is set to true, then the derivative term is computed as:

\[ d[k] = k_d wrap(r_{d}[k] - y_{d}[k], -\pi, \pi) \]

Here, \(r_{d}\) is the d_setpoint signal and \(y_{d}\) is the d_feedback signal.

The final PD is computed with the added feedforward term \(k_{ff} * ff[k]\):

\[ y[k] = p[k] + d[k] + k_{ff} * ff[k] \]

Limits configured in proc_pd_limit_out_h and proc_pd_limit_out_l are applied to the output:

\[ y[k] = \begin{cases} limit_h,& \text{if } y[k]\geq limit_h\\ y[k], & limit_l \lt y[k] \lt limit_h \\ limit_l,& \text{if } y[k]\leq limit_l\\ \end{cases} \]

Following the limits, a rate limit may be applied to the output by parameters proc_pd_rate_limit_rising and proc_pd_rate_limit_falling. If these parameters are set as \(0\) or left unconfigured the rate limiter is disabled.

\[ y[k] = y[k-1] + \begin{cases} dt \times rate_{rising} ,& \text{if } y[k] - y[k-1] \geq dt \times rate_{rising}\\ 0, & dt \times rate_{falling} \lt y[k] - y[k-1] \lt dt \times rate_{rising} \\ dt \times rate_{falling} ,& \text{if } y[k] - y[k-1] \leq dt \times rate_{falling}\\ \end{cases} \]

Startup

During controller startup an aggressive rate limit may be applied via parameter proc_pd_startup_rate_limit. This parameter rate limits the controller limits, starting from \(0\) until the limits reach the value defined by parameters proc_pd_limit_out_h and proc_pd_limit_out_l or the value defined by signal output_limit (whichever is configured). Once the rate limited limits equal the pre-defined limits, the startup rate limiter is disabled.

The effect of this limiter is to provide a 'soft' startup, in case of any large controller error present as the system starts.

Set parameter proc_pd_startup_rate_limit to \(0\), or leave unconfigured to disable the startup rate limiter.